Statistics and the law: the prosecutor ’ s fallacy

Conclusions. Although this argument uses an artificial example that is simpler than most real cases, it illustrates some important principles. (1) The likelihood ratio is not a good way to evaluate evidence, unless there is good reason to believe that there is a 50:50 chance that the suspect is guilty before any evidence is presented. (2) In order to calculate what we need, Prob(guilty | evidence), you need to give numerical values of how common the possession of characteristic x (the evidence) is the whole population of possible suspects (a reasonable value might be estimated in the case of DNA evidence),  We also need to know the size of the population.  In the case of the island example, this was 1000, but in general, that would be hard to answer and any answer might well be contested by an advocate who understood the problem. These arguments lead to four conclusions. (1) If a lawyer uses the prosecutor’s fallacy, (s)he should be told that it’s nonsense. (2) If a lawyer advocates conviction on the basis of likelihood ratio alone, s(he) should be asked to justify the implicit assumption that there was a 50:50 chance that the suspect was guilty before any evidence was presented. (3) If a lawyer uses Defence counter-argument, or, equivalently, the version of Bayesian argument given here, (s)he should be asked to justify the estimates of the numerical value given to the prevalence of x in the population (P) and the numerical value of the size of this population (...
Source: DC's goodscience - Category: Science Authors: Tags: Law statistics Clive Stafford Smith false conviction false discovery rate False positive risk false positives FPR lawyers Michael Mansfield Philip Dawid Squier Waney Squier Source Type: blogs