A Basic Overview of 

Probabilistic Genotyping

Michael D. Coble

National Institute of Standards and Technology

Probabilistic Genotyping 

Webcast (Part 1)

May 28, 2014
NIST and NIJ Disclaimer

Past and Present Funding: Interagency Agreement 

between the National Institute of Justice and NIST 

Office of Law Enforcement Standards

Points of view are mine and do not necessarily represent 

the official position or policies of the US Department of Justice or the 

National Institute of Standards and Technology. 

Certain commercial equipment, instruments, software and materials are 

identified in order to specify experimental procedures as completely 

as possible. In no case does such identification imply a 

recommendation or endorsement by the National Institute of 

Standards and Technology nor does it imply that any of the 

materials, instruments or equipment identified are necessarily the 

best available for the purpose.
Two Parts to Mixture Interpretation

• Determination of alleles present in the 

evidence and deconvolution of mixture 

components where possible 

– Many times through comparison to victim and 

suspect profiles

• Providing some kind of statistical answer

regarding the weight of the evidence

– There are multiple approaches and philosophies
Statistical Approaches with Mixtures

See Ladd et al. (2001) Croat Med J. 42:244-246

“Exclusionary” Approach “Inferred Genotype” Approach

Random Man Not Excluded

(RMNE)

Combined Prob. of Inclusion

(CPI)

Combined Prob. of Exclusion

(CPE)

Random Match Probability

(RMP)

(mRMP)

Likelihood Ratio 

(LR)
Exclusionary Approach
Statistical Approaches with Mixtures

• Random Man Not Excluded (CPE/CPI) - The 

probability that a random person (unrelated 

individual) would be included/excluded as a 

contributor to the observed DNA mixture. 

a b c d

CPI = (f(a) + f(b) + f(c) + f(d))2

CPI = PIM1 X PIM2

...

CPE = 1 - CPI
RMNE example with FGA

Possible Combinations

20, 28 and 23, 23

20, 23 and 23, 28

Assume ST = 150 RFU
RMNE example with FGA

Possible Combinations

20, 28 and 23, 23

20, 23 and 23, 28

20, 23 and 28, 28

Assume ST = 150 RFU
RMNE example with FGA

Possible Combinations

20, 28 and 23, 23

20, 23 and 23, 28

20, 23 and 28, 28

20, 20 and 23, 28

Assume ST = 150 RFU
RMNE example with FGA

Possible Combinations

20, 28 and 23, 23

20, 23 and 23, 28

20, 23 and 28, 28

20, 20 and 23, 28

Assume ST = 150 RFU

PI = (p + q + r)2

PI = (f20 + f23 + f28)

2

PI = (0.145 + 0.158 + 0.013)2

PI = (0.316)2

PI = 0.099

PE = 1 – CPI = 0.901
“Advantages and Disadvantages”

RMNE

Summarized from John Buckleton, Forensic DNA Evidence Interpretation, p. 223

Buckleton and Curran (2008) FSI-G 343-348.

Advantages

- Does not require an assumption of the number of contributors to a mixture

- Easier to explain in court

- Deconvolution is not necessary 

Disadvantages

- Weaker use of the available information (robs the evidence of its true 

probative power because this approach does not consider the suspect’s 

genotype).

- Alleles below ST cannot be used for statistical purpose

- There is a potential to include a non-contributor

RMNE (CPE/CPI)
Notes from Charles Brenner’s AAFS 2011 talk

The Mythical “Exclusion” Method for Analyzing DNA Mixtures – Does it Make Any Sense at All?

1. The claim that it requires no assumption about number of 

contributors is mostly wrong.

2. The supposed ease of understanding by judge or jury is really an 

illusion.

3. Ease of use is claimed to be an advantage particularly for 

complicated mixture profiles, those with many peaks of varying 

heights. The truth is the exact opposite. The exclusion method is 

completely invalid for complicated mixtures.

