Abstract
Statistical modeling of the evaluation of evidence with the use of the likelihood ratio has a long history. It dates from the Dreyfus case at the end of the nineteenth century through the work at Bletchley Park in the Second World War to the present day. The development received a significant boost in 1977 with a seminal work by Dennis Lindley which introduced a Bayesian hierarchical random effects model for the evaluation of evidence with an example of refractive index measurements on fragments of glass. Many models have been developed since then. The methods have now been sufficiently well-developed and have become so widespread that it is timely to try and provide a software package to assist in their implementation. With that in mind, a project (SAILR: Software for the Analysis and Implementation of Likelihood Ratios) was funded by the European Network of Forensic Science Institutes through their Monopoly programme to develop a software package for use by forensic scientists world-wide that would assist in the statistical analysis and implementation of the approach based on likelihood ratios. It is the purpose of this document to provide a short review of a small part of this history. The review also provides a background, or landscape, for the development of some of the models within the SAILR package and references to SAILR as made as appropriate.
Highlights
Statistical analyses for the evaluation of evidence have a considerable history
The prior odds can be combined with the likelihood ratio to obtain posterior odds
The role of the likelihood ratio as the factor that updates the prior odds to the posterior odds has a very intuitive interpretation
Summary
Statistical analyses for the evaluation of evidence have a considerable history. It is the purpose of this document to provide a short review of a small part of this history. It brings together ideas from the last forty years for statistical models when the evidence is in the form of measurements and of continuous data. The first level is that of source, the origin of the data. The models are chosen from analyses of samples of sources from some relevant population. The nature of the prior distributions is informed from training data based on the samples from the relevant population. An Appendix gives formulae for some of the more commonly used models
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