Bayesian Statistics is a subset of the field of statistics in which the evidence about the true state of the world is expressed in terms of degrees of Bayesian probabilities. Bayesian analysis requires evaluating expectations of functions of random quantities as a basis for inference, where these quantities may have posterior distributions which are multivariate or of complex form or often both. Bayesian statistics is a system for describing epistemological uncertainty using the mathematical language of probability. Bayesian statistical methods start with existing 'prior' beliefs, and update these using data to give 'posterior' beliefs, which may be used as the basis for inferential decisions.
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