4. The exclusion method is only conservative for guilty suspects.

Conclusion: “Certainly no one has laid out an explicit and rigorous 

chain of reasoning from first principles to support the exclusion 

method. It is at best guesswork.”

Brenner, C.H. (2011). The mythical “exclusion” method for analyzing DNA mixtures – does it make any sense 

at all? Proceedings of the American Academy of Forensic Sciences, Feb 2011, Volume 17, p. 79
modified Random Match Probability
Statistical Approaches with Mixtures

• Random Match Probability (RMP) – The major 

and minor components can be successfully 

separated into individual profiles. A random 

match probability is calculated on the evidence 

as if the component was from a single source 

sample.

a b c d

RMPminor = 2pq 

= 2 x f(b) x f(c) 
2013 JFS Article
When data is above ST

7 9 11

K = 7,9

S = 7,11

U = 7,11

9,11 or

11,11

CPI = (f7 + f9 + f11)

2

mRMP = 2f7f11 + 2f9f11 

+ (f11)

2
When data is below ST

7 9 11

Q = any other allele

“2p” rule

CPI = n/a mRMP = 2p
The “2p” Rule

• The “2p” rule can be used to statistically account 

for zygosity ambiguity – i.e. is this single peak 

below the stochastic threshold the result of a 

homozygous genotype or the result of a 

heterozygous genotype with allele drop-out of 

the sister allele?

ST

AT
The “2p” Rule

• “This rule arose during the VNTR era. At that 

time many smaller alleles “ran off the end of the 

gel” and were not visualised.”

- Buckleton and Triggs (2006)

Is the 2p rule always conservative?” 
The “2p” Rule

Stain = AA

Suspect = AA

ST

LR = 5 LR = 100 f(a) = 0.10 1/p2 = 100 1/2p = 5 
The “2p” Rule

Stain = AA

Suspect = AB

ST

LR = 5 Exclusion

f(a) = 0.10 1/2p = 5 
Likelihood Ratio
Statistical Approaches with Mixtures

• Likelihood Ratio - Comparing the probability of 

observing the mixture data under two (or more) 

alternative hypotheses
Likelihood Ratios in Forensic DNA Work

• We evaluate the evidence (E) relative to alternative 

pairs of hypotheses

• Usually these hypotheses are formulated as follows:

– The probability of the evidence if the crime stain originated with 

the suspect or Pr(E|S)

– The probability of the evidence if the crime stain originated from 

an unknown, unrelated individual or Pr(E|U)

Pr( | )

Pr( | )

E U

E S

LR 

The numerator

The denominator

Slide information from Peter Gill
Likelihood Ratio (LR)

• Provides ability to express and evaluate both the prosecution 

hypothesis, Hp(the suspect is the perpetrator) and the defense 

hypothesis, Hd(an unknown individual with a matching profile is the 

perpetrator)

• The numerator, Hp, is usually 1 – since in theory the prosecution 

would only prosecute the suspect if they are 100% certain he/she is 

the perpetrator

• The denominator, Hd, is typically the profile frequency in a particular 

population (based on individual allele frequencies and assuming 

HWE) – i.e., the random match probability

d

p

H

H

LR 

Slide information from Peter Gill
We conclude that the two matters that appear to 

have real force are:

(1) LRs are more difficult to present in court and

(2) the RMNE statistic wastes information that 

should be utilised.
What kind of mixtures were being seen 

in the early days of STR testing?

• Torres et al. (2003) published the casework 

experience in a Spanish laboratory over a four-year 

time period (Jan 1997 to Dec 2000)

• 2412 samples typed

– 955 samples from sexual assaults

– 1408 samples from other offenses

– 49 samples from human remains identifications

• 163/2412 samples (6.7% showed a mixed profile)

• Only 8 samples (0.3% of total samples) were a >2 

person mixture!

