Chapter 14:1 

Bayesian Journey-to-Crime Modeling

 Ned Levine Richard Block

 Ned Levine & Associates Loyola University

 Houston, TX Chicago, IL 

The authors would like to thank Ms. Haiyan Teng, Dr. Wim Bernasco, Dr. Michael Leitner, Dr. Josh Kent, 

Dr. Craig Bennell, Dr. Brent Snook, Dr. Paul Taylor, and Ms. Patsy Lee for extensively testing the Bayesian 

Journey-to-crime module. 

1 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Table of Contents 

Bayesian Probability 14.1 

 Bayesian Inference 14.3 

Application of Bayesian Inference to Journey-to-crime Analysis 14.4 

The Bayesian Journey-to-crime Estimation Module 14.10 

Data Preparation for Bayesian Journey-to-crime Estimation 14.10 

 Serial Offender Data 14.12 

 Journey-to-crime Travel Function 14.12 

 Origin-destination Matrix 14.13 

 Diagnostics file for Bayesian Jtc Routine 14.13 

 Logic of the Routine 14.15 

Bayesian Journey-to-crime Diagnostics 14.16

 Data Input 14.16 

 Methods Tested 14.16 

 Interpolated Grid 14.17 

Output 14.19 

 Output matrices 14.19 

Which is the Most Accurate and Precise Method? 14.20 

 Measures of Accuracy and Precision 14.21 

 Accuracy Measures 14.23 

 Precision Measures 14.24 

 Summary Statistics 14.24 

Testing the Routine with Serial Offenders from Baltimore County 14.25 

 Results: Accuracy 14.26 

 Results: Precision 14.28 

 Conclusion of the Evaluation 14.28 

 Tests with Other Data Sets 14.30 

Estimate Likely Origin of a Serial Offender 14.30 

 Data Input 14.30 

 Selected Method 14.31 

 Interpolated Grid 14.32 

Output 14.33 

 Accumulator Matrix 14.33 

Two Examples of Using the Bayesian Journey-to-crime Routine 14.34 

 Offender S14A 14.34 

 Offender TS15A 14.42 

Potential to Add New Information to Improve the Methodology 14.47 
 

 

 

 

 

Table of Contents (continued) 

Probability Filters 14.47 

Defining Filters in the Bayesian Journey-to-crime Routine 14.48 

 Example of the Use of a Probability Filter 14.49 

Guidelines for Analysts 14.54 

Summary 14.58 

Caveat 14.58 

References 14.59 
	 	 

Chapter 14: 

Bayesian Journey-to-crime Modeling 

The Bayesian Journey-to-crime module (Bayesian Jtc) includes a set of tools for 

estimating the likely residence location of a serial offender. It is an extension of the Journey-tocrime routine (Jtc) that uses a travel distance function to make an estimate about the likely 

residence location of a serial offender. The Bayesian Jtc routine adds information about specific 

origins of offenders who committed crimes in the same locations to the Jtc to update the 

estimate. Before proceeding with this chapter, users should be thoroughly familiar with the 

material on Jtc modeling discussed in Chapter 13. 

First, the theory behind the Bayesian Jtc routine will be described. While this material is 

not essential for running the routine, it does provide the background behind the routine. Users 

who want to go immediately into the routine should skip to the data section on p. 14.10. 

Second, data requirements will be discussed. Third, the routine will be illustrated with 

data from Baltimore County and from Chicago. Fourth, the use of probability filters as 

extensions will be illustrated. Fifth, and finally, some guidelines are provided for analysts. 

Bayesian Probability 

Bayes Theorem is a formulation that relates the conditional and marginal probability 

distributions of random variables. The marginal probability distribution is a probability 

independent of any other conditions. Hence, P(A) and P(B) is the marginal probability (or just 

plain probability) of A and B respectively. 

The conditional probability is the probability of an event given that some other event has 

occurred. It is written in the form of P(A|B) (i.e., event A given that event B has occurred). In 

probability theory, it is defined as: 

(14.1)

Conditional probabilities can be best be seen in contingency tables. Table 14.1 below 

shows a possible sequence of counts for two variables (e.g., taking a sample of persons and 

counting their gender - male = 1 v. female = 0, and their age - older than 30 = 1 v. 30 or younger 

= 0). The probabilities can be obtained just by counting: 

14.1 
 

 

 

 

P(A) = 30/50 = 0.6 

P(B) = 35/50 = 0.7 

P(A and B) = 25/50 = 0.5 

P(A or B) = (30+35-25)/50 = 0.8 

P(A|B) = 25/35 = 0.71 

P(B|A) = 25/30 = 0.83 

However, if four of these six calculations are known, Bayes Theorem can be used to 

solve for the other two. Two logical terms in probability are the >and= condition and the >or=

condition. Usually, the symbol 1 is used for >and= c is used for >or=, but writing it in words 

might make it easier to understand. 

Table 14.1:

Example of Determining Probabilities by Counting 

A has 

NOT A has 

occurred occurred TOTAL 

B has NOT 

occurred 10 5 

10 25 

15 

B has occurred 35 

TOTAL 20 30 50 

The following two theorems define these. 

 1. The probability that either A or B will occur is :

2. The probability that both A and B will occur is:

(14.2) 

 (14.3) 

 (14.4) 

14.2 

Bayes Theorem relates the two equivalents of the >and= condition together: 
 

 

 

 

 

 

 (14.5) 

The theorem is sometimes called the >inverse probability= in that it can invert two 

conditional probabilities: 

(14.6) 

By plugging in the values from the example in Table 14.1, the reader can verify that 

Bayes Theorem produces the correct results, for example: 

(14.7) 

 Bayesian Inference 

In the statistical interpretation of Bayes Theorem, the probabilities are estimates of a 

random variable. Let θ be a parameter of interest and let X be some data. Thus, Bayes Theorem 

can be expressed as: 

 (14.8) 

 Interpreting this equation, P(θ|X) is the probability of θ given the data, X, and is called 

the posterior probability (or posterior distribution). P(θ) is the probability that θ has a certain 

distribution and is often called the prior probability. P(X|θ) is the probability that the data would 

be obtained given that θ is true and is often called the likelihood function (i.e., it is the likelihood 

that the data will be obtained given the distribution of θ). Finally, P(X) is the marginal 

probability of the data, the probability of obtaining the data under all possible scenarios; 

essentially, it is the data. 

The equation can be rephrased in words: 

Posterior Likelihood of Prior 

probability that 

θ is true given the 

data, X = 

obtaining the data probability 

given θ is true * of θ

------------------------------------------------ 

Marginal probability of X 

(14.9) 

In other words, this formulation allows an estimate of the probability of a particular 

parameter, θ, to be updated given new information. Since θ is the prior probability of an event, 

14.3 
 

 

given some new data, X, Bayes Theorem can be used to update the estimate of θ. The prior 

probability of θ can come from prior studies, an assumption of no difference between any of the 

conditions affecting θ, or an assumed mathematical distribution. The likelihood function can 

also come from empirical studies or an assumed mathematical function. Irrespective of how 

these are interpreted, the result is an estimate of the parameter, θ, given the evidence, X. 

A point that is often made is that the prior probability of obtaining the data (the 

denominator of the above equation) is not known or cannot easily be evaluated. The data are 

what was obtained from some data gathering exercise (either experimental or from observations). 

Thus, it is not easy to estimate it. Consequently, often the numerator only is used for estimate the 

posterior probability since: 

(14.10) 

where ∝ means >proportional to=. In some statistical methods (e.g., the Markov Chain Monte 

Carlo simulation, or MCMC, discussed in Chapters 17, 18 &19), the parameter of interest is 

estimated by thousands of random simulations using approximations to P(X|θ) and P(θ) 

respectively. 

The key point is that estimates of parameters can be systematically updated by additional 

information. The formula requires that a prior probability for the estimate be given with new 

information being added which is conditional on the prior estimate, meaning that it takes into 

account information from the prior. Bayesian approaches are increasingly being used to provide 

estimates for complex calculations that previously were intractable (Denison, Holmes, Mallilck, 

& Smith, 2002; Lee, 2004; Gelman, Carlin, Stern, & Rubin, 2004). Our regression module 

includes the use of the MCMC algorithm to estimate complex equations. 

Application of Bayesian Inference to Journey-to-crime Analysis 

Bayes Theorem can be applied to the Journey-to-crime methodology. In the Journey-tocrime (Jtc) method, an estimate is made about where a serial offender is living. The Jtc method 

produces probability estimates based on an assumed travel distance function (or, in more refined 

uses of the method, travel time). That is, it is assumed that an offender follows a typical travel 

distance/time function. This function can be estimated from prior studies (Canter & Gregory, 

1994; Canter, 2003) or from creating a sample of known offenders - a calibration sample (see 

Chapter 13; Levine, 2000) or from assuming that every offender follows a particular 

mathematical function (Rossmo, 1995; 2000). Essentially, it is a prior probability for a particular 

location, P(θ). That is, it is a guess about where the offender lives on the assumption that the 

offender of interest is following an existing travel distance model. 

14.4 
 

However, additional information from a sample of known offenders where both the crime 

location and the residence location are known can be added. This information would be obtained 

from arrest records, each of which will have a crime location defined (a >destination=) and a 

residence location (an >origin=). If these locations are then assigned to a set of zones, a matrix 

that relates the origin zones to the destination zones can be created (Figure 14.1). This is called 

an origin-destination matrix (also known as a trip distribution or O-D matrix, for short). 

In this figure, the numbers indicate crimes committed in each destination zone which 

originated from each origin zone (i.e., where the offender lived). For example, taking the first 

row in Figure 14.1, there were 37 crimes that were committed in zone 1 and in which the 

offender also lived in zone 1; there were 15 crimes committed in zone 2 in which the offender 

lived in zone 1; however, there were only 7 crimes committed in zone 1 in which the offender 

lived in zone 2; and so forth. 

Note two things about the matrix. First, the number of origin zones can be (and usually 

is) greater than the number of destination zones because crimes can originate outside the study 

area. Second, the marginal totals have to be equal. That is, the number of crimes committed in 

all destination zones must equal the number of crimes originating in all origin zones. 

This information can be treated as the likelihood estimate for the Journey-to-crime 

framework. That is, if a certain distribution of incidents committed by a particular serial 

offender is known, then this matrix can be used to estimate the likely origin zones from which 

offenders came, independent of any assumption about travel distance. In other words, this matrix 

is equivalent to the likelihood function in Equation 14.8, which is repeated below: 

repeat (14.8) 

The estimate of the likely origin location of a serial offender can be improved by 

updating the Jtc estimate, P(θ), with information from an empirically-derived likelihood 

estimate, P(X|θ). 

