In cases such as Prisoner and Gatecrasher, the likelihood ratio of naked statistical evidence can take a range of different values depending on the background information taken into account.
Prisoner (case/problem)(as used in epistemology and law)
A famous legal thought experiment about whether a judge should convict someone based only on statistics showing people like them commit crimes, even without direct evidence they did it.
likelihood ratio(Used as an alternative to posterior probability as a measure of evidential strength in legal proof standards.)
The ratio P(E|H) / P(E|H'), representing how much more probable the evidence E is given hypothesis H than given the alternative hypothesis H'.
naked statistical evidence(Paradigm cases include Prisoner (a prisoner is guilty based on the proportion of guilty prisoners in the yard) and Gatecrasher (a spectator is liable based on the proportion of non-paying attendees).)
Evidence consisting solely of statistical base rates or aggregate frequencies, without individualized evidence linking the specific defendant to the alleged conduct.
Fifth, another line of response for legal probabilists is to concede that the paradoxes of naked statistical evidence demonstrate the inadequacy of simple probabilistic thresholds as proof standards (Urbaniak 2019). Instead of the posterior probability of liability, a number of scholars have focused on the likelihood ratio \(P(E\pmid H)/P(E \pmid H')\). Their argument is that, even though naked statistical evidence can support a high posterior probability of liability, the likelihood ratio of th