Annex 1: Glossary of Terms
This Glossary contains terms identified at the Paris Workshop, and some added subsequently. It isprovisional, and comments are invited both on the definitions provided, and on additional terms.
Please send comments to Ian Galbally (name and contact details in Annex 6)
Absolute Error

1

The absolute deviation of a variable from its ‘true’ value. See also Deviation from the Mean.
Accuracy2

The tendency of values of an estimator to come close to the quantity they are intended to estimate.
See also Precision. So far as inventories are concerned accuracy means that estimates are neither
over estimates nor underestimates of true avulse, so far as can be judged, and that the uncertainties
are reduced so far as practicable
Arithmetic Mean

8

The arithmetic mean of n quantities x1, x2, … , xn is the sum of the quantities divided by their numbern.
Average
A generic term for a measure of central tendency for a set of sample observations.
Bias2(1) In problems of estimation, an estimator is said to be biased if its expected value does not equalthe parameter it is intended to estimate. (2) In sampling, a bias is a systematic error introduced by
selecting items from a wrong population, favouring some of the elements of a population, or poorly
phrasing questions.
Comparability
In the IPCC inventory context inventories are said to be comparable with the Guidelines if they are
produced using the Guidelines, or by using methods that are mathematically equivalent to those in
the Guidelines, or which can be shown to give more accurate estimates than the methods in theGuidelines for source categories contained in the Guidelines.
Compliance3Compliance is the act of conforming or yielding to a specified norm or protocol. In the inventory
development process, compliance indicates conformity to development protocols or international
agreements. In this sense the compliance issue can be thought of as verification of adherence to theseestablished and agreed norms.
Confidence

3

The term confidence is used to represent trust in a measurement or estimate. Having confidence ininventory estimates does not make those estimates accurate or precise, but will help to develop aconsensus that the data can be applied to problem solving.
Confidence Interval

2An interval for which one can assert with a given probability, called the degree of confidence or theconfidence coefficient, that it will contain the true value of the parameter it is intended to estimate.
The endpoints of a confidence interval are referred to as the (upper and lower) confidence limits; they22are generally values of random variables calculated on the basis of sample data. In the IPCC
Guidelines specified confidence intervals correspond to a two standard deviations or 95%.
Consistency

2An estimator (depending on the sample size of n) is said to be consistent if the probability that it willassume a value arbitrarily close to the parameter it is intended to estimate approaches one when nbecomes infinite. In the IPCC inventory context, consistency can mean that the methods used are thesame throughout the time series being reported.
Correlation

2In general, the term denotes the relationship (association or dependence) between two or morequalitative or quantitative variables. See also Correlation Coefficient.
Correlation Coefficient

2A measure of the linear relationship between two quantitative variables. It is denoted by the letter r
and its values range from -1 to +1, where 0 indicates the absence of linear relationship, while -1 and+1 indicate, respectively, a perfect negative (inverse) and a perfect positive (direct) relationship.
Deviation from the Mean2

For a given set of data, the amount by which an individual observation differs from the mean; thus,
the deviation of the ith observation xi from the mean x is given by xi - x . An important property ofdeviations from the mean is that, for any set of data, their sum is always equal to zero. The absolutevalue of xi - x , namely | xi - x | , is referred to as an absolute deviation from the mean.
Distribution function

2A function whose values F(t) are the probabilities that a random variable assumes a value less than orequal to t.
Error of estimation

1

In regression analysis where the regression equation is used to estimate the ‘dependent’ from given
values of the ‘independent’ variates, the difference between the estimated and the observed value ofthe dependent variate.
Estimate

2

A number or an interval, based on sample data produced by an estimator; also the result of a model
calculation or other estimation procedure.
Estimator

1

A rule or method of estimating a constant of a parent population.
Expected Value8
The expected value of a random variable is a theoretically defined quantity intended to be ananalogue of the (observable) arithmetic mean. It can be regarded as corresponding to a limit of thearithmetic mean as the sample size increases indefinitely.
Gaussian Distribution
See Normal Distribution
Mean
See Arithmetic Mean23

Median9
The median value of a sample is the value which divides an ordered sample into two equal halves. If
there are 2n + 1 observations, the median is taken as the (n + 1)th member of the ordered sample. If
there are 2n it is taken as being halfway between the nth and (n +1)th.
Normal Distribution
The normal distribution is the probability distribution function whose probability density function is:f ( x) =Precision (x − µ)2 exp  −2σ 2 2π σ1for -∞ < x < ∞2The precision of an estimator is its tendency to have its values cluster closely about the expectedvalue of its sampling distribution; thus, it is related inversely to the variance of this sampling
distribution - the smaller the variance, the greater the precision.
Probability density function

2A function with non-negative values, whose integral from a to b ( a ≤ b ) gives the probability that acorresponding random variable assumes a value on the interval from a to b.
Probability distribution

2The probability distribution (or simply the distribution) of a random variable is its probability
structure as described, for example, by a probability density function or a probability distributionfunction.
Quality Assurance

3

In the context of emissions inventory development, quality assurance is used to represent the sum ofactivities that are implemented to ensure the collection and presentation of high quality data.
More generally, quality assurance describes the activities that are completed after the development ofa product, usually by an independent party to verify that data quality objectives were met and that theproduct conforms to specifications. In experimental programs, audits with standard instruments andstandard measures are used to establish the reliability of the experimental procedures. In thecalculated emission inventories development, however, few such standards have been developed sofar.
Quality Control

