Bayesian model assessment using pivotal quantities
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Suppose that S(Y, ) is a function of data Y and a model parameter , and suppose that the sampling distribution of S(Y, ) is invariant when evaluated at 0, the "true" (i.e., data-generating) value of . Then S(Y, ) is a pivotal quantity, and it follows from simple probability calculus that the distribution of S(Y, 0) is identical to the distribution of S(Y, Y), where Y is a value of drawn from the posterior distribution given Y. This fact makes it possible to define a large number of Bayesian model diagnostics having a known sampling distribution. It also facilitates the calibration of the joint sampling of model diagnostics based on pivotal quantities. 2007 International Society for Bayesian Analysis.