Figure 14.2 illustrates the process. Suppose a serial offender committed crimes in three 

zones. These are shown in terms of grid cell zones. In reality, most zones are not grid cells but 

are irregular. However, illustrating with grid cells makes the process more understandable. 

Using an O-D matrix based on those cells, only the destination zones corresponding to those 

cells are selected (Figure 14.3). This process is repeated for all serial offenders in the calibration 

file. Destination zones that are repeated by different serial offenders are counted multiple times, 

once for each occurrence. This results in marginal totals that correspond to frequencies for those 

serial offenders who committed crimes in the selected zones. The marginal totals are then 

14.5 
Figure 14.1: 

Crime Origin-Destination Matrix 

Crime destination zone 

1 2 3 4 5 . . . . N Σ

12345

...

M

37 15 21 4 3 12

7 53 14 0 4 15

12 9 81 7 6 33

4 10 6 12 1 0

8 7 28 2 24 14

12 5 43 3 10 92

34

10

71

8

17

14

Crime origin zone 

Σ 153 276 1245 99 110 812 43,2
 

 

converted to probabilities. In other words, the distribution of crimes is conditioned on the 

locations that correspond to where the serial offender of interest committed his or her crimes. It 

is a conditional probability. 

But, what about the denominator of the Bayesian formula, P(X)? Essentially, it is the 

spatial distribution of all crimes irrespective of which particular model or scenario we are 

exploring. In practice, it is very difficult, if not impossible, to estimate the probability of 

obtaining the data under all circumstances. Therefore, only the numerator in equation 14.8 is 

estimated and the final probabilities are re-scaled so that they sum to 1.0 over the study area: 

(14.11) 

where k is a scaling constant. 

We are going to change the symbols at this point so the Jtc represents the distance-based 

Journey-to-crime estimate, O represents an estimate based on an origin-destination matrix, and 

O|Jtc represents the particular origins associated with crimes committed in the same zones as 

that identified in the Jtc estimate. Therefore, there are three different probability estimates of 

where an offender lives: 

1. A probability estimate of the residence location of a single offender based on the

location of the incidents that this person committed and an assumed travel

distance function, P(Jtc);

2. A probability estimate of the residence location of a single offender based on a

general distribution of all offenders, irrespective of any particular destinations for

incidents, P(O). Essentially, this is the distribution of origins irrespective of the

destinations; and

3. A probability estimate of the residence location of a single offender based on the

distribution of offenders given the distribution of incidents committed by other

offenders who committed crimes in the same location, P(O|Jtc).

Therefore, Bayes Theorem can be used to create an estimate that combines information 

both from a travel distance function and an origin-destination matrix in which the posterior 

probability of the Journey-to-crime location taking into account the origin-destination matrix is 

proportional to the product of the prior probability of the Journey-to-crime function, P(Jtc), and 

the conditional probability of the origins for other offenders who committed crimes in the same 

locations, P(O). This will be called the product probability. 

14.7 
Figure 14.2: 
Figure 14.3: 

Conditional Origin-Destination Matrix 

Destination zones where serial Destination zones where serial Marginal total

Marginal total

Crime destination zone 

1 2 3 4 5 . . . . N Σ

offender committed crimes selected zone

Crime origin zone 

12345

...

M

15 4 12

53 0 15

9 7 33

10 12 0

7 2 14

5 3 92

1220

634

14

Σ 276 99 812 1,5
 

 

 

As mentioned above, it is very difficult to determine the probability of obtaining the data 

under any circumstance, P(O). Consequently, the Bayesian estimate is usually calculated only 

with respect to the numerator, the product of the prior probability and the likelihood function, 

and the result re-scaled so that the probabilities over the study area sum to 1.0. 

A very rough approximation to the full Bayesian probability can be obtained by taking 

the product probability and dividing it by the general probability: It relates the product term (the 

numerator) to the general distribution of crimes. This will produce a relative risk measure, 

which is called Bayesian Risk: 

(14.12) 

In this case, the product probability is being compared to the general distribution of the 

origins of all offenders irrespective of where they committed their crimes. Note that this 

measure will correlate with the product term because they both have the same numerator. 

The Bayesian Journey-to-crime Estimation Module 

The Bayesian Journey-to-crime estimation module is made up of two routines, one for 

diagnosing which Journey-to-crime method is best and one for applying that method to a 

particular serial offender. Figure 14.4 show the layout of the module. 

Data Preparation for Bayesian Journey-to-crime Estimation 

There are four data sets that are required: 

1. The incidents committed by a single offender for which an estimate will be made

of where that individual lives;

2. A Journey-to-crime travel distance function that estimates the likelihood of an

offender committing crimes at a certain distance (or travel time if a network is

used);

3. An origin-destination matrix; and

4. A diagnostics file of multiple known serial offenders for which both their

residence and crime locations are known (optional for use in diagnostics routine).

14.10 
Figure 14.4: 

Bayesian Journey-to-crime Screen 
 

Serial Offender Data 

The first required data set is information on the location of crimes committed by a single 

serial offender. For each serial offender for whom an estimate will be made of where that person 

lives, the data set must include the location of the incidents committed by the offender. The data 

are a series of records in which each represents a single event. On each record, there are X and 

Y coordinates identifying the location of the incidents this person has committed (Table 14.2). 

There may be other data on the records, but the X and Y coordinates are essential. 

Table 14.2:

Minimum Information Required for Serial Offenders: 

Example for Offender Who Committed Seven Incidents 

ID UCR INCIDX INCIDY 

TS7C 430.00 -76.494300 39.2846 

TS7C 440.00 -76.450900 39.3185 

TS7C 630.00 -76.460600 39.3157 

TS7C 430.00 -76.450700 39.3181 

TS7C 311.00 -76.449700 39.3162 

TS7C 440.00 -76.450300 39.3178 

TS7C 341.00 -76.448200 39.3123 

Journey-to-crime Travel Function 

The second data set that is required is a journey-to-crime (Jtc) function. The Journey-tocrime travel function is an estimate of the likelihood of an offender traveling a certain distance. 

Typically, it represents a frequency distribution of distances traveled, though it could be a 

frequency distribution of travel times if a network was used to calibrate the function with the 

Journey-to-crime estimation routine. It can come from an a priori assumption about travel 

distances, prior research, or a calibration data set of offenders who have already been caught. 

The ACalibrate Journey-to-crime function@ routine (on the Journey-to-crime page under Spatial 

modeling) can be used to estimate this function (see Chapter 13). 

The BJtc routine can use two different travel distance functions: 

1. An already-calibrated distance function; and

2. A mathematical formula.

Either direct or indirect (Manhattan) distances can be used though the default is direct 

distance (see Measurement Parameters in Chapter 3, p. 3.29). In practice, an empirically-derived 

14.12 
 

travel function is often as accurate, if not better, than a mathematically-defined one. Given that 

an origin-destination matrix is also needed, it is easy for the user to estimate the travel function 

using the ACalibrate Journey-to-crime function@. 

If the user does not have data to calibrate a journey-to-crime travel function, then a 

mathematical model should be used. Typically, the negative exponential function is used for this 

purpose; the default values will work for many distributions.

 Origin-destination Matrix 

The third required data set is an origin-destination matrix. The origin-destination matrix 

relates the number of offenders who commit crimes in one of N zones who live (originate) in one 

of M zones, similar to Figure 14.1 above. It can be created from the ACalculate observed origindestination trips@ routine (on the >Describe origin-destination trips= page under the Trip 

distribution module of the Crime Travel Demand model; see Chapter 28). 

How many incidents are needed where the origin and destination location are known? 

While there is no simple answer to this, the numbers ideally should be in the tens of thousands. 

If there are N destinations and M rows, ideally one would want an average of 30 cases for each 

cell to produce a reliable estimate. Obviously, that is a huge amount of data that cannot easily 

found with any real database. For example, if there are 325 destination zones and 532 origin 

zones (for the Baltimore County example given below), that would be 172,900 individual cells. 

If the 30 cases or more rule is applied, then that would require 5,187,000 records or more to 

produce a barely reliable estimate for most cells. 

The task becomes even more daunting when it is realized that most of these links (cells) 

have few or no cases in them as offenders typically travel along certain pathways. Obviously, 

such a demand for data is impractical even in the largest jurisdictions. Therefore, we 

recommend that as much data as possible be used to produce the origin-destination (O-D) matrix, 

at least several years worth. The matrix can be built with what data is available and then 

periodically updated to produce better estimates. 

Diagnostics File for Bayesian Jtc Routine 

The fourth data set is an optional diagnostics file. It is used for estimating which of 

several alternative parameters is best at predicting the residence location of serial offenders. 

Essentially, it is a set of serial offenders, each record of which has the X and Y coordinates of 

both the residence location and the crime location. For example, offender T7B committed seven 

incidents while offender S8A committed eight incidents. The records of both offenders are 

placed in the same file along with the records for all other offenders in the diagnostics file. 

14.13 
 

The diagnostics file provides information about which parameter (to be described below) 

is best at guessing where an offender lives. The assumption is that if a particular parameter was 

best with the K offenders in a diagnostics file in which the residence location was known, then it 

also will be best for a serial offender for whom the residence location is not known. 

How many serial offenders are needed to make up a diagnostics file? Again, there is no 

simple answer to this although the number is much less than for the O-D matrix. Clearly, the 

more, the better since the aim is to identify which parameter is most sensitive with a certain level 

of precision and accuracy. We used 88 offenders in the diagnostics file for Baltimore County 

(see below). Certainly, a minimum of 10 would be necessary. But, more would certainly be 

more accurate. Further, the offender records used in the diagnostics file should be similar in 

other dimensions to the offender that is being tracked. However, this may be impractical. In the 

example data set, we combined offenders who committed different types of crimes. The results 

may be different if offenders who had committed only one type of crimes were tested (though 

Leitner and Kent, 2009, found that using records for all crimes produced more accurate measures 

than using crime-specific records). 

Once the data sets have been collected, they need to be placed in an appended file, with 

one serial offender on top of another. Each record has to represent a single incident. Further, the 

records have to be arranged sequentially with all the records for a single offender being grouped 

together. The routine automatically sorts the data by the offender ID. But, to be sure that the 

result is consistent, the data should be prepared in this way. 

The structure of the records is similar to the example in Table 14.3 below. At the 

minimum, there needs to be an ID field and the X and Y coordinates of both crime location and 

the residence location. Thus, in the example, all the records for the first offender (Num 1) are 

together; all the records for the second offender (Num 2) are together; and so forth. The ID field 

is any numeric or string variable. In Table 14.3, the ID field is labeled AID@, but any label would 

be acceptable as long as it is consistent (i.e., all the records of a single offender are together). 

