Bayesian statistical methods applied to the quantification of forensic evidence
Submitting InstitutionsUniversity of Edinburgh,
Unit of AssessmentMathematical Sciences
Summary Impact TypePolitical
Research Subject Area(s)
Mathematical Sciences: Statistics
Economics: Applied Economics
Summary of the impact
In a series of papers published from 1999 on, Aitken (Maxwell Institute)
and collaborators applied Bayesian statistics to develop a methodology for
the quantification of judicial evidence derived from forensic analyses.
They proposed and implemented procedures for (i) determining the optimal
size of samples that should be taken from potentially incriminating
material (such as drugs seized); and (ii) the estimation of likelihood
ratios characterising evidence provided by multivariate hierarchical data
(such as the chemical composition of crime-scene samples). Their
procedures have been recommended in international guideline documents
(including a 2009 publication by the United Nations Office on Drugs and
Crime) and have been routinely used by forensic science laboratories
worldwide since 2008. The research has therefore had an impact on the
administration of justice, leading to a better use of evidence and
accompanying judicial and economic benefits. Examples are given from
laboratories in Australia, Sweden and The Netherlands.
Our judicial system increasingly relies on the quantification of the
value of evidence presented in court. As a result, advanced statistical
methods have a strong impact on the administration of justice. The key
research insight in this area is the recognition that the Bayesian
framework provides the tools needed for the interpretation of forensic
evidence. This has led to the development of increasingly sophisticated
statistical analyses driven by new measuring equipment for the examination
of trace evidence and by the increase in computing power that enables the
lengthy calculations required to be performed efficiently. In papers
published from 1999 on Aitken (Maxwell Institute, MI) and co-workers have
contributed to this development and tackled two important problems: the
determination of the optimal size of samples to be taken from seized
material and the treatment of multivariate, hierarchical evidence data.
The methodology issued from his research has since been adopted by
forensic laboratories worldwide.
Optimal sample size. When large quantities of potentially
incriminating material are seized, it is difficult to determine what
fraction should be used for forensic testing: small samples are open to
challenge as providing too little information; large samples are costly. A
procedure that determines optimal sample sizes in terms of clearly
expressed criteria is therefore of obvious benefit for the administration
of justice. This led the Scottish Forensic Science Liaison Group (SFSLG)
to approach Aitken in the late 1990s to resolve the problem of the lack of
criteria for the choice of sample size. Motivated by this, Aitken
developed a Bayesian procedure and published the underpinning statistical
research in 1999 . The theory applies when the sampling unit may be
classified into two or more possible categories (e.g., licit or illicit).
As examples we cite cases about which Aitken was directly consulted: (a)
the sampling of drug tablets from consignments; (b) the sampling of
computer files for evidence of child pornography; and (c) the sampling of
CDs for evidence of piracy. In such cases, the theory provides an estimate
of the number of tablets, computer files or CDs that need to be inspected
to obtain reliable evidence, potentially sufficient for a prosecution.
Further work by Aitken and collaborators (see  and references therein)
considered the estimation of the quantity of drugs in a consignment and
provided the probability distribution for the amount of illicit material
as a function of the sample size.
Likelihood ratios for multivariate hierarchical data. When samples
of material obtained from a crime scene are compared with those obtained
from a suspect, it is necessary to quantify the support for the
proposition that they come from the same source. In many cases the data
characterising the material is multivariate, continuous and hierarchical.
Examples include the composition of glass taken from fragments of windows,
or the composition of drugs. The hierarchical nature then arises because
variations within-source and between-source differ (variation of glass
composition in a single window pane versus variation between different
panes, or variation of composition within a drug batch versus variations
between batches). Research in the MI developed a Bayesian methodology to
quantify the value of the evidence derived from such multivariate and
hierarchical data. This overcame the drawbacks of earlier methodologies
(which often incorrectly assumed the independence of the different
variables) by providing a likelihood ratio (LR) that can be combined with
other forms of evidence in an integrated analysis and leads to readily
interpretable conclusions. The initial work by Lucy and Aitken 
considering a two-level hierarchy of data was extended to a three-level
hierarchy in [4-5]. The paper  also developed an implementation based
on graphical modelling techniques which is adapted to multivariate data.
Dissemination. The methodology developed by Aitken and
collaborators and published in [1-3] has been further disseminated through
its inclusion in the book , a well-cited authority on the role of
statistics in the evaluation of evidence in forensic science (1740 sales
to 31st August 2013).
Software implementing the sampling method of [1-2] has been
developed and is available on the website http://www.enfsi.org
(see ). A R package `comparison' computing LRs following  has been
developed by Lucy and is freely available at
Attribution. C. G. G. Aitken has been with the Maxwell Institute
since 1979. D. Lucy was a PDRA at the Maxwell Institute from 2001 and
joined the University of Lancaster in 2006. G. Zadora is at the Institute
for Forensic Research in Krakow (Poland), J.M. Curran at the University of
Auckland, New Zealand and F. Taroni at the Institute of Forensic Science
at the University of Lausanne.
