The Bayesian Inference Method and Its Application to Reliability Problems

摘要

Statistical inference is the activity of characterizing the parameters of mathematical models by utilizing available sampling data. This report discusses as a specific motivation the modeling of reliability problems and deals only with inference while avoiding the larger area of decision theory. The classical and Bayesian approaches to evaluating the parameter of the familiar exponential reliability model are compared. Classically, model parameters are unknown constants which can be estimated. From the Bayesian viewpoint model parameters are treated as distributed random variables. As is also ture of the classical maximum likelihood method, the determining or informational impact of the sampling data is represented completely by the likelihood function. Operationally, Bayesian inference involves applying Bayes theorem, a celecbrated consequence of conditional probability theory. The relevant probability background is developed and Bayes theorem derives. Bayesian inference has the very appealing capacity to incorporate previous information as well as current sampling inputs. Classical results are reproduced in the limiting forms of this involving noninformative prior distributions. Several application examples are discussed illustrating the use of both continuously and discretely distributed data and in one case emphasizing numerical methods.