In addition to the ID field, the X and Y coordinates of both the crime and residence 

location must be included on each record. In the example table, the ID variable is called 

OffenderID, the crime location coordinates are called IncidX and IncidY while the residence 

location coordinates are called HomeX and HomeY. Again, any label is acceptable as long as 

the column locations in each record are consistent. As with the Journey-to-crime calibration file, 

other fields can be included. 

14.14 
Table 14.3: 

Example Records in Bayesian Journey-to-crime Diagnostics File 

OffenderID HomeX HomeY IncidX IncidY 

Num 1 -77.1496 39.3762 -76.6101 39.3729 

Num 1 -77.1496 39.3762 -76.5385 39.3790 

Num 1 -77.1496 39.3762 -76.5240 39.3944 

Num 2 -76.3098 39.4696 -76.5427 39.3989 

Num 2 -76.3098 39.4696 -76.5140 39.2940 

Num 2 -76.3098 39.4696 -76.4710 39.3741 

Num 3 -76.7104 39.3619 -76.7195 39.3704 

Num 3 -76.7104 39.3619 -76.8091 39.4428 

Num 3 -76.7104 39.3619 -76.7114 39.3625 

Num 4 -76.5179 39.2501 -76.5144 39.3177 

Num 4 -76.5179 39.2501 -76.4804 39.2609 

Num 4 -76.5179 39.2501 -76.5099 39.2952 

Num 5 -76.3793 39.3524 -76.4684 39.3526 

Num 5 -76.3793 39.3524 -76.4579 39.3590 

Num 5 -76.3793 39.3524 -76.4576 39.3590 

Num 5 -76.3793 39.3524 -76.4512 39.3347 

Num 6 -76.5920 39.3719 -76.5867 39.3745 

Num 6 -76.5920 39.3719 -76.5879 39.3730 

Num 6 -76.5920 39.3719 -76.7166 39.2757 

Num 6 -76.5920 39.3719 -76.6015 39.4042 

Num 7 -76.7152 39.3468 -76.7542 39.2815 

Num 7 -76.7152 39.3468 -76.7516 39.2832 

Num 7 -76.7152 39.3468 -76.7331 39.2878 

Num 7 -76.7152 39.3468 -76.7281 39.2889 

. 

. 

. 

. 

Num Last -76.4320 39.3182 -76.4297 39.3172 

Num Last -76.4880 39.3372 -76.4297 39.3172 

Num Last -76.4437 39.3300 -76.4297 39.3172 

Num Last -76.4085 39.3342 -76.4297 39.3172 

Num Last -76.4083 39.3332 -76.4297 39.3172 

Num Last -76.4082 39.3324 -76.4297 39.3172 

Num Last -76.4081 39.3335 -76.4297 39.3172 

Logic of the Routine 

The module is divided into two parts (under the ABayesian Journey-to-crime Estimation@

page of ASpatial Modeling@): 

1. Diagnostics for Journey-to-crime methods; and 

2. Estimate likely origin location of a serial offender. 

14.15 
 The Adiagnostics@ routine takes the diagnostics calibration file and estimates a number of 

methods for each serial offender in the file and tests the accuracy of each parameter against the 

known residence location. The result is a comparison of the different methods in terms of 

accuracy in predicting both where the offender lives as well as minimizing the distance between 

where the method predicts the most likely location for the offender and where the offender 

actually lives. 

The Aestimate@ routine allows the user to choose one method and to apply it to the data 

for a single serial offender. The result is a probability surface showing the results of the method 

in predicting where the offender is liable to be living. 

Bayesian Journey-to-crime Diagnostics 

The following applies to the Bayesian Journey-to-crime (BJtc) Diagnostics routine only. 

Data Input 

The user inputs the four required data sets. 

1. Any primary file with an X and Y location. A suggestion is to use the file for the 

one of the serial offenders, but this is not essential; 

2. A grid that will be overlaid on the study area. Use the Reference File under Data 

Setup to define the X and Y coordinates of the lower-left and upper-right corners 

of the grid as well as the number of columns (see Chapter 3, p. 3.21); 

3. A Journey-to-crime travel function (Jtc) that estimates the likelihood of an 

offender committing crimes at various distances or travel times if a network is 

used (see Chapter 13). 

4. An observed origin-destination matrix (see Chapter 28, p. 28.17); and 

5. A diagnostics file of known serial offenders in which both their residence and 

crime locations are known (BJtc Diagnostics) 

Methods Tested 

The BJtc Diagnostics routine compares six methods for estimating the likely location of a 

serial offender and will include up to four additional methods if filters are used (see below). 

14.16 
1. The Jtc distance method, P(Jtc); 

2. The general crime distribution based on the origin-destination matrix, P(O). 

Essentially, this is the distribution of origins irrespective of the destinations; 

3. The distribution of origins in the O-D matrix based only on the incidents in zones 

that are identical to those committed by the serial offender, P(O|Jtc); 

4. The product of the Jtc estimate (1 above) and the distribution of origins based 

only on those incidents committed in zones identical to those by the serial 

offender (3 above), P(Jtc)*P(O|Jtc). This is the numerator of the Bayesian 

function (Equation 14.8), the product of the prior probability times the likelihood 

estimate; 

5. The Bayesian Risk estimate as indicated in Equation 14.8 above (method 4 above 

divided by method 2 above), P(Bayesian). This is a rough approximation to the 

full Bayesian function in Equation 14.12 above; and 

6. The center of minimum distance, Cmd. Previous research has shown that the 

center of minimum of distance has the least error in minimizing the distance 

between the most likely location for the offender and where the offender actually 

lives (Paulsen, 2006a; Snook, Zito, Bennell, & Taylor, 2005; Levine, 2000). 

7. If filters are used: The product of the Jtc estimate and the filters, P(Jtc)*F1*F2. 

8. If filters are used: The product of the Conditional estimate and the filters, 

P(O|Jtc)*F1*F2. 

9. If filters are used: The product of the “Product” estimate and the filters, 

P(Jtc)*P(O|Jtc)*F1*F2. 

10. If filters are used: The product of the Bayesian Risk estimate and the filters, 

P(Bayesian)*F1*F2. 

 Interpolated Grid 

For each serial offender in turn in the BJtc Diagnostics file and for each method, the 

routine overlays a grid over the study area. The grid is defined by the Reference File parameters 

(see Chapter 3). The routine then interpolates each input data set into a probability estimate for 

each grid cell with the sum of the cells equaling 1.0 (within three decimal places). 

14.17 
The manner in which the interpolation is done varies by the method: 

1. For the Jtc method, P(Jtc), the routine interpolates the selected distance function 

to each grid cell to produce a density estimate. The densities are then re-scaled so 

that the sum of the grid cells equals 1.0 (see Chapter 10 on kernel density 

interpolation); 

2. For the general crime distribution method, P(O), the routine sums up the incidents 

by each origin zone from the origin-destination matrix and interpolates that using 

the normal distribution method of the single kernel density routine (see Chapter 

10 on kernel density interpolation). The density estimates are converted to 

probabilities so that the sum of the grid cells equals 1.0; 

3. For the distribution of origins based only on the incidents committed by the serial 

offender, from the origin-destination matrix the routine identifies the zone in 

which the incidents occurred and reads only those origins associated with those 

destination zones. Multiple incidents committed in the same origin zone are 

counted multiple times. The routine adds up the number of incidents counted for 

each zone and uses the single kernel density routine to interpolate the distribution 

to the grid (see Chapter 10 on kernel density interpolation). The density estimates 

are converted to probabilities so that the sum of the grid cells equals 1.0; 

4. For the product of the Jtc estimate and the distribution of origins based only on 

the incidents committed by the serial offender, the routine multiples the 

probability estimate obtained in 1 above by the probability estimate obtained in 3 

above. The probabilities are then re-scaled so that the sum of the grid cells equals 

1.0; 

5. For the Bayesian Risk estimate, the routine takes the product estimate (4 above) 

and divides it by the general crime distribution estimate (2 above). The resulting 

probabilities are then re-scaled so that the sum of the grid cells equals 1.0; and 

6. For the center of minimum distance estimate, the routine calculates the center of 

minimum distance for each serial offender in the Adiagnostics@ file and calculates 

the distance between this statistic and the location where the offender is actually 

residing. This is used only for the distance error comparisons. 

7. For the interaction of the Jtc, Conditional, “Product” and Bayesian Risk estimates 

with the filters, the estimates are obtained by multiplying the filters times these 

terms and then re-scaling so that the sum of the grid cells equals 1.0. 

14.18 
Note in all of the probability estimates (excluding 6), the cells are converted to 

probabilities prior to any multiplication or division. The results are then re-scaled so that the 

resulting grid is a probability (i.e., all cells sum to 1.0). 

Output 

For each offender in the BJtc Diagnostics file, the routine calculates three different 

statistics for each of the methods: 

1. The estimated probability in the cell where the offender actually lives. It does this 

by, first, identifying the grid cell in which the offender lives (i.e., the grid cell 

where the offender=s residence X and Y coordinate is found) and, second, by 

noting the probability associated with that grid cell; 

2. The percentile of all grid cells in the entire grid that have to be searched to find 

the cell where the offender lives based on the probability estimate from 1 above, 

ranked from those with the highest probability to the lowest. Obviously, this 

percentage will vary by how large a reference grid is used (e.g., with a very large 

reference grid, the percentile where the offender actually lives will be small 

whereas with a small reference grid, the percentile will be larger). But, since the 

purpose is to compare methods, the actual percentage should be treated as a 

relative index. 

The result is sorted from low to high so that the smaller the percentile, the better. 

For example, a percentile of 1% indicates that the probability estimate for the cell 

where the offender lives is within the top 1% of all grid cells. Conversely, a 

percentile of 30% indicates that the probability estimate for the cell where the 

offender lives in within the top 30% of all grid cells; and 

3. The distance between the cell with the highest probability and the cell where the 

offender lives. 

These three indices provide information about the accuracy and precision of the method. 

Table 14.4 illustrates a typical probability output for four of the methods. Only five serial 

offenders are shown in the table. 

