From Prior Information to Prior Distributions
Undoubtedly, the most critical and most criticized point of Bayesian analysis deals with the choice of the prior distribution. Indeed, in practice, it seldom occurs that the available prior information is precise enough to lead to an exact determination of the prior distribution, in the sense that many probability distributions are compatible with this information. It is then necessary to use an approximation which choice can drastically alter the subsequent inference. In particular, the systematic use of parametrized distributions (like the normal, gamma, beta, etc., distributions) or conjugate distributions cannot be justified, because it trades an improvement in the analytical treatment of the problem for the subjective determination of the prior distribution. It may therefore ignore part of the prior information. Some settings call for a partially automated determination of the prior distribution when prior information is too expensive, sparse, or totally lacking. We propose in this chapter two appropriate methods, the conjugate prior approach, which requires a limited amount of information, and the Jeffreys noninformative priors, which can be directly derived from the sampling distribution.
KeywordsPosterior Distribution Prior Distribution Prior Information Maximum Likelihood Estimator Exponential Family
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