3

Quality control activities are those procedures and tests that can be performed during the planningand development of an inventory to ensure that the data quality objectives are being met. These
activities may include criteria tests for data on operations, completeness criteria, or averaging
techniques for use in developing default parameters. Quality control activities are generally appliedby the developers.
Random error

4

Is the result of a measurement minus its expected value. Random error is equal to absolute error
minus systematic bias. Because only a finite number of measurements can be made, it is possible todetermine only an estimate of random error.
Reliability

2

When speaking of the reliability of an estimator, one is referring to the possible size of chance errors.
This term is often used interchangeably with consistency. In the context of emissions inventories,24reliability and confidence are closely linked. If the approaches and data sources used in an inventory
development project are considered reliable, then users will have an acceptable degree of confidence
in the emissions data developed from those techniques.
SampleA sample among other meanings, can be a set of data.
Sampling Distribution

2

The distribution of a statistic; for example, the distribution of the arithmetic mean for random
samples from normal populations, or the distribution of the coefficient of correlation under theassumptions of normal correlation analysis.
Sensitivity Analysis5, 6(1) Determining the contribution of individual analysis inputs to the variability in model parameters.
(2) The systematic investigation of the reaction of the simulation and response to either extreme
values of the model’s quantitative factors (parameter and input variables) or to drastic changes in themodel’s quantitative factors (modules). So the focus is not on marginal changes in inputs.
Standard Deviation

2

The standard deviation of a sample of size n (usually called the “sample standard deviation”) is givenby the square root of the sum of the squared deviations from the arithmetic mean divided by n -1.
Systematic error
See Bias
Transparency

3Transparency is used to represent the condition of being clear and free from pretence. In the contextof compiling emission inventories under the UNFCCC this means (1) the construction of theemission estimates is clearly explained; (2) the documentation of the inventory is sufficient foranother party to reconstruct it; (3) the documentation sufficiently clarifies the major causes ofemission trends in the inventory. Transparency will be greatly increased if the data collected andreported by different agencies will be similar and, therefore, easily understood by other parties andcomparable to the data presented by the other parties.
Uncertainty

3Uncertainty is a statistical term that is used to represent the degree of accuracy and precision of data.
It often expresses the range of possible values of a parameter or a measurement around a mean orpreferred value.
Uncertainty analysis

6

In uncertainty analysis values of the model inputs are sampled from pre-defined distributions toquantify the consequences of the uncertainties in the model inputs, for the model outputs. So in
uncertainty analysis the input variables range between extreme values investigated in sensitivityanalysis.
Validation

3Validation is the establishment of sound approach and foundation. The legal use of validation is to
give an official confirmation or approval of an act or product. In the context of emission inventories
validation involves checking to ensure that the inventory has been compiled correctly in line with
reporting instructions and guidelines. It checks the internal consistency of the inventory.

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Variability 7This refers to observed differences attributable to true heterogeneity or diversity in a population orparameter. Sources of variability are the result of random processes. Variability is usually not
reducible by further measurement or study, but can be characterised.
Variance

8

The variance of a sample is (1) the square of the standard deviation (2) the second central moment ofa population.
Verification

3

Verification refers to the collection of activities and procedures that can be followed during theplanning and development, or after completion of an inventory that can help to establish its reliability
for the intended applications of that inventory. Typically, methods external to the inventory are used
to check the truth of the inventory, including comparisons with estimates made by other bodies orwith emission and uptake measurements determined from atmospheric concentrations and/orconcentration gradients of these gases.

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Definitions are extracted from:
1. M.G. Kendall and W.R. Buckland, A Dictionary of Statistical Terms; International Statistics
Institute; UK 1975.
2. Freund, J.E., and F.J. Williams, Dictionary/Outline of Basic Statistics, 195 pp., DoverPublications, Inc., New York, NY, 1966.
3. The European Environment Agency, Atmospheric Emission Inventory Guidebook (CD-ROM),
section on Procedures for Verification of Emission Inventories; Copenhagen, 1997.
4. International Organisation of Standardisation, International Vocabulary of Basic and General
Terms in Meteorology (VIM),1993.
5. J.C. Helton, Uncertainty and Sensitivity Analysis in Performance Assessment for the Waste
Isolation Pilot Plant, In: Second International Symposium on Sensitivity Analysis of Model Output(SAMO, 98), edited by K. Chan, S. Tarantola, and F. Campolongo, Office of Official Publications ofthe European Communities, Luxembourg, 1998.
6. Kleijnen, J.P.C., Statistical Theory on Design of Experiments, Applied to Simulation. In Second
International Symposium on Sensitivity Analysis of Model Output (SAMO ‘98), edited by K. Chan,S. Tarantola, and F. Campolongo, Office of Official Publications of the European Communities,
Luxembourg, 1998.
7. United States Environmental Protection Agency, Guiding principles for Monte Carlo Analysis,
1997.
8. Kotz, S. and Johnson, N.L., Encyclopedia of Statistical Sciences, 9 volumes, John Wiley & Sons,
New York, 1988.
9. Kendall M.G. and Stuart A., The Advanced Theory of Statistics, Charles Griffin and Company Ltd,London, 1969.

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