The Philosophy and Mathematics of Bayes' Equation

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Abstract
The rudiments of Bayesian philosophy are introduced, and the mathematics of its application are surveyed; there is no uniformity of thought concerning either. The more extreme Bayesian philosophy, which allows subjective probabilities, is a means of plausible reasoning, or of making inferences, through inductive logic. Because inferences concerning reliability concepts are important in the decision process, this philosophy has a place in the reliability field. The difficulties of interpreting the probability function and of assigning prior distributions restrict the presentation of a unified philosophy. Thus, only techniques for describing prior probabilities under various circumstances can be given. Application of the Bayesian approach depends on how the reliability decision is conceptualized.