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(Y,theta) is defined to be a pivotal quantity, and I show that the distribution of S(Y,theta(0))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.
Statistical Methodology | Statistical Theory
Johnson, Valen E., "Bayesian Model Assessment Using Pivotal Quantities" (April 2006). UT MD Anderson Cancer Center Department of Biostatistics Working Paper Series. Working Paper 25.