References to the research
Those marked with a * best indicate the quality of the research
 Aitken, C.G.G., Lucy, D., Zadora, G. and Curran, J.M., Evaluation of
trace evidence for three-level multivariate data with the use of graphical
models, Computational Statistics and Data Analysis, 50,
2571-2588 (2006). http://dx.doi.org/10.1016/j.csda.2005.04.005
* Aitken, C.G.G. and Taroni, F., Statistics and the evaluation of
evidence for forensic scientists, John Wiley and Sons Ltd (2004, 2nd
Grants. Aitken's research on been funded by a series of research
SHEFC (01.03.01-31.07.04), value: £338,366.
ESRC RES-000-23-0729 (01.10.04-31.03.08), value: £205,292.
EPSRC GR/S98603/01 (01.12.04-31.03.07), value: £90,598.
EPSRC EP/C532627 (01.08.2006-31.07.2008), value: £95,538.
Details of the impact
Beneficiaries. The beneficiaries of the research are forensic
science services and law-enforcement agencies worldwide. They can now
optimise the size of the samples they test and quantify in precise
Bayesian terms the weight of evidence. This impact on professional
practice in turn improves the judicial system of the countries relying on
these services and agencies by enabling the best use of the evidence
available and ultimately leading to safer verdicts.
Impact on beneficiaries. The impact started in the late 1990s with
the initial work leading up to : the procedure was referred by the
SFSLG to the Crown Office in Scotland which approved the ideas and issued
guidance to the Scottish forensic science laboratories for the procedure
to be used in cases in which sampling was desirable . Cases (a)-(c) are
examples of this early impact which led to cost savings and, in the case
(b) of sampling of pornographic files, to a reduction of stress-related
illnesses amongst the law enforcement agents examining the files (prior to
Aitken's involvement, out of four officers of the Strathclyde Police Force
who examined all files on certain seized computers in a particular case,
three had to take sick leave on stress-related grounds).
The impact of [1-2] has considerably extended since 2008, due in part to
the publication of high-profile guidance documents published by crime
enforcement agencies that refer to the work; these include the `Guidance
for best practice sampling in forensic science' published in 2007 by the
European Network of Forensic Science Institutes (ENFSI, which represents
forensic science laboratories throughout Europe including Russia, also
Turkey and some trans-Caucasian countries), and the `Guidelines on
representative drug sampling'  published in 2009 jointly by the United
Nations Office on Drugs and Crime and ENSFI. The software implementing the
sampling method of [1-2] is available on the ENFSI website: http://www.enfsi.org
(see ). It is used widely in
Europe (including Sweden, The Netherlands, Poland, Switzerland, UK) and is
We document the adoption of Aitken's methodology for both sample-size
determination [1-2] and LR for multivariate hierarchical data [3-5] by
describing three specific examples of applications in laboratories in
Australia, Sweden, and the Netherlands.
Australian National University. [text removed for publication].
The method of  was applied by ANU consultants to a high-profile court
case in Australia to estimate the strength of the evidence of a telephone
conversation. [text removed for publication].
Since this case, the LR derived in  has been used more broadly in
cases involving voice comparison. A senior staff member of the Forensic
Voice Comparison Laboratory (University of New South Wales, Australia) has
commented that `the work on statistical modelling for numerical
calculation of the strength of forensic evidence  has become a
standard tool in the field of forensic voice comparison' .
Statens Kriminaltekniska Laboratorium (SKL, Swedish National
Laboratory of Forensic Science). SKL, practices a framework for sampling
of drug units that is built on . The paper  gave rise to a research
project within SKL, that led to general rules for sampling of pills;
according to senior SKL staff, the process `has substantially reduced
the amount of material that needs to be analysed, still preserving the
precision needed for legal purposes, and has hence increased
cost-efficiency' . SKL are in the process of implementing the
approach described in  for the comparison of amphetamine seizures and
for the strengthening of glass evidence by the use of composition
Netherlands Forensic Institute. The glass experts at the
Netherlands Forensic Institute now use the method developed in  in
every case as a support to earlier analyses. The verbal statements of the
value of the evidence that they issue to the court are on both methods and
on graphical displays. A senior forensic statistician at the Netherlands
Forensic Institute has commented that `the ground breaking work of
Aitken and others has transformed the way we evaluate forensic evidence'
and `the LR method is the next step in the evolution from forensic
craft to forensic science '.
Sources to corroborate the impact
 United Nations Office on Drugs and Crime Guidelines on representative
drug sampling. UNITED NATIONS PUBLICATION; Sales No. E.09.XI.13
ISBN 978-92-1-148241-6 (2009). See http://www.maths.ed.ac.uk/~mthdat25/forensic/UN-Office-on-Drugs-and-Crime-Drugs-Sampling-Guidelines
 ENFSI publications may be found on the website: http://www.enfsi.org
Click on `Documents' then `External Publications'. Three are of relevance:
a. Validation of the `Guidelines on representative
b. Drugs Sampling Guideline UNODC-ENFSI.
c. ENFSI DWG Calculator for Qualitative Sampling of seized drugs (2012)
Confirmation of the benefits of the research to forensic science can be
 Senior manager of the Forensic Science Services, Scottish Police
 Senior member of the Forensic Speech Science Committee, Australasian
 Senior member of the Forensic Voice Comparison Laboratory, School of
Electrical Engineering & Telecommunications, University of New South
Wales, Sydney, New South Wales, Australia.
 Senior statistician at SKL.
 Senior statistician the Netherlands Forensic Institute.