Torres, Y., et al. (2003). DNA mixtures in forensic casework: a 4-year retrospective 

study. Forensic Science International, 134, 180-186. 
From Torres et al. (2003)

• “In our own and other authors’ experience 

(Clayton et al. 1998) two-person mixtures 

account for the overwhelming majority of 

mixtures encountered during casework, but 

occasionally mixtures of three or more persons 

are seen with more than four alleles at some 

loci. Eight of the 163 mixed samples (0.3% of 

the total typed samples) corresponded to such 

higher-order profiles.”

Torres, Y., et al. (2003). DNA mixtures in forensic casework: a 4-year retrospective 

study. Forensic Science International, 134, 180-186. 

Clayton, T.M., et al. (1998). Analysis and interpretation of mixed forensic stains 

using DNA STR profiling. Forensic Science International, 91, 55-70.
Gathered Case Summary Data

During 2007 and early 2008, Ann Gross (MN BCA) from 

the SWGDAM Mixture Interpretation Committee 

coordinated the collection of case summary data

from 14 different forensic labs who collectively

reported on >4500 samples. 

A preliminary summary of this information is divided by 

crime classifications: sexual assault, major crime 

(homicide), and high volume (burglary). Over half of the 

samples examined were single source and ~75% of 

all reported mixtures were 2-person.

This is why the SWGDAM 2010 Interpretation 

Guidelines focused on 2-person mixtures
Mixture Case Summaries (2007-2008)

minimum # of contributors

Crime Class 1 2 3 4 >4 N

Sexual Assault 884 787 145 11 0 1827

Major Crime 1261 519 182 32 0 1994

High Volume 344 220 140 11 5 720

Total 2489 1526 467 54 5 4541

54.8% 33.6% 10.3% 1.2% 0.1%

http://www.cstl.nist.gov/strbase/pub_pres/Promega2008poster.pdf

Single 

source

mixtures

Data Set from 14 Different Labs

2-person 

mixtures 11.6%

>2-person 

mixtures
Challenging Mixtures

12 Allele

56 RFU 

13 Allele

60 RFU “Q” Allele

??
How to handle low level data

• Continue to use RMNE (CPI, CPE) 
Michael Donley

Dr. Roger Kahn

Harris Co. (TX) IFS

CPI = 1 in 119

?

?

?

?
What should we do with data below our 

Stochastic Threshold?

• Continue to use RMNE (CPI, CPE) (not optimal)

• Use the Binary LR with 2p (not optimal)
Suspect

Evidence

Suspect

Evidence

LR 1

2pq

=

Suspect

Evidence

“2p”

LR 0

2pq

= LR ?

2pq

=

The Binary LR approach
Probabilistic Approaches

• “Semi-Continuous” or “Fully Continuous” 

• Semi-Continuous – information is determined 

from the alleles present – peak heights are not 

considered.

• Fully Continuous – incorporation of biological 

parameters (PHR [Hb], Mx ratio, Stutter 

percentage, etc...).
What should we do with discordant 

data?

• Continue to use RMNE (CPI, CPE) (not optimal)

• Use the Binary LR with 2p (not optimal)

• Semi-continuous methods with a LR (Drop 

models)
R. v Garside and Bates

• James Garside was accused of hiring Richard 

Bates to kill his estranged wife, Marilyn 

Garside.

• Marilyn was visiting her mother when 

someone knocked on the door. Marilyn 

answered and was stabbed to death.

• A profile from the crime scene stain gave a 

low-level DNA profile of the perpetrator. 
Summary

Three alleles were not present in the evidence 
Court case

• Crown expert dropped the D18 locus (gave a 

LR = 1) from the statistical results and used 

“2p” for D2 to give an overall odds for Bates of 

1 in 610,000.

