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.

Scales balancing Evidence

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 (and other forensic disciplines).
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Forewarned…

Forewarned is forearmed or, if Latin is your thing, “praemonitus, praemunitus”. So the saying goes and clearly there is great value in knowing what lies ahead for us. If we know what is coming our way we can, in theory, prepare properly for any challenge.

Challenges are nothing new to forensic scientists. Critics routinely point out issues with our work. Some of those criticisms are fair and reasonable, others not so much. Much of the critical commentary affects a discipline as a whole demanding an overall, or group, response by members of each discipline. In my experience, disciplines are generally behind the curve in their responses to critics. Nonetheless, over time some issues have been addressed, at least partially if not completely, through empirical research.  Others have not. To be fair, the activities needed to properly address the critics are not trivial and require both time and resources; scarce commodities in modern forensic labs. Overall, things are improving, albeit very slowly.

Criticism takes on a whole new meaning in the context of a court of law. Indeed, I think that criticism is the essence of cross-examination — a fundamental and important aspect of any adversarial justice system. Although essential, it is rarely an enjoyable part of the proceedings for any expert. Read more