Kirmani, Syed N. U. A. Department of Mathematics, University of Northern Iowa, Cedar Falls, Iowa.
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- Example of Bayesian statistics
- Conjugate priors
- Noninformative and improper priors
- Bayesian estimation
- Bayesian hypothesis testing
- Links to Primary Literature
- Additional Readings
An approach to statistics in which estimates are based on a synthesis of a prior distribution and current sample data. Bayesian statistics is not a branch of statistics in the way that, say, nonparametric statistics is. It is, in fact, a self-contained paradigm providing tools and techniques for all statistical problems. In the classical, "frequentist" viewpoint of statistical theory, a statistical procedure is judged by averaging its performance over all possible data. However, the Bayesian approach gives prime importance to how a given procedure performs for the actual data observed in a given situation. Further, in contrast to the classical procedures, the Bayesian procedures formally utilize information available from sources other than the statistical investigation. Such information, available through expert judgment, past experience, or prior belief, is described by a probability distribution on the set of all possible values of the unknown parameter of the statistical model at hand. This probability distribution is called the prior distribution. The crux of the Bayesian approach is the synthesis of the prior distribution and the current sample data into a posterior probability distribution from which all decisions and inferences are made (Fig. 1). This synthesis is achieved by using a theorem proved by English statistician Thomas Bayes in the eighteenth century.
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