• David Balding argued for the defense that 

dropping loci is not conservative. 
Balding and Buckleton (2009)

Present the “Drop model” for interpreting LT-DNA profiles
Drop Model

V = 20, 20

S = 19, 22

P(E H1)

Pr(Drop-out) = 0.05

Pr(Drop-in) = 0.01

= Pr(no Drop-out at 22) Pr(Drop-out at 19) Pr(No Drop-in)

= 0.95 0.05 0.99

= 0.047

19 20 22

D2
Drop Model

V = 20, 20

S = 19, 22

Pr(Drop-out) = 0.05

Pr(Drop-in) = 0.01

= 

0.047

P(E H2)

P(E H1)

The defense can now argue 

that someone else in the 

population unrelated to Bates 

was the true perpetrator! 

D2

19 20 22
Drop Model

V = 20, 20

UC = 17, 23

Pr(Drop-out) = 0.05

Pr(Drop-in) = 0.01

P(E H2)

20 23

D2

Pr(Drop-out at 17) Pr(Drop-out at 23) Pr(Drop-in at 22)

0.05 0.05 0.01

= 0.000025 x 2pq17,23 (0.027) = 0.000000675 

17 22
Summary

• Using “2p” for D2 gave a LR = 11. This is nonconservative compared to the probabilistic 

approach where a Pr(D) was incorporated into 

the calculation, the LR = 2.8

• The use of a probabilistic approach uses all of 

the information in the profile. 
Some Semi-Continuous Examples

• LR mix (Haned and Gill)

• Balding (likeLTD - R program)

• FST (NYOCME, Mitchell et al.)

• Kelly et al. (University of Auckland, ESR)

• Lab Retriever (Lohmueller, Rudin and Inman) 

• Armed Expert (NicheVision)

• Puch-Solis et al. (LiRa and LiRaHT)

• GenoProof Mixture (Qualitype)
Semi-continuous methods

• Use a Pr(DO) and LRs

• Speed of analysis – “relatively fast”

• The methods do not make full use of data -

only the alleles present.
What should we do with discordant data?

• Continue to use RMNE (CPI, CPE) (not optimal)

• Use the Binary LR with 2p (not optimal)

• Semi-continuous methods with a LR (Drop 

models)

• Fully continuous methods with LR
Continuous Models

• Mathematical modeling of “molecular 

biology” of the profile (mix ratio, PHR (Hb), 

stutter, etc...) to find optimal genotypes, giving 

WEIGHT to the results. 

A B C

Distribution of

Probable Genotypes

AC – 40%

BC – 25%

CC – 20%

CQ – 15%

Q
Some Continuous Model Examples

• TrueAllele (Cybergenetics)

• STRmix (ESR [NZ] and Australian collaboration)

• DNA-View Mixture Solution (Charles Brenner)

• DNAmixtures (Graversen 2013a,b) – open 

source, but requires HUGIN.

Weights may be determined by performing

simulations of the data (Markov Chain Monte

Carlo - MCMC).
Fully continuous methods

• Use a Pr(DO) and LRs

• Biological modeling of the data parameters

• Speed of analysis – can vary

• Attempts to use all of the data 
Summary

• Probabilistic Methods make better use of the data than 

RMNE or the binary LR with 2p. 

• The goal of the software programs should not be to simply 

“get bigger numbers” but to understand the details of 

these approaches and not treat the software as a “black 

box.” 

• Semi-continuous approaches will produce a LR that could 

be replicated by hand if necessary.

• Each approach has it’s own advantages and 

disadvantages.
Use modern tools for today’s mixtures!
Annual Review of Statistics and Its Application (2014): 361-384
Acknowledgments

Contact info:

mcoble@nist.gov

+1-301-975-4330

National Institute of Justice and 

NIST OLES

John Butler

Charlotte Word

Robin Cotton

Catherine Grgicak

Bruce Heidebrecht

John Paul Jones

Points of view are mine and do not necessarily represent the official position or policies 

of the US Department of Justice or the National Institute of Standards and Technology. 

Certain commercial equipment, instruments, software and materials are identified in order 

to specify experimental procedures as completely as possible. In no case does such 

identification imply a recommendation or endorsement by the National Institute of 

Standards and Technology nor does it imply that any of the materials, instruments or 

equipment identified are necessarily the best available for the purpose.