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Selection of Inverse Gamma and Half-t Priors for Hierarchical Models: Sensitivity and Recommendations by Brehm, Zachary; Wagner, Aaron; VonKaenel, Erik; Burton, David; Weisenthal, Samuel J.; Cole, Martin; Pang, Yiping; Thurston, Sally W. is a scholarly article available to read on EtoBox.

What is Selection of Inverse Gamma and Half-t Priors for Hierarchical Models: Sensitivity and Recommendations about?

While the importance of prior selection is well understood, establishing guidelines for selecting priors in hierarchical models has remained an active, and sometimes contentious, area of Bayesian methodology research. Choices of hyperparameters for individual families of priors are often discussed in the literature, but rarely are different families of priors compared under similar models and hyperparameters. Using simulated data, we evaluate the performance of inverse gamma and half-$t$ priors for estimating the standard deviation of random effects in three hierarchical models: the 8-schools model, a random intercepts longitudinal model, and a simple multiple outcomes model. We compare the performance of the two prior families using a range of prior hyperparameters, some of which have been suggested in the literature, and others that allow