Output matrices 

The BJtc Diagnostics routine outputs two separate matrices. The probability estimates 

(numbers 1 and 2 above) are presented in a separate matrix from the distance estimates (number 

14.19 
 

 

 

 

 

 

 

 

Table 14.4: 

Sample Output of Probability Matrix 

Percentile for Percentile for Percentile for Percentile for 

Offender P(Jtc) P(Jtc) P(O|Jtc) P(O|Jtc) P(O) P(O) P(Jtc)*P(O|Jtc) P(Jtc)*P(O|Jtc) 

1 0.001169 0.01% 0.000663 0.01% 0.0003 11.38% 0.002587 0.01% 

2 0.000292 5.68% 0.000483 0.12% 0.000377 0.33% 0.000673 0.40% 

3 0.000838 0.14% 0.000409 0.18% 0.0002 30.28% 0.00172 0.10% 

4 0.000611 1.56% 0.000525 1.47% 0.0004 2.37% 0.000993 1.37% 

5 0.001619 0.04% 0.000943 0.03% 0.000266 11.98% 0.004286 0.04% 

Table 14.5 illustrates a typical distance output for four of the methods. Only five serial 

offenders are shown in the table. 

Table 14.5: 

Sample Output of Distance Matrix 

Distance for 

Offender Distance(Jtc) Distance(O|Jtc) Distance(O) P(Jtc)*P(O|Jtc) 

1 0.060644 0.060644 7.510158 0.060644 

2 6.406375 0.673807 2.23202 0.840291 

3 0.906104 0.407762 11.53447 0.407762 

4 3.694369 3.672257 2.20705 3.672257 

5 0.423577 0.405526 6.772228 0.423577 

3 above). The user can save the total output as a text file or can copy and paste each of the two 

output matrices into a spreadsheet separately. We recommend the copying-and-pasting method 

into a spreadsheet as it will be difficult to line up differing column widths for the two matrices 

and summary tables in a text file. 

Which is the Most Accurate and Precise Method? 

Accuracy and precision are two different criteria for evaluating a method. With 

accuracy, one wants to know how close a method comes to a target. The target can be an exact 

location (e.g., the residence of a serial offender) or it can be a zone (e.g., a high probability area 

within which the serial offender lives). Precision, on the other hand, refers to the consistency of 

the method, irrespective of how accurate it is. A more precise measure is one in which the 

method has a limited variability in estimating the central location whereas a less precise measure 

has a higher degree of variability. These two criteria - accuracy and precision, often conflict. 

14.20 
The following example is from Jessen (1979). Consider a target that one is trying to >hit=

(Figure 14.5A). The target can be a physical target, such as a dart board, or it can be a location 

in space, such as the residence of a serial offender. One can think of three different >throwers= or 

methods attempting to hit the center of target, the Bulls Eye. The throwers make repeated 

attempts to hit the target and the >throws= (or estimates from the method) can be evaluated in 

terms of accuracy and precision. In Figure 14.5B, the thrower is all over the dartboard. There is 

no consistency at all. However, if the center of minimum distance (Cmd) is calculated, it is very 

close to the actual center of the target, the Bulls Eye. In this case, the thrower is accurate but not 

precise. That is, there is no systematic bias in the thrower=s throws, but they are not reliable. 

This thrower is accurate (or unbiased) but not precise. 

In Figure 14.5C, there is an opposite condition. In this case, the thrower is precise but 

not accurate. That is, there is a systematic bias in the throws even though the throws (or method) 

are relatively consistent. Finally in Figure 14.5D, the thrower is both relatively precise and 

accurate as the Cmd of the throws is almost exactly on the Bulls Eye. 

One can apply this analogy to a method. A method produces estimates from a sample. 

For each sample, one can evaluate how accurate is the method (i.e., how close to the target did it 

come) and how consistent is it (how much of variability does it produce). Perhaps the analogy is 

not perfect because the thrower makes multiple throws whereas the method produces a single 

estimate. But, clearly, we want a method that is both accurate and precise. 

Measures of Accuracy and Precision 

Much of the debate in the area of Journey-to-crime estimation has revolved around 

arguments about the accuracy and precision of the method. Levine (2000) first raised the issue 

of accuracy by proposing distance from the location with the highest probability to the location 

where the offender lived as a measure of accuracy, and suggested that simple, centrographic 

measures were as accurate as more precise Journey-to-crime methods in estimating this. Paulsen 

(2006a; 2006b) confirmed that centrgraphic methods were more accurate than journey-to-crime 

method. Snook and colleagues also confirmed this conclusion and showed that human subjects 

could do as well as any of the algorithms (Snook, Zito, Bennell, & Taylor, 2005; Snook, Taylor 

& Bennell, 2004). 

On the other hand, Canter, Coffey and Missen (2000), Canter (2003), and Rossmo (2000) 

have argued for an area of highest probability being the criterion for evaluating accuracy, 

indicating a >search cost= or a >hit score= with the aim being to narrow the search area to as small 

14.21 
Figure 14.5: 

Accuracy and Precision in Estimates 

A C 

B D 
 

as possible. Rich and Shivley (2004) compared different Journey-to-crime/geographic profiling 

software packages and concluded that there were at least five different criteria for evaluating 

accuracy and precision - error distance, search cost/hit score, profile error distance, top profile 

area, and profile accuracy. 

Rossmo (2005a; b) and Rossmo and Filer (2005) have critiqued these measures as being 

too simple and have rejected error distance. Levine (2005) justified the use of error distance as 

being fundamental to statistical error while acknowledging that an area measure is necessary, 

too. 

While the debate continues to develop, practically a distinction can be made between 

measures of accuracy and measures of precision. Accuracy is measured by how close to the 

target is the estimate while precision refers to how large or small an area the method produces. 

The two become identical when the precision is extremely small, similar to a variance 

converging into a mean as the distance between observations and the mean approach zero. 

In evaluating the methods, five different measures are used: 

 Accuracy Measures 

1. True accuracy - the probability in the cell where the offender actually lives. The 

Bayesian Jtc diagnostics routine evaluates the six above mentioned methods on a 

sample of serial offenders with known residence address. Each of the methods 

(except for the center of minimum distance, Cmd) has a probability distribution. 

That method which has the highest probability in the cell where the offender lives 

is the most accurate. 

2. Diagnostic accuracy - the distance between the cell with the highest probability 

estimate and the cell where the offender lives. Each of the methods produces 

probability estimates for each cell. The cell with the highest probability is the 

best guess for where the offender lives. The distance from this location to where 

the offender lives is an indicator of the diagnostic accuracy of the method. 

3. Neighborhood accuracy - the percent of offenders who reside within the cell 

with the highest probability. Since the grid cell is the smallest unit of resolution, 

this measures the percent of all offenders who live at the highest probability cell. 

This was estimated by those cases where the error distance was smaller than half 

the grid cell size. 

14.23 
 Precision Measures 

4. Search cost/hit score - the percent of the total study area that has to be searched 

to find the cell where the offender actually lived after having sorted the output 

cells from the highest probability to the lowest 

5. Potential search cost - the percent of offenders who live within a specified 

distance of the cell with the highest probability. In this evaluation, two distances 

are used though others can certainly be used: 

A. The percent of offender who live within one mile of the cell with the 

highest probability. 

B. The percent of offenders who live within one-half mile of the cell with the 

highest probability (AProbable search area in miles@). 

Summary Statistics

 The Adiagnostics@ routine will also provide summary information at the bottom of each 

matrix. There are summary measures and counts of the number of times a method had the 

highest probability or the closest distance from the cell with the highest probability to the cell 

where the offender actually lived; ties between methods are counted as fractions (e.g., two tied 

methods are given 0.5 each; three tied methods are give 0.33 each). For the probability matrix, 

these statistics include: 

1. The mean (probability or percentile); 

2. The median (probability or percentile); 

3. The standard deviation (probability or percentile); 

4. The number of times the P(Jtc) estimate produces the highest probility; 

5. The number of times the P(O|Jtc) estimate produces the highest probability; 

6. The number of times the P(O) estimate produces the highest probability; 

7. The number of times the product term estimate produces the highest probability; 

8. The number of times the Bayesian estimate produces the highest probability. 

9. If filters are used: The number of times the Jtc, Conditional, Product, and 

Bayesian Risk estimates times the filters produce the highest probability. 

14.24 
For the distance matrix, these statistics include: 

1. The mean distance; 

2. The median distance; 

3. The standard deviation distance; 

4. The number of times the P(Jtc) estimate produces the closest distance; 

5. The number of times the P(O|Jtc) estimate produces the closest distance; 

6. The number of times the P(O) estimate produces the closest distance; 

7. The number of times the product term estimate produces the closest distance; 

8. The number of times the Bayesian Risk estimate produces the closest distance; 

and 

9. The number of times the CMD produces the closest distance. 

10. If filters are used: The number of times the Jtc, Conditional, Product, and 

Bayesian Risk estimates times the filters produce the closest distance. 

Testing the Routine with Serial Offenders from Baltimore County 

To illustrate the use of the Bayesian Jtc diagnostics routine, the records of 88 serial 

offenders who had committed crimes in Baltimore County, MD, between 1993 and 1997 were 

compiled into a diagnostics file. The number of incidents committed by these offenders varied 

from 3 to 33 and included a range of different crime types (larceny, burglary, robbery, vehicle 

theft, arson, and bank robbery). 

Because the methods are interdependent, traditional parametric statistical tests cannot be 

used. Instead, non-parametric tests have been applied. For the probability and distance 

measures, two tests were used. First, the Friedman two-way analysis of variance test examines 

differences in the overall rank orders of multiple measures (treatments) for a group of subjects 

(Kanji, 1993, 115; Siegel, 1956). This is a Chi-square test and measures whether there are 

significant differences in the rank orders across all measures (treatments). Second, differences 

between specific pairs of measures can be tested using the Wilcoxon matched pairs signed-ranks 

test (Siegel, 1956, 75-83). This examines pairs of methods by not only their rank, but also by the 

difference in the values of the measurements. 

For the percentage of offenders who lived in the same grid cell, within one mile, and 

within one half-mile of the cell with the peak likelihood, the Cochran Q test for k related samples 

was used to test differences among the methods (Kanji, 1993, 74; Siegel, 1956, 161-166). This 

is a Chi-square test of whether there are overall differences among the methods in the 

percentages, but cannot indicate whether any one method has a statistically higher percentage. 

Consequently, the method with the highest percentage was tested against the method with the 

second highest percentage using the Cochran Q test to see whether the best method stood out. 

14.25 
 

 

 

 

 

 

 

 

 

_____________________________________________________________________ 

 Results: Accuracy 

Table 14.6 presents the results three accuracy measures. For the first measure, the 

probability estimate in the cell where the offender actually lived, the product probability is far 

superior to any of the others. It has the highest mean probability of any of the measures and is 

more than double the probability of the Journey-to-crime method. The Friedman test indicates 

that these differences are significant and the Wilcoxon matched pairs test indicates that the 

product has a significantly higher probability than the second best measure, the Bayesian Risk, 

which in turn is significantly higher than the Journey-to-crime measure. At the low end, the 

general probability has the lowest average and is significantly lower than the other measures. 

