Bayesian model assessment using pivotal quantities
Year: 2007
Type: article
Abstract: Suppose that $S({\bf Y},\Theta)$ is a function of data ${\bf Y}$ and a model parameter $\Theta$, and suppose that the sampling distribution of $S({\bf Y},\Theta)$ is invariant when evaluated at $\Theta_0$, the "true" (i.e., data-generating) value of $\Theta$. Then $S({\bf Y},\Theta)$ is a pivotal quantity, and it follows from simple probability calculus that the distribution of $S({\bf Y},\Theta_0)$ is identical to the distribution of $S({\bf Y},\Theta_{\bf Y})$, where $\Theta_{\bf Y}$ is a value of $\Theta$ drawn from the posterior distribution given ${\bf Y}$. 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.
Source: Bayesian Analysis
DOI: 10.1214/07-ba229
Author: Valen E. Johnson
Institution: The University of Texas MD Anderson Cancer Center
Language: English
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W2057661989