Reference class problem

In statistics, the reference class problem is the problem of defining a bayesian prior distribution by the method of imaginary reference sets. It follows from the elementary foundations of probability theory that there is no unique way of doing this.

Applying bayesian probability in practice involves assessing a prior probability which is then applied to a likelihood function and updated through the use Bayes' theorem. Suppose we wish to assess the probability of guilt of a defendant in a court case in which DNA (or other probabilistic) evidence is available. We first need to assess the prior probability of guilt of the defendant. We could say that the crime occurred in a city of 1,000,000 people, of whom 15% meet the requirements of being the same sex, age group and approximate description as the perpetrator. That suggests a prior probability of guilt of 1 in 150,000. We could cast the net wider and say that there is, say, a 25% chance that the perpetrator is from out of town, but still from this country, and construct a different prior estimate. We could say that the perpetrator could come from anywhere in the world, and so on.