In terms of the individual offenders, the product probability had the highest probability 

for 74 of the 88 offenders. For the other methods, the Bayesian Risk measure had the highest 

probability for 10 offenders, the Journey-to-crime measure for one offender, the conditional 

probability for two offenders and the general probability for one offender. 

Table 14.6: 

Accuracy Measures of Total Sample 

 Mean distance Percent of 

Method 

Mean 

 probability in 

offender cella 

 from highest 

 probability cell to 

offender cell (mi)

b 

 offenders whose 

residence is in 

highest prob. cellc 

Journey-to-crime 0.00082 2.78 12.5% 

General 0.00025 8.21 0.0% 

Conditional 0.00052 3.22 3.4% 

Product 0.00170 2.65 13.6% 

Bayesian Risk 0.00131 3.15 10.2% 

 Cmd n.a. 2.62 18.2% 

a Friedman χ

2

 =236.0 ; d.f. = 4; p≤.001; Wilcoxon signed-ranks test at p≤.05: Product > Bayesian 

Risk > JTC = Conditional > General 

b Friedman χ

2

 = 114.2; d.f. = 5; p≤.001; Wilcoxon signed-ranks test at p≤.05: CMD = Product = 

JTC > Bayesian Risk = Conditional < General 

c Cochran Q=33.9, d.f. =5, p≤.001; Cochran Q of difference between best & second best=1.14, n.s. 

14.26 
 

Finally, for the third accuracy measure, the percent of offenders residing in the area 

covered by the cell with the highest probability estimate, the Cmd has the highest percentage 

(18.2%) followed by the product probability (13.6%), and the Journey-to-crime probability 

(12.5%). The Cochran Q shows significant differences over all these measures. However, the 

difference between the measure with the highest percentage in the same grid cell (the Cmd) and 

the measure with the second highest percentage (the product probability) is not significant. 

For accuracy, the product probability appears to be better than the Journey-to-crime 

estimate and almost as accurate as the Cmd. It has the highest probability in the cell where the 

offender lived and a lower error distance than the Journey-to-crime method (though not 

significantly so). Finally, it had a slightly higher percentage of offenders living in the area 

covered by cell with the highest probability than for the Journey-to-crime. 

The Cmd, on the other hand, which had been shown to be the most accurate in previous 

studies (Paulsen, 2006a; 2006b; Snook, Zito, Bennell, and Taylor, 2005; Snook, Taylor and 

Bennell, 2004; Levine, 2000), does not appear to be more accurate than the product probability. 

It has only a slightly lower error distance and a slightly higher percentage of offenders residing 

in the area covered by the cell with the highest probability. Thus, the product term has equaled 

the Cmd in terms of accuracy. Both, however, are more accurate than the Journey-to-crime 

estimate. 

For the measure of diagnostic accuracy (the distance from the cell with the highest 

probability to the cell where the offender lived), the center of minimum distance (Cmd) had the 

lowest error distance followed closely by the product term. The Journey-to-crime method had a 

slightly larger error. Again, the general probability had the greatest error, as might be expected. 

The Friedman test indicates there are overall differences among the six measures in the mean 

distance. The Wilcoxon signed-ranks test, however, showed that the Cmd, the product, and the 

Journey-to-crime estimates are not significantly different, though all are significantly lower than 

the Bayesian Risk measure and the conditional probability which, in turn, are significantly lower 

than the general probability. 

In terms of individual cases, the Cmd produced the lowest average error distance for 30 

of the 88 cases while the conditional term (O|Jtc) had the lowest error distance in 17.9 cases 

(including ties). The product term produced a lower average error distance for 9.5 cases 

(including ties) and the Jtc estimate produced lower average distance errors in 8.2 cases (again, 

including ties). In other words, the Cmd will either be very accurate or very inaccurate, which is 

not surprising given that it is only a point estimate. 

14.27 
Results: Precision 

Table 14.7 presents the three precision measures used to evaluate the six different 

measures. For the first measure, the mean percent of the study area with a higher probability 

(what Canter called >search cost= and Rossmo called >hit score=; Canter, 2003; Rossmo, 2005a, 

2005b), the Bayesian Risk measure had the lowest percentage followed closely by the product 

term. The conditional probability was third followed by the Journey-to-crime probability 

followed by the general probability. The Friedman test indicates that these differences are 

significant overall and the Wilcoxon test shows that the Bayesian Risk, product term, conditional 

probability and Journey-to-crime estimates are not significantly different from each other. The 

general probability estimate, however, is much worse. 

In terms of individual cases, the product probability had either the lowest percentage or 

was tied with other measures for the lowest percentage in 36 of the 88 cases. The Bayesian Risk 

and Journey-to-crime measures had the lowest percentage or were tied with other measures for 

the lowest percentage in 34 of the 88 cases. The conditional probability had the lowest 

percentage or was tied with other measures for the lowest percentage in 23 of the cases. Finally, 

the general probability had the lowest percentage or was tied with other measures for the lowest 

percentage in only 7 of the cases. 

Similar results are seen for the percent of offenders living within one mile of the cell with 

the highest probability and also for the percent living within a half mile. For the percent within 

one mile, the product term had the highest percentage followed closely by the Journey-to-crime 

measure and the Cmd. Again, at the low end is the general probability. The Cochran Q test 

indicates that these differences are significant over all measures though the difference between 

the best method (the product) and the second best (the Journey-to-crime) is not significant. 

Conclusion of the Evaluation 

In conclusion, the product method appears to be an improvement over the Journey-tocrime method, at least with these data from Baltimore County. It is substantially more accurate 

and about as precise. Further, the product probability appears to be, on average, almost as 

accurate as the Cmd, though the Cmd still is more accurate in assessing the exact location of 

offenders. That is, the Cmd will identify about one-sixth of all offenders exactly. For a single 

guess of where a serial offender is living, the center of minimum distance produced the lowest 

distance error. But, since it is only a point estimate, it cannot point to a search area where the 

offender might be living. The product term, on the other hand, produced an average distance 

error almost as small as the center of minimum distance, but produced estimates for other grid 

cells too. Among all the probability measures, it had the highest probability in the cell where the 

offender lived and was among the most efficient in terms of reducing the search area. 

14.28 
 

 

 

 

 

 

 

 

 

 

Table 14.7: 

Precision Measures of Total Sample

 Mean percent Percent of offenders living within 

 of study area distance of highest probability cell: 

 with higher

 Method probabilitya 1 mileb 0.5 milesc 

Journey-to-crime 4.7% 56.8% 44.3% 

General 16.8% 2.3% 0.0% 

Conditional 4.6% 47.7% 31.8% 

Product 4.2% 59.1% 48.9% 

Bayesian Risk 4.1% 51.1% 42.0% 

Cmd n.a. 54.5% 42.0% 

________________________________________________________________ 

a Friedman χ

2

 =115.4 ; d.f. = 4; p_.001; Wilcoxon signed-ranks test at p_.05: Bayesian 

Risk =Product= JTC = Conditional> General 

b Cochran Q = 141.0, d.f. = 5, p_.001; Cochran Q of difference between best and second 

best = 0.7, n.s. 

c Cochran Q = 112.2, d.f. = 5, p_.001; Cochran Q of difference between best and second 

best = 2.0, n.s. 

In other words, using information about the origin location of other offenders appears to 

improve the accuracy of the Jtc method. The result is an index (the product term) that is almost 

as good as the center of minimum distance, but one that is more useful since the center of 

minimum distance is only a single point. 

Of course, each jurisdiction should re-run these diagnostics to determine the most 

appropriate measure. It is very possible that other jurisdictions will have different results due to 

the uniqueness of their land uses, street layout, and location in relation to the center of the 

metropolitan area. Baltimore County surrounds the City of Baltimore on three sides. It has a 

mixture of neighborhoods including parts of the central city, older suburbs, newer suburbs, 

separate communities and rural areas. The model results which fit Baltimore County might not 

fit other places. 

14.29 
Tests with Other Data Sets 

The Bayesian Journey-to-crime model was tested in 2009 in several jurisdictions: 

1. In Baltimore County with 850 serial offenders (Leitner & Kent, 2009); 

2. In the Hague, Netherlands with 62 serial burglars (Block & Bernasco, 2009); 

3. In Chicago, with 103 serial robbers (Levine & Block, 2011); and 

4. In Manchester, England with 171 serial offenders (Levine & Lee, 2009). 

In all cases, the product probability measure was both more accurate and more precise 

than the Journey-to-crime measure. In two of the studies (Chicago and the Hague), the product 

term was also more accurate than the Center of Minimum Distance. In the other two studies 

(Baltimore County and Manchester), the Center of Minimum Distance was slightly more 

accurate than the product term. 

Among the probability methods, the product term was more accurate than all other 

measures for three of the studies (Baltimore County, Chicago, Manchester). For the Hague 

study, however, the conditional estimate was more accurate. This was because the journey-tocrime estimate was very inaccurate due to the small size of the Hague (Block & Bernasco, 2009). 

The mathematics of these models has been explored by O=Leary (2009). These studies 

are presented in a special issue of the Journal of Investigative Psychology and Offender 

Profiling. Introductions are provided by Canter (2009) and Levine (2009). 

In short, the product term appears to be almost as good a method as the Center of 

Minimum Distance and generally the best of the probability methods. However, users should 

first test whether this conclusion holds for their jurisdiction. 

Estimate Likely Origin Location of a Serial Offender 

The following applies to the Bayesian Jtc Estimate Likely Origin Location (BJtc) of a 

Serial Offender routine. Once the BJtc Diagnostic routine has been run and a preferred method 

selected, the next routine allows the application of that method to a single serial offender. 

Data Input 

The user inputs the three required data sets and a reference file grid: 

14.30 
1. The incidents committed by a single offender that we are interested in catching. 

This must be the Primary File; 

2. A Jtc function that estimates the likelihood of an offender committing crimes at a 

certain distance (or travel time if a network is used). This can be either a 

mathematically-defined function or an empirically-derived one (see Chapter 13 on 

Journey-to-crime Estimation). In general, the empirically-derived function is 

slightly more accurate than the mathematically-defined one though the differences 

are not large; 

3. An origin-destination matrix; and 

4. The reference file also needs to be defined and should include all locations where 

crimes have been committed (see Reference File). 

