Chapter 8 Bayesian Approach to Inference
In 1954 I proved that the only sound methods were Bayesian; yet you continue to use non-Bayesian ideas without pointing out a flaw in either my premise or my proof, why?
– Leonard Jimmie Savage
8.1 Introduction
Several paradigms provide a basis for statistical inference; the two most dominant are the frequentist (sometimes called classical, traditional, or Neyman–Pearsonian) and Bayesian. The term Bayesian refers to Reverend Thomas Bayes, a nonconformist minister interested in mathematics whose posthumously published essay (Bayes, 1763) is fundamental for this kind of inference. According to the Bayesian paradigm, the unobservable parameters in a statistical model are treated as random. Before data are collected, prior distributions are elicited to quantify our knowledge about the parameters. This knowledge comes from expert opinion, theoretical considerations, or previous similar experiments. When data are available, the prior distributions are updated to the posterior distributions. These are conditional distributions that incorporate the observed data. The transition from the prior to the ...
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