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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R you ready for statistics?

The R program for statistics is an amazingly powerful and completely free program (under the terms of the Free Software Foundation’s GNU General Public License).  If you have any need to do statistics, then you really must take a look at R or, more formally, “The R Project for Statistical Computing“.

What exactly is R?  Simply put, “R is a language and environment for statistical computing and graphics.”  It is a special open-source implementation of S which is one of the earlier statistical programming languages.
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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?

Statistics lies, Mallett 2006

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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Introduction to the Logical Approach to Evidence Evaluation

It is absolutely true that most forensic scientists want to be completely logical, open and transparent in their approach to the evaluation of evidence.  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 Bayesian in nature.  After all, an approach to evidence evaluation conforming to the Bayesian philosophy or approach would be quite literally the embodiment of logic (more specifically, probabilistic logic).

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