Selected Method 

The BJtc routine interpolates the incidents committed by the serial offender to a grid, 

yielding an estimate of where the offender is liable to live. There are five standard methods that 

can be used and ten additional methods if filters are used. However, the user has to choose one 

of these: 

1. The Jtc distance method, P(Jtc); 

2. The general crime distribution based on the origin-destination matrix, P(O). 

Essentially, this is the distribution of origins irrespective of the destinations; 

3. The conditional Jtc distance. This is the distribution of origins based only on the 

incidents committed by other offenders in the same zones as those committed by 

the serial offender, P(O|Jtc). This is extracted from the O-D matrix; 

4. The product of the Jtc estimate (1 above) and the distribution of origins based 

only on the incidents committed by the serial offender (3 above), P(Jtc)*P(O|Jtc). 

This is the numerator of the Bayesian function (Equation 14.8), the product of the 

prior probability times the likelihood estimate; and 

4. The Bayesian Risk estimate as indicated in Equation 14.12 above (method 4 

above divided by method 2 above), P(Bayesian). 

14.31 
5. If one filter is used: the interaction between the Jtc, the Conditional, the Product, 

and the Bayesian Risk measures with the one filter. Also, the filter by itself can be 

checked. 

6. If two filters are used: the interaction between the Jtc, the Conditional, the 

Product, and the Bayesian measures with the two filters. Also, the two filters by 

themselves can be checked. 

As mentioned, however, the user must choose only one of these for estimation. 

 Interpolated Grid 

For the BJtc method that is selected, the routine overlays a grid on the study area. The 

grid is defined by the reference file parameters (see Chapter 3). The routine then interpolates the 

input data set (the primary file) into a probability estimate for each grid cell with the sum of the 

cells equaling 1.0 (within three decimal places). The manner in which the interpolation is done 

varies by the method chosen: 

1. For the Jtc method, P(Jtc), the routine interpolates the selected distance function 

to each grid cell to produce a density estimate. The density estimates are 

converted to probabilities so that the sum of the grid cells equals 1.0 (see Chapter 

10 on kernel density interpolation); 

2. For the general crime distribution method, P(O), the routine sums up the incidents 

by each origin zone and interpolates this to the grid using the normal distribution 

method of the single kernel density routine (see Chapter 10 on kernel density 

interpolation). The density estimates are converted to probabilities so that the 

sum of the grid cells equals 1.0. 

3. For the distribution of origins based only on the incident committed by the serial 

offender, the routine identifies the zone in which the incident occurs and reads 

only those origins associated with those destination zones in the origin-destination 

matrix. Multiple incidents committed in the same origin zone are counted multiple 

times. The routine then uses the single kernel density routine to interpolate the 

distribution to the grid (see Chapter 10). The density estimates are converted to 

probabilities so that the sum of the grid cells equals 1.0; 

14.32 
4. For the product of the Jtc estimate and the distribution of origins based only on 

the incidents committed by the serial offender, the routine multiples the 

probability estimate obtained in 1 above by the probability estimate obtained in 3 

above. The product probabilities are then re-scaled so that the sum of the grid 

cells equals 1.0; and 

5. For the full Bayesian estimate as indicated in equation 14.12 above, the routine 

takes the product estimate (4 above) and divides it by the general crime 

distribution estimate (2 above). The resulting density estimates are converted to 

probabilities so that the sum of the grid cells equals 1.0. 

6. For any of the interactions with filters, the routine takes the filters and interpolates 

them to a grid and converts the estimates to probabilities. If there is only filter, 

then this layer is interpolated to the grid and converted into probabilities. If there 

are two filters, each is first interpolated to the grid and converted into 

probabilities. Then the two probability interpolations are multiplied by each 

other. The routine then multiplies the resulting filter probability by the 

probability estimate of the selected measure (Jtc, Conditional, Product, or 

Bayesian Risk). The resulting multiplication product is then re-scaled so that sum 

of the grid cells equals 1.0. 

Note in all estimates, the results are then re-scaled so that the resulting grid is a 

probability (i.e., all cells sum to 1.0). 

Output 

Once the method has been selected, the routine interpolates the data to the grid cell and 

outputs it as a >shp=, >mif/mid=, or Ascii file for display in a GIS program. The tabular output 

shows the probability values for each cell in the matrix and also indicates which grid cell has the 

highest probability estimate. 

Accumulator Matrix 

There is also an intermediate output, called the accumulator matrix which the user can 

save. This lists the number of origins identified in each origin zone for the specific pattern of 

incidents committed by the offender, prior to the interpolation to grid cells. That is, in reading 

the origin-destination file, the routine first identifies which zone each incident committed by the 

offender falls within. Second, it reads the origin-destination matrix and identifies which origin 

zones are associated with incidents committed in the particular destination zones. Finally, it 

sums up the number of origins by zone ID associated with the incident distribution of the 

14.33 
offender. This can be useful for examining the distribution of origins by zones prior to 

interpolating these to the grid. 

Two Examples of Using the Bayesian Journey-to-crime Routine 

Two examples will illustrate the routine. Figure 14.6 presents the probability output for 

the general origin model, that is for the origins of all offenders irrespective of where they 

committed their crimes. It is a probability surface in that all the grid cells sum to 1.0. The map is 

scaled so that each bin covers a probability of 0.0001. The cell with the highest probability is 

highlighted in light blue. 

As seen, the distribution is heavily weighted towards the center of the metropolitan area, 

particularly in the City of Baltimore. For the crimes committed in Baltimore County between 

1993 and 1997 in which both the crime location and the residence location was known, about 

40% of the offenders resided within the City of Baltimore and the bulk of those living within 

Baltimore County lived close to the border with City. In other words, as a general condition, 

most offenders in Baltimore County live relatively close to the center. 

 Offender S14A 

The general probability output does not take into consideration information about the 

particular pattern of an offender. Therefore, we will examine specifically a particular offender. 

Figure 14.7 maps the distribution of an offender who committed 14 offenses between 1993 and 

1997 (offender S14A) before being caught and the residence location where the individual lived 

when arrested 

Of the 14 offenses, seven were thefts (larceny), four were assaults, two were robberies, 

and one was a burglary. As seen, most of the incidents occurred in the southeast corner of 

Baltimore County though two incidents were committed more than five miles away from the 

offender=s residence. 

The general probability model is not very precise since it assigns the same probability to 

all grid cells for all offenders. In the case of offender S14A, the error distance between the cell 

with the highest probability and the cell where the offender actually lived was 7.4 miles. 

On the other hand, the Jtc method uses the distribution of the incidents committed by a 

particular offender and a model of a typical travel distance distribution to estimate the likely 

origin of the offender=s residence. A travel distance estimate based on the distribution of 41,424 

offenders from Baltimore County was created using the CrimeStat Journey-to-crime calibration 

routine (see Chapter 13 on Journey-to-crime Estimation). 

14.34 
Figure 14.6: 
Figure 14.7: 
Figure 14.8 shows the results of the Jtc probability output. In this map and the following 

maps, the bins represent probability ranges of 0.0001. The cell with the highest likelihood is 

highlighted in light blue. As seen, this cell is very close to the cell where the actual offender 

lived. The distance between the two cells was 0.34 miles. With the Jtc probability estimate, 

however, the area with a higher probability (dark red) covers a fairly large area. However, the 

precision of the Jtc estimate is good since only 0.03% of the cells have higher probabilities that 

the cell associated with the area where the offender lived. In other words, the Jtc estimate has 

produced a very good estimate of the location of the offender, as might be expected given the 

concentration of the incidents committed by this person. 

For this same offender, Figure 14.9 show the results of the conditional probability 

estimate of the offender=s residence location, that is the distribution of the likely origin based on 

the origins of offenders who committed crimes in the same locations as that by S14A. Again, 

the cell with the highest probability is highlighted (in light green). As seen, this method has also 

produced a fairly close estimate, with the distance between the cell with the highest probability 

and the cell where the offender actually lived being 0.18 miles, about half the error distance of 

the Jtc method. Further, the conditional estimate is more precise than the Jtc with only 0.01% 

of the cells having a higher probability than the cell associated with the residence of hte 

offender. Thus, the conditional probability estimate is not only more accurate than the Jtc 

method, but also more precise (i.e., more efficient in terms of search area). 

For this same offender, Figure 14.10 shows the results of the Bayesian product estimate, 

the product of the Jtc probability and the conditional probability re-scaled to be a single 

probability (i.e., with the sum of the grid cells equal to 1.0). It is a Bayesian estimate because it 

updates the Jtc probability estimate with the information on the likely origins of offenders who 

committed crimes in the same locations (the conditional estimate). Again, the cell with the 

highest probability is highlighted (in dark tan). The distance error for this method is 0.26 miles, 

not as accurate as the conditional probability estimate but more accurate than the Jtc estimate. 

Further, this method is about as precise as the Jtc since 0.03% of the cells having probabilities 

higher than that associated with the location where the offender lived. 

Figure 14.11 shows the results of the Bayesian Risk probability estimate. This method 

takes the Bayesian product estimate and divides it by the general origin probability estimate. It 

is analogous to a risk measure that relates the number of events to a baseline population. In this 

case, it is the estimate of the probability of the updated Jtc estimate relative to the probability of 

where offenders live in general. Again, the cell with the highest likelihood is highlighted (in 

dark yellow). The Bayesian Risk estimate produces an error of 0.34 miles, the same as the Jtc 

estimate, with 0.04% of the cells having probabilities higher than that associated with the 

residence of the offender. 

14.37 
Figure 14.8: 
Figure 14.9: 
Figure 14.10: 
Figure 14.11: 
 

Finally, the center of minimum distance (Cmd) is indicated on each of the maps with a 

grey cross. In this case, the Cmd is not as accurate as any of the other methods since it has an 

error distance of 0.58 miles. 

In summary, all of the Journey-to-crime estimate methods produced relatively accurate 

estimates of the location of the offender (S14A). Given that the incidents committed by this 

person were within a fairly concentrated pattern, it is not surprising that each of the method 

produced reasonable accuracy. In Canter and Larkin’s (1994) terminology, this offender is a 

‘marauder’. 

Offender TS15A 

But what happens if an offender who did not commit crimes in the same part of town is 

selected, what Canter and Larkin (1994) call a ‘commuter’? Figure 14.12 shows the 

distribution of an offender who committed 15 offenses (TS15A). Of the 15 offenses 

committed by this individual, there were six larceny thefts, two assaults, two vehicle thefts, one 

robbery, one burglary, and three incidents of arson. Twelve of the offenses are relatively 

concentrated but two are more than eight miles away. 

