Foundations II: Bayesianism and Data Analysis
The frequency approach of Neyman and Wald (which built on a formulation of Fisher ) assumed a statistical model that was only partially known. The unknown aspect was specified by certain parameters θ, which were unknown constants. A different approach, later called Bayesian, was developed by Savage (1954) following earlier work of Ramsey and de Finetti. It was based on the assumption, justified by axioms of rational behavior, that θ was a random quantity with a known distribution. The probabilities defining this distribution were interpreted as being subjective, representing the investigator’s degree of belief in their possible values. The outcome of the statistical analysis was to be an action, in accordance with Neyman’s behavioristic approach. This foundation, unlike that of Neyman and Wald, led to a unique optimal procedure—the Bayes solution.
KeywordsPrior Distribution Bayesian Approach Exploratory Data Analysis Statistical Decision Theory Play Machine
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