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Activity Number: 521
Type: Invited
Date/Time: Thursday, August 10, 2006 : 10:30 AM to 12:20 PM
Sponsor: WNAR
Abstract - #305210
Title: Bayesian Model Assessment Using Pivotal Quantities
Author(s): Valen Johnson*+
Companies: M. D. Anderson Cancer Center
Address: 1515 Holcombe Blvd., Unit 448, Houston, TX, 77030-4009,
Keywords: prior-predictive density ; posterior-predictive density ; Bayesian chi-squared test
Abstract:

Suppose that S(Y,theta)$ is a function of data Y and a model parameter theta, and suppose that the sampling distribution of S(Y,theta) is invariant when evaluated at theta(0), the true (i.e., data-generating) value of theta. Then S is defined to be a pivotal quantity, and I show that the distribution of S(Y,theta) is identical to the distribution of S(Y,theta(Y)), where theta(Y) is a value of theta drawn from the posterior distribution given Y. This fact is used to investigate the properties of a number of Bayesian model diagnostic and assessment tools.

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