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Prior odds — their meaning and significance

The concepts of ‘prior odds’, a.k.a., prior probabilities or simply priors, and ‘posterior odds’ come up in most discussions about the evaluation of evidence. The significance and meaning of both terms becomes clear when viewed in the context of a “Bayesian approach”, or the logical approach, to evidence evaluation. That approach has been discussed at length elsewhere and relates to the updating of one’s belief about events based upon new information. A key aspect is that some existing belief, encapsulated as the ‘prior odds’ of two competing possibilities or events, will be updated on the basis of new information, encapsulated in the ‘likelihood-ratio’1 (another term you will undoubtedly have seen), to produce some new belief, encapsulated as ‘posterior odds’ about those same competing possibilities.

But what precisely do these terms, ‘prior odds’ and ‘posterior odds’, mean and how do they relate to the work of a forensic examiner?
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Hilton and Mathematical Probability

In 1958 Ordway Hilton participated in Session #5 of the RCMP Seminar Series. His article was originally published in that series by the RCMP, and subsequently republished in 1995 in the International Journal of Forensic Document Examiners.1

The later republication included the following abstract:

In every handwriting identification we are dealing with the theory of probability. If an opinion is reached that two writings are by the same person, we are saying in effect that with the identification factors considered the likelihood of two different writers having this combination of writing characteristics in common is so remote that for all practical purposes it can be disregarded. Such an opinion is derived from our experience and is made without formal reference to any mathematical measure. However, the mathematician provides us with a means by which the likelihood of chance duplication can be measured. It is the purpose of this paper to explore the possibility of applying such mathematical measure to the handwriting identification problem to see how we might quantitatively measure the likelihood of chance duplication.

Hilton’s article was written in 8 main sections with references, and is followed by a discussion between seminar participants. Today’s review will discuss each section of the article in turn.
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Propositions — key to the evaluation process

One of the key elements in the logical approach to evidence evaluation are the propositions used for the evaluation. They are, in a certain sense, the most important part of the whole process. At the same time, they are also one of the least understood.

Today’s post explores the concept of propositions. I will attempt to describe what they are, how they are used, why we don’t change them once set and why they matter so much, among other things… all from the perspective of forensic document examination (though also applicable to other forensic disciplines).

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When is a ‘Bayesian’ not a ‘Bayesian’?

Several of the posts on this blog relate to the logical approach to evidence evaluation; aka, the coherent logical approach, or the likelihood-ratio (LR) approach. In my opinion, it is the best way to evaluate evidence for forensic purposes no matter what type of evidence is being discussed. I say “best” because it is simple, logically sound, and relatively straight-forward to apply in forensic work.  It helps to promote transparency through the application of a thorough and complete evaluation process (all points I have explained in other posts).

The reality is, however, that this approach is still not well understood by forensic practitioners, nor by members of the legal profession.

I hope that in time, and with education, that will change. Several workshops I have presented have been aimed at helping examiners understand what it really means, how it works, the philosophical basis behind the approach as well as the need for and benefit of doing things that particular way. It really does work to the benefit of both the examiner and their ultimate client, the court.

One recurring issue at these workshops relates to the very basic and fundamental concept of what the term “Bayesian” means. For various reasons, but mainly just misunderstanding, many people in the forensic document examination community hold the term “Bayesian” in negative regard. When the word ‘Bayes’, or any of its many derivations, come up in the conversation eyes glaze over while heads sag ever so slightly. And those are the positive people in the crowd.

I find such reactions understandable, but unfortunate.  The fact is that an understanding of the term is beneficial for anyone interested in how it might be applied in a forensic evidence context, whether or not one chooses to do so.  Indeed, for myself the answer to the question posed above — when is a Bayesian not a Bayesian? — lies in knowing how the overall Bayesian philosophy and theorem (or rule) differs from the more constrained and limited logical approach to evidence evaluation. These two are not the same or even close to equivalent.

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2014 ASQDE-ASFDE Panel Discussion “Conclusions…”

The 2014 ASQDE–ASFDE conference included an interesting panel discussion with the title “Conclusions… Signature and Handwriting Conclusion Terminology and Scales”. I was fortunate to be able to take part, albeit only remotely via Skype.

ASQDE ASFDE logos

 

The abstract for the session was as follows:

A current and global issue in our field is the topic of conclusion terminology and conclusion scales, particularly in respect of signature and handwriting conclusions. It is an important yet difficult topic to address because, while there is some commonality in the conclusion scales used in different geographical regions around the world, within a number of geographical regions there are multiple scales in use. It is for this very reason that it is also a topic in great need of discussion and there is a strong argument that we should attempt to reach a consensus (even if the result is that we agree to disagree).

This panel discussion is a collaboration of insights from numerous colleagues in our field in person, via Skype and in writing from private and government laboratories in geographical regions across the Americas, Australia, Asia, Africa, the Middle East and Europe.
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ICFIS 2014 — Teaching the Logical Approach for Evidence Evaluation to FDEs

This year’s International Conference on Forensic Inference and Statistics (ICFIS) is being held at Leiden University in the Netherlands.  ICFIS 2014 logoICFIS conferences are always very good and this is the 9th such event.  I am hoping to attend to present my thoughts on the topic of education relating to the logical (a.k.a. likelihood-ratio or LR) approach to evidence evaluation. Over the last few years I have given several one and two-day seminars and workshops on this topic, mainly for Forensic Document Examiners (FDEs) though the subject matter relates to all disciplines equally.  Those workshops have been great and provided a relatively unusual opportunity to learn about how fully trained examiners come to grips with a complicated and difficult topic.  One that is fundamental to FDE work.
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Statistics — Worse than a lie

It has oft been said that “there are three kinds of lies: lies, damned lies and statistics”.  That phrase, according to Mark Twain, came from Benjamin Disraeli. Interestingly, it has never been found in Disraeli’s written works so that attribution is likely incorrect.

A lie, perhaps, by Twain?

Lies - Mallett

But I digress.  The source of the statement doesn’t really matter.  It is enough that the phrase reflects the belief that many people have when they think about statistics.1

It is a catchy little phrase.  Yet most reasonable people know that numbers — and statistics are simply numbers after all — cannot do anything on their own.  Hence, statistics can no more lie than they can sing or dance.

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ASQDE “Conclusions and Logical Inference” Workshop 2013

This year the Annual General Meeting of the American Society of Questioned Document Examiners (ASQDE) ASQDE 2013 is being held in Indianapolis, Indiana on August 24 through 29, 2013. In keeping with the theme, “Demonstrative Science: Illustrating Findings in Reports and Court Testimony”, I will be presenting a one-day workshop entitled “Conclusion Scales and Logical Inference” on Sunday, August 25.
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Introduction to the Logical Approach to Evidence Evaluation

Forensic scientists, individually and as a group, want to be completely logical, open and transparent in their approach to the evaluation of evidence. Such an assertion is unquestionable. Further, I am sure that most document examiners believe this is exactly what they are achieving when they apply the procedures outlined in various traditional textbooks or the SWGDOC/ ASTM standards; for example, the SWGDOC Standard for Examination of Handwritten Items. Given the very understandable desire to be logical, I find it strange that so many people have a negative attitude towards anything and everything “Bayesian” in nature. After all, a logical approach to evidence evaluation that conforms to the overall Bayesian philosophy or approach is, quite literally, the embodiment of logic (more specifically, probabilistic logic).

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