Evidence, probability and relative plausibility
| Author | Colin Aitken,Franco Taroni,Silvia Bozza |
| DOI | http://doi.org/10.1177/13657127221114508 |
| Published date | 01 October 2022 |
| Date | 01 October 2022 |
| Subject Matter | Articles |
Evidence, probability and relative
plausibility
Colin Aitken
School of Mathematics, The University of Edinburgh, UK
Franco Taroni
School of Criminal Justice, The University of Lausanne, Switzerland
Silvia Bozza
Department of Economics, The Ca’Foscari University of Venice, Italy
Abstract
A comparison is made between probability and relative plausibility as approaches for the inter-
pretation of evidence. It is argued that a probabilistic approach is capable of answering the cri-
ticisms of the proponents of relative plausibility. It is also shown that a probabilistic approach
can answer the problem of overlapping where there is evidence that each side claims supports
its theory of what happened.
Keywords
conjunction, interpretation, likelihood ratio, overlapping problem, relative plausibility
Introduction
Over a period of 25 years and three editions, a seminal book Statistics and the Evaluation of Evidence for
Forensic Scientists has described the underlying ideas and mapped the progress of these ideas in the area
of the book title, an area which has come to be known as forensic statistics. The first edition of Statistics
and the Evaluation of Evidence for Forensic Scientists was published in 1995 (Aitken, 1995). As the
manuscript neared completion, there were two suggestions of the publisher that did not proceed to the
published version of the book. The first related to the title where it was suggested to include the word
‘interpretation’until it was pointed out that the book was about ‘evaluation’not ‘interpretation’and
that the two words were not synonymous. The second suggestion was that the cover could include a
picture of a fingerprint. It was pointed out in this case that there was very little on fingerprints in the
book. There is an analogy of evidence evaluation with the scales of justice. Thus, it was that the book
cover included scales of justice, images of which have appeared on the two subsequent editions.
Corresponding author:
Colin Aitken, School of Mathematics, The University of Edinburgh, King’s Buildings, Peter Guthrie Tait Road,
Edinburgh EH9 3FD, UK.
E-mail: C.G.G.Aitken@ed.ac.uk
Article
The International Journal of
Evidence & Proof
2022, Vol. 26(4) 309–324
© The Author(s) 2022
Article reuse guidelines:
sagepub.com/journals-permissions
DOI: 10.1177/13657127221114508
journals.sagepub.com/home/epj
There may have been little on interpretation in the first edition, a reflection on the relationship between
statistics and forensic science at the time. In the second edition, in 2004, there were about 80 pages on
interpretation and a discussion of transfer evidence, reflecting the work on propositions done in the late
1990s; see Cook et al. (1998a, 1998b). Now, 25 years after the appearance of the first edition, there are
about 300 pages on interpretation within nearly 1000 pages of material, an increase which can only par-
tially be explained by an increase in type size and margin sizes from the previous two editions. However,
the title remains unchanged to ensure continuity of ideas from the beginning.
The primary concern of the first edition was with technical matters. DNA profiling was in its relative
infancy, having been around less than 10 years. Its introduction helped the introduction of probabilistic
reasoning to the courts. There were many teething problems, as the court transcripts of the time show.
These were being overcome and there were thoughts as to which other areas of forensic science may
be amenable to probabilistic treatment. Much probabilistic work had been done on evidence in the
form of the refractive index of glass fragments with a seminal paper by Lindley (1977). The data for
that paper had been provided by Ian Evett, who has published many papers on statistics, probabilistic
inference and forensic science over the years. Since then, the technical aspects of the evaluation of sci-
entific evidence have become increasingly accepted in the courts and the emphasis has become increas-
ingly on interpretation and the best approach for the communication of evidential value to the fact-finder,
judge or jury depending on jurisdiction.
The likelihood ratio is generally accepted as the best way of evaluating evidence. That it is the best
way was first explained by Good (1989) and it is explicitly recommended by the European Network
of Forensic Science Institutes (ENFSI) in their guidelines for evaluative reporting (ENFSI, 2015). One
can read:
Evaluation of forensic science findings in court uses probability as a measure of uncertainty. This is based
upon the findings, associated data and expert knowledge, case specific propositions and conditioning informa-
tion. (ENFSI Guideline, point n. 2.3, at p. 6)
and
Evaluation will follow the principles outlined in Guidance note 1 (refer to paragraph 4.0). It is based on the
assignment of a likelihood ratio. Reporting practice should conform to these logical principles. This frame-
work for evaluative reporting applies to all forensic science disciplines. The likelihood ratio measures the
strength of support the findings provide to discriminate between propositions of interest. It is scientifically
accepted, providing a logically defensible way to deal with inferential reasoning. (ENFSI Guideline, point
n. 2.4, at p. 6)
The likelihood ratio is part of the odds form of Bayes’theorem. Consider two propositions in the
context of a criminal trial, Hp: the defendant is guilty, Hd: the defendant is not guilty. The value of evi-
dence Eis of interest. The odds form of Bayes’theorem states that
Pr (Hp∣E)
Pr (Hd∣E)=Pr (E∣Hp)
Pr (E∣Hd)×Pr (Hp)
Pr (Hd).(1)
The term Pr (Hp)Pr(Hd)is the odds in favour of guilt before the presentation of the evidence (prior odds),
the term Pr (Hp∣E)Pr(Hd∣E) is the odds in favour of guilt after the presentation of the evidence (pos-
terior odds) and the third fraction Pr (E∣Hp)Pr(E∣Hd) is the likelihood ratio, the term which converts
prior odds to posterior odds. For those familiar with probabilistic reasoning, the interpretation of the like-
lihood ratio is straightforward. It can be interpreted to someone with words like: ‘Consider your odds in
favour of guilt prior to hearing the evidence. Listen to the evidence and determine how much more likely
the evidence is if the defendant is guilty than if they are innocent. Multiply your prior odds by that amount
and the result is your posterior odds in favour of guilt.’This wording is not new. In the context of the
310 The International Journal of Evidence & Proof 26(4)
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