3 interpretations of the prior distribution:

1. a frequency distribution whose parameters reflect an analysis and synthesis of existing data;
2. an "objective" statement of what is rational to believe about the initial parameter or its distribution, given initial ignorance of this parameter;
3. a subjective measure of what the investigator actually believes;

Since Bayesian inference is an iterative process, even the posterior probability distribution of a parameter can be used as a prior for a new set of experiments, should further refinement of an estimate or additional hypothesis testing be required. But if the prior dominates the likelihood, the experiment is likely to be irrelevant, since that implies the existence of more prior information than the subsequent testing can supply to influence posterior estimates.

back