Only three of the estimates will be shown. The general method produces an error of 4.6 

miles. Figure 14.13 show the results of the Jtc method. Again, the map bins are in ranges of 

0.0001 and the cell with the highest probability is highlighted. As seen, the cell with the 

highest probability is located north and west of the actual offender=s residence. The error 

distance is 1.89 miles. The precision of this estimate is good with only 0.08% of the cells 

having higher probabilities than the cell where the offender lived. 

Figure 14.14 show the result of the conditional probability estimate for this offender. In 

this case, the conditional probability method is less accurate than the Jtc method with an error 

distance between the cell with the highest probability and the cell where the offender lived 

being 2.39 miles. However, this method is less precise than the Jtc method with 1.6% of the 

study area having probabilities higher than that in the cell where the offender lived. 

Finally, Figure 14.15 shows the results of the product probability estimate. For this 

method, the error distance is only 0.47 miles, much less than the Jtc method. Further, it is 

smaller than the CMD which has an error distance of 1.33 miles. Again, updating the Jtc 

estimate with information from the conditional estimate produces a more accurate guess where 

the offender lives. Further, the product estimate is more precise with only 0.02% of the study 

area having probabilities higher than the cell covering the area where the offender lived. 

14.42 
Figure 14.12: 
Figure 14.13: 
Figure 14.14: 
Figure 14.15: 
 

In other words, the BJtc routine allows the estimation of a probability grid based on a 

single selected method. The user must decide which probability method to select and the 

routine then calculates that estimate and assigns it to a grid. As mentioned above, the BJtc 

Diagnostics routine should be first run to decide on which method is most appropriate for the 

jurisdiction in question. In these 88 cases, the Bayesian product estimate was the most accurate 

of all the probability methods. However, differences in the balance between central-city and 

suburbs, the road network, and land uses may change the travel patterns of offenders. So far, as 

mentioned above, in tests in four cities (Baltimore County, Chicago, the Hague, Manchester), 

the product estimate has consistently been better than the Journey-to-crime estimate and almost 

as good, if not better, than the center of minimum distance. Further, the product term appears to 

be more precise than the Journey-to-crime method though in the Hague study, the conditional 

estimate was more accurate than the product estimate. The center of minimum distance, while 

generally more accurate than other methods, has no probability distribution; it is simply a point. 

Consequently, one cannot select a search area from the estimate. 

Potential to Add New Information to Improve the Methodology 

Further, it should be possible to add more information to this framework to improve the 

accuracy and precision of the estimates. One obvious dimension that should be added is an 

opportunity matrix, a distribution of targets that are crime attractions for offenders. Among 

these are convenience stores, shopping malls, parking lots, and other types of land use that 

attract offenders. It will be necessary to create a probability matrix for quantifying these 

attractions. Further, the opportunity matrix would have to be conditional on the distribution of 

the crimes and on the distribution of origins of offenders who committed crimes in the same 

location. The Bayesian framework is a conditional one where factors are added to the 

framework but conditioned on the distribution of earlier factors: 

 (14.13) 

where A is the attractions (or opportunities), Jtc is the distribution of incidents, and O is the 

distribution of other offender origins. It will not be an easy task to estimate an opportunity 

matrix that is conditioned (dependent) upon both the distribution of offences (Jtc) and the origin 

of other offenders who committed crimes in the same location (O|Jtc) and it may be necessary 

to approximate this through a series of filters. 

Probability Filters 

A filter is a probability matrix that is applied to the estimate but is not conditioned on 

the existing variables in the model. For example, an opportunity matrix that was independent of 

14.47 
 

 

the distribution of offences by a single serial offender or the origins of other offenders who 

committed crimes in the same locations could be applied as an alternative (equation 14.14): 

 (14.14) 

In this case, P(A) is an independent matrix. Another filter that could be applied is 

residential land use. The vast majority of offenders are going to live in residential areas. Thus, 

a residential land use filter estimates the probability of a residential land use for every cell, 

P(R), could be applied to screen out cells that are not residential, such as 

 (14.15) 

In this way, additional information can be integrated into the Journey-to-crime 

methodology to improve the accuracy and precision of the estimates. Clearly, having additional 

variables be conditioned upon existing variables in the model would be ideal since that would 

fit the true Bayesian approach. But, even if independent filters were brought in, the model 

might be improved. 

Defining Filters in the Bayesian Journey-to-crime Routine 

The Bayesian Journey-to-crime routine allows filters to be applied. The routine can be 

run with or without filters and the user has a choice of running the routine with no filters, one 

filter (called ‘Filter 1’) and two filters (called ‘Filter 1’ and ‘Filter 2’). See Figure 14.4 above 

that illustrates how to define the filters on the Bayesian Journey-to-crime page. 

For example, one filter could be whether the grid cell is residential or not. Each zone in 

the filter variable could have a dummy variable indicating whether it is primarily residential (1) 

or not (0). The criteria for defining residential could be having a minimum number of 

residential units but also having less than a specified number of persons employed in the zone. 

A ‘pure’ residential zone would have only residences and no employment. 

Kent and Leitner (2009) showed that the use of residential land covers improved 

accuracy for Jtc estimates, but did not improve estimates for the Bayesian approach. 

Nevertheless, it is likely that a subset of residential land cover might improve the precision of 

an estimate. 

Another filter could be the amount of employment in a zone. Zones with many 

employees (e.g., commercial areas) would have high values on the filter variable while zones 

with few, if any, employees would have low values on the filter. 

14.48 
function, .

A third filter could be the number of businesses of a certain type for crimes of a 

particular type. For example, to model liquor store robberies, the filter variable could be the 

number of liquor stores in each zone. Or, to model bank robberies, the filter variable could be 

the number of banks in each zone. 

Whichever variable is used for the filter, the routine interpolates this to the same grid as 

the Journey-to-crime function, P(O), the conditional probability function, P(O|Jtc), the general 

function, P(O), the production probability function, P(Jtc)*P(O|Jtc), and the Bayesian Risk 

The interpolated filter grid is then multiplied by four functions - the Journey-to-crime 

grid, P(Jtc), the conditional probability function, P(O|Jtc), the product probability function, 

௉ሺ௃௧௖ሻ∗௉ሺை|௃௧௖ሻ P(Jtc)*P(O|Jtc), and the Bayesian Risk function, . ௉ሺைሻሻ

Example of the Use of a Probability Filter 

To illustrate this, Figure 14.16 shows the location of 22 crimes committed by a single 

offender, S22A, and the offender’s residence when arrested. The incidents are shown in blue 

and the residence location in black. The crimes committed were 6 commercial burglaries, 1 

residential burglary, 11 vehicle break-ins and 4 vehicle thefts. 

Figure 14.17 shows the result of the Journey-to-crime probability estimate. As with the 

other maps, the center of minimum distance (CMD) is shown as a gray cross. Notice that 

neither the center of minimum distance nor the journey-to-crime estimates were particularly 

accurate as the cell with the peak probability was 2.5 miles and the CMD was 2.6 miles 

respectively away from the actual home location of the offender. 

Figure 14.18 shows the conditional probability estimate. With this estimate, the cell 

with the peak probability was much more accurate, being about 0.5 miles away. 

Figure 14.19 shows the product probability estimate which multiplies the Journey-tocrime estimate by the conditional probability estimate and then re-scales the grid to sum to 1.0. 

This estimate was not particularly accurate as well with the cell having the peak probability 

being 2.5 miles away. The reason is that the inaccurate Journey-to-crime estimate also made the 

product estimate inaccurate. In some cases, a more accurate conditional estimate will improve 

the product probability but in other cases it will not. Block and Bernasco (2009) found that 

journey-to-crime estimates were inaccurate with serial burglars in The Hague, Netherlands, and 

that the conditional probability estimate was more accurate than the product probability estimate 

because the poor journey-to-crime estimates degraded the product estimates. That is why it is 

14.49 
Figure 14.16: 
Figure 14.17: 
Figure 14.18: 
Figure 14.19: 
important to analyze which method is best for a single jurisdiction using the Bayesian journeyto-crime diagnostics routine before applying a particular method a single serial offender. 

With offender S22A, a residential land use probability filter was defined by a zonal data 

base of Traffic Analysis Zones (TAZ) in Baltimore County that included both residential 

population variables and employment variables. A dummy variable was created by defining 

TAZ’s that had 100 or more persons living in them but 200 or fewer employees working in 

them. Thus, these TAZ’s were primarily residential. When the TAZ layer was interpolated to 

the grid in the routine, each grid cell had a probability value that varied from 0 to 1 and which 

indicated the likelihood of the cell residential. 

Figure 14.20 shows the result of combining the product probability estimate with this 

residential land use filter. The results were as accurate as the conditional probability estimate in 

distance as the cell with the peak probability was about 0.5 miles away. But, more important is 

the probability estimate in the cell with the peak probability was much higher than the 

probability estimated for the conditional (0.008842 compared to 0.000345, a ratio that was 25.6 

times higher). 

In other words, the effect of narrowing the probability estimates of the product 

probability by discounting cells that were not residential actually improved the accuracy of the 

product probability estimate. We do not yet know whether using a residential filter will always 

improve accuracy since we have not tested it on a number of cases yet. It is possible that these 

filters will improve accuracy but it is also possible that they will make precision worse since 

they multiply a conditional probability by a matrix that is constant for all offenders. 

Until a thorough evaluation is conducted, the filters are provided as tools for users to 

experiment with in modeling the likely residence location of a serial offender. 

Guidelines for Analysts 

The following discussion is for analysts wishing to utilize the technique to try to narrow 

down the geographic areas for particular serial offenders. The hardest part of using the 

technique is collecting the data and constructing a journey-to-crime (Jtc) function and an origindestination (O-D) matrix. However, once the data have been assembled and the Jtc function 

and the O-D matrix constructed, the technique can be used for multiple serial offenders. These 

estimates need to be only updated every few years in order to account for changes in travel 

patterns by offenders. 

14.54 
Figure 14.20: 
We have argued that an analyst should test which of the different methods produces the 

best estimate for a particular jurisdiction. However, if an analyst wants to choose a single best 

technique without testing which method works best in the jurisdiction, we recommend sticking 

with the Product probability by itself (without filters). We have found that the Product estimate 

(the product of the Jtc and Conditional probability estimates) generally produces more accurate 

results than the Jtc function by itself or the Conditional probability by itself, though some 

exceptions have been noted. The use of filters to improve estimates is still too new a technique 

and needs to be evaluated further. 

To simplify, seven basic steps are required to run the “Estimate likely location of a serial 

offender” routine and one additional step if the analyst wants to test which method works best 

for the jurisdiction. 

