Bayesian interpretation of discrete class characteristics.Bayesian interpretation of forensic evidence has become dominated by the likelihood ratio (LR) with a large LR generally considered favourable to the prosecution hypothesis, HP, over the defence hypothesis, HD. 
Bayesian
Bayesian interpretation of discrete class characteristics.Bayesian interpretation of forensic evidence has become dominated by the likelihood ratio (LR) with a large LR generally considered favourable to the prosecution hypothesis, HP, over the defence hypothesis, HD.  However, the LR simply quantifies by how much the prior odds ratio of the probability of HP relative to HD has been improved by the forensic evidence to provide a posterior ratio.  Because the prior ratio is mostly neglected, the posterior ratio is largely unknown, regardless of the LR used to improve it.  In fact, we show that the posterior ratio will only favour HP when LR is at least as large as the number of things that could possibly be the source of that evidence, all being equally able to contribute.  Finally, we conclude that a frequentist interpretation is inappropriate as a measure of the strength of forensic evidence precisely because it only estimates the denominator of the LR.
LR
Bayesian interpretation of discrete class characteristics.Bayesian interpretation of forensic evidence has become dominated by the likelihood ratio (LR) with a large LR generally considered favourable to the prosecution hypothesis, HP, over the defence hypothesis, HD.  However, the LR simply quantifies by how much the prior odds ratio of the probability of HP relative to HD has been improved by the forensic evidence to provide a posterior ratio.  In fact, we show that the posterior ratio will only favour HP when LR is at least as large as the number of things that could possibly be the source of that evidence, all being equally able to contribute. 
HP
Bayesian interpretation of discrete class characteristics.Bayesian interpretation of forensic evidence has become dominated by the likelihood ratio (LR) with a large LR generally considered favourable to the prosecution hypothesis, HP, over the defence hypothesis, HD.  However, the LR simply quantifies by how much the prior odds ratio of the probability of HP relative to HD has been improved by the forensic evidence to provide a posterior ratio. 
HD
Bayesian interpretation of discrete class characteristics.Bayesian interpretation of forensic evidence has become dominated by the likelihood ratio (LR) with a large LR generally considered favourable to the prosecution hypothesis, HP, over the defence hypothesis, HD.  However, the LR simply quantifies by how much the prior odds ratio of the probability of HP relative to HD has been improved by the forensic evidence to provide a posterior ratio.  Because the prior ratio is mostly neglected, the posterior ratio is largely unknown, regardless of the LR used to improve it.  In fact, we show that the posterior ratio will only favour HP when LR is at least as large as the number of things that could possibly be the source of that evidence, all being equally able to contribute.  Finally, we conclude that a frequentist interpretation is inappropriate as a measure of the strength of forensic evidence precisely because it only estimates the denominator of the LR.
LR
The limitation can be overcome by examining more than one individual characteristic, as long as they are independent of each other, as they are for the genotypes at multiple loci combined for DNA evidence. 
DNA