All posts by Erik Erhardt

Erik Barry Erhardt, PhD, is an Associate Professor of Statistics at the University of New Mexico Department of Mathematics and Statistics, where he has served as Director of the Statistics Consulting Clinic, and is currently Director of the Biostatistics and NeuroInformatics (BNI) Core for the second phase of the Center for Biomedical Research Excellence (COBRE) in Brain Function and Mental Illness at the Mind Research Network. His research interests include Bayesian and Frequentist statistical methods for stable isotope sourcing and brain imaging. Erik is a Howard Hughes Medical Institute Interfaces Scholar collaborating in interdisciplinary research and offering consulting services in statistics.

Wishart distribution in WinBUGS, nonstandard parameterization

The Wishart distribution and especially the inverse-Wishart distribution are the source of some confusion because they occasionally appear with alternative parameterizations. Also, the Wishart distribution can be used to model a covariance matrix or a precision matrix (the inverse of a covariance matrix) in different situations, and the inverse-Wishart the same, but the other way round. It’s already becoming complicated. Hal Stern, coauthor of Bayesian Data Analysis (BDA), helped to clarify many issues for me in an email conversation. In this post I hope to clarify the differences in Wishart parameterizations of BDA, the wikipedia pages, and the WinBUGS and OpenBUGS softwares, and show an example in OpenBUGS where the inverse parameterization has to be specified relative to the distribution’s definition for the correct posterior to result.
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