Links to discussion, some technical, about prior probability.
Sometimes a DNA analyst wants to “convert” the likelihood ratio LR supporting some hypothesis H into the posterior (i.e. bottom-line) probability of the hypothesis Pr(H | DNA). That is a common mistake.
|H||hypothesis to be established|
|LR||likelihood ratio supporting H|
|Pr(H)||prior probability; probability of H without considering the DNA|
|Pr(H | DNA)||posterior probability; probability of H taking the DNA into account|
For example the hypothesis H that the body X is the person missing from the Smith family is supported by LR=100; the analyst wrongly writes a report that X is 99% to be the missing person — Pr(H | DNA)=99%. That’s wrong because obtaining the conclusion Pr(H)=99% from LR=100 is not just a matter of “converting”. We can convert between Celsius and Fahrenheit; 0°C and 32°F mean the same thing. But LR=100 and Pr(H | DNA)=99% are not the same. The latter includes an additional assumption, an assumption about the value of the prior probability that X is the missing Smith. (In particular if LR=100 then Pr(H | DNA)=99% if and only if Pr(H)=50%.) But when armed with both LR and prior probability, one can derive the posterior probability by applying Bayes’ theorem. (Look it up.)
Sometimes I am asked “How does one figure out what number to choose for prior probability?” The answer is that, as a DNA analyst, you don’t.
We are not qualified to evaluate subjective "data" and more importantly we are not qualified to judge information that we do not have. Evaluation of non-DNA data, which I typically describe as "subjective" (but it doesn't have to be and to be honest there's some subjectivity about interpreting DNA), is the purview of the court, or sometimes of a lawyer or concerned or curious customer. As specialists in the science and mathematics of DNA we don't have any special qualification to evaluate other kinds of evidence, and in fact we do not even have the other evidence. It would be very wrong and ridiculous for a DNA analyst to testify in court that “Considering both the DNA evidence and also the story that the prosecutor and one of the witnesses told me about the circumstances, it is extremely probable that the prosecutor is correct!”
Consequently it is wrong for the DNA expert to assume a 50% prior probability or any other prior. However, it is honest to write a report that says