ABSTRACT
The practical expression of existing belief in the context of Bayesian statistical modeling is in the assumed shape of the prior distribution. The selection of a prior density is an attempt to formalize the beliefs of researchers in regard to the potential or expected values of the parameters in question. There are several specific approaches to selecting priors. These range from very subjective, almost free form approaches, to empirical methods based on previous datasets, properties of the likelihood function, and properties of overall model fit. The Jeffreys prior however is interpretable and useful in a wide variety of likelihood based models. Conjugate priors are prior densities that, for a given likelihood, give a posterior function that is similar in form to the prior. Elicitation is difficult to do well, but may be a useful approach to defining priors based on carefully assessed expert opinion.