Steps 

1. Obtain Required Data 

First, the data that will be needed is a large number of records where both the residence 

location and the crime location are known. Most likely, these will come from arrest records. 

By large, we mean at least 10,000 cases. 

2. Construct Journey-to-crime Function 

Second, once these data have been assembled, the user should create a journey-to-crime 

function using the “Calibrate journey-to-crime function” routine (discussed in Chapter 13). 

3. Define Zonal Framework 

Third, to construct an origin-destination matrix, the analyst will need a zonal framework 

for allocating the incidents to both origin and destination locations. Commonly used zones are 

census tracts or traffic analysis zones, though others can be used. Also, we have found good 

results by using a grid as the zone structure, especially with small-sized grid cells (e.g., a 100 

column x 100 row grid). The single kernel density interpolation tool (discussed in Chapter 10) 

is a useful tool for creating a grid overlay that can be used as a zone framework. 

4. Construct Origin-Destination Matrix 

Fourth, using the data on offenders where both the residence location and the crime 

location are known and the zonal framework, the origin-destination matrix can be constructed 

using the “Calculate observed origin-destination trips” routine that is discussed in Chapter 28. 

14.56 
The routine reads in an origin file (the zonal framework) and a destination file (also the zonal 

framework) and a data file (the set of records of offenders where both residence and crime 

location are known) and outputs the O-D matrix. The user should save the matrix as a dbf file. 

5. Input Jtc Function and O-D Matrix 

Fifth, the Jtc function and the O-D matrix are input on the Bayesian Journey-to-crime 

page. 

6. Input Records of Single Serial Offender 

Sixth, to estimate the likely origin (residence) location of a serial offender, the records 

for that serial offender need to be input as the Primary File. As with all Primary File inputs, the 

coordinate system and the data metrics need to be defined. 

7. Estimate Likely Origin Location of a Serial Offender 

Seventh, and finally, the user selects one estimation method on the Bayesian Journey-tocrime page and runs the routine. As mentioned above, unless there is contrary information, we 

recommend using the Product estimate by itself (“Use product of P(Jtc) and P(O|Jtc) estimate”). 

8. (Optional) Evaluate which Method Produces the Best Results for the 

Jurisdiction 

The Product estimate will generally produce good results for medium-to-large cities. 

However, for small cities, it may not work well and other measures may work better (e.g., the 

Conditional or the Bayesian Risk estimate). Therefore, an optional strategy is to evaluate which 

of the methods works best in the jurisdiction. 

To do this, the analyst will have to assemble a diagnostics file on multiple serial 

offenders where the offender has committed multiple offences (e.g., 5 or more) and where both 

the residence and crime locations are known. The number of offenders included should be as 

large as possible, at least 50. The four studies mentioned on page 14.30 all used sizeable data 

sets (60 or more). The reason is that there needs to be sufficient variability to allow the routine 

to properly estimate the accuracy and precision of each of the methods. 

While this requires even more data to be collected, the advantage is that the best 

estimation method can be determined for the jurisdiction. As mentioned, the use of the Product 

estimate may or may not produce the best estimates. 

14.57 
 

Summary 

In summary, the Bayesian Jtc methodology is an improvement over the current Journeyto-crime method and appears to be as good, and more useful, than the center of minimum 

distance. First, it adds new information to the Journey-to-crime function to yield a more 

accurate and precise estimate. Second, it can sometimes predict the origin of >commuter=-type 

serial offenders, those individuals who do not commit crimes in their neighborhoods (Paulsen, 

2007; Canter & Larkin, 1994). The traditional Journey-to-crime function cannot predict the 

origin location of a >commuter=-type. Of course, this will only work if there are prior offenders 

who lived in the same location as the serial offender of interest. If the offender lived in a 

neighborhood where there were no previous serial offenders that were documented in the origindestination matrix, the Bayesian approach would not detect that location, either. 

Caveat 

A caveat should be noted, however. The Bayesian method still has a substantial amount 

of error. Much of this error reflects the inherent mobility of offenders, especially those living in 

in suburbs outside of central cities. While adolescent offenders, especially juvenile males, tend 

to commit crimes within a more circumscribed area (Levine & Lee, 2013), the almost-universal 

ability adults to own automobiles and to travel outside their residential neighborhoods is turning 

crime into a much more mobile phenomena than it was, say, 50 years ago when only about half 

of American households owned an automobile. 

Thus, the Bayesian approach to Journey-to-crime estimation must be seen as a tool that 

produces an incremental improvement in accuracy and precision. Geographic profiling is but 

one tool in the arsenal of methods that police must use to catch serial offenders. 

14.58 
References 

Block, R. & Bernasco, W. (2009). Finding a serial burglar=s home using distance decay and 

conditional origin-destination patterns: A test of Empirical Bayes Journey-to-crime estimation 

in The Hague. Journal of Investigative Psychology & Offender Profiling. 6(3), 187-211. 

Canter, D. (2009). Developments in geographical offender profiling: Commentary on Bayesian 

journey-to-crime modeling. Journal of Investigative Psychology & Offender Profiling. 6(3), 

161-166. 

Canter, D. (2003). Dragnet: A Geographical Prioritisation Package. Center for Investigative 

Psychology, Department of Psychology, The University of Liverpool: Liverpool, UK. 

http://www.i-psy.com/publications/publications_dragnet.php. 

Canter, D., Coffey, T., Huntley, M., & Missen, C. (2000). Predicting serial killers' home base 

using a decision support system. Journal of Quantitative Criminology, 16 (4), 457 -- 478. 

Canter, D. & Gregory, A. (1994). Identifying the residential location of rapists, Journal of the 

Forensic Science Society, 34 (3), 169-175. 

Canter, D. & Larkin, P. (1993). The environmental range of serial rapists, Journal of 

Environmental Psychology, 13, 63-69. 

Denison, D.G.T., Holmes, C.C. Mallilck, B. K. & Smith, A. F. M. (2002). Bayesian Methods 

for Nonlinear Classification and Regression. John Wiley & Sons, Ltd: New York. 

Gelman, A., Carlin, J. B. Stern, H. S. & Rubin, D. B. (2004). Bayesian Data Analysis (second 

edition). Chapman & Hall/CRC: Boca Raton, FL. 

Jessen, R. J. (1979). Statistical Survey Techniques. John Wiley & Sons: New York. 

Kanji, G. K. (1993). 100 Statistical Tests. Sage Publications: Thousand Oaks, CA. 

Kent, J. & Leitner, M. (2009). Utilizing land cover characteristics to enhance journey-to-crime 

estimation models. Crime Mapping, 1. 

Lee, P. M. (2004). Bayesian Statistics: An Introduction (third edition). Hodder Arnold: 

London. 

14.59 
 

References (continued) 

Leitner, M. & Kent, J. (2009). Bayesian Journey-to-crime modeling of single- and multiple 

crime type series in Baltimore County, MD. Journal of Investigative Psychology & Offender 

Profiling. 6(3), 213-236. 

Levine, N. (2009). Introduction to the special issue on Bayesian Journey-to-crime modeling. 

Journal of Investigative Psychology & Offender Profiling. 6(3), 167-185. 

Levine, N. (2005). AThe evaluation of geographic profiling software: Response to Kim Rossmo's 

critique of the NIJ methodology@. http://www.nedlevine.com/Response to Kim Rossmo Critique 

of the GP Evaluation Methodology.May 8 2005.doc 

Levine, N. (2000). Journey-to-crime Estimation. Chapter 10 of Levine, N. (ed), CrimeStat III: 

A Spatial Statistics Program for the Analysis of Crime Incident Locations (version 1.1). Ned 

Levine & Associates, Annandale, VA; National Institute of Justice, Washington, DC. August. 

See archived files at http://www.icpsr.umich.edu/CrimeStat. 

Levine, N. & Lee, P. (2013). Crime travel of offenders by gender and age in Manchester, 

England. Leitner, M. (ed), Crime Modeling and Mapping Using Geospatial Technologies, 

Springer. 145-178. 

Levine, N., & Block, R. (2010). Bayesian Journey-to-Crime Estimation: An Improvement in 

Geographic Profiling Methodology. The Professional Geographer. 63(2), 213-229. 

Levine, N. & Lee, P. (2009). Bayesian Journey-to-crime modeling of juvenile and adult 

offenders by gender in Manchester. Journal of Investigative Psychology & Offender Profiling. 

6(3), 237-251. 

O=Leary, M. (2009). The mathematics of geographical profiling. Journal of Investigative 

Psychology & Offender Profiling. 6(3), 253-265. 

Paulsen, D. (2007). Improving geographic profiling through commuter/marauder 

prediction.. Police Practice and Research, 8: 347-357 

Paulsen, D. (2006a). Connecting the dots: assessing the accuracy of geographic profiling 

software. Policing: An International Journal of Police Strategies and Management. 20 (2), 

306-334. 

14.60 
 

References (continued) 

Paulsen, D. (2006b). Human versus machine: A comparison of the accuracy of geographic 

profiling methods. Journal of Investigative Psychology and Offender Profiling 3: 77-89. 

Rich, T., & Shively, M. (2004). A Methodology for Evaluating Geographic Profiling Software. 

Final Report for the National Institute of Justice, Abt Associates: Cambridge, MA. 

http://www.ojp.usdoj.gov/nij/maps/gp.pdf. 

Rossmo, D. K. (2005a). Geographic heuristics or shortcuts to failure?: Response to Snook et al. 

Applied Cognitive Psychology 19: 651-654. 

Rossmo, D. K. (2005b). Response to NIJ=s methodology for evaluating geographic profiling 

software. http://www.ojp.usdoj.gov/nij/maps/gp.htm. 

Rossmo, D. K., & Filer, S. (2005). Analysis versus guesswork. Blue Line Magazine, , August / 

September, 24:26. 

Rossmo, D. K. (2000). Geographic Profiling. CRC Press: Boca Raton Fl. 

Rossmo, D. K. (1995). Overview: multivariate spatial profiles as a tool in crime investigation. 

In Block, C. R., Dabdoub, M. & Fregly, S., Crime Analysis Through Computer Mapping. Police 

Executive Research Forum: Washington, DC. 65-97. 

Siegel, S. (1956). Nonparametric Statistics for the Behavioral Sciences. McGraw-Hill: New 

York. 

Snook, B., Zito, M., Bennell, C. & Taylor, P. J. (2005). On the complexity and accuracy of 

geographic profiling strategies. Journal of Quantitative Criminology, 21 (1), 1-26. 

Snook, B., Taylor, P. J. & Bennell, C. (2004). Geographic profiling; the fast, fugal and accurate 

way. Applied Cognitive Psychology 18: 105-121. 

14.61