Reasoning to a foregone conclusion.

The protection given by Bayesian theory against sampling to a foregone conclusion may be constrained in several situations although it is based on the law of total probability. The first is when an inference is based on an improper prior. The second is in situations entailing the usage of a finite probability corresponding to an improper prior. Generally, however, the problem of designing an experiment to ensure that the posterior probability of a hypothesis is more than its prior probability is related to the experimenter's stopping rule. When can a Bayesian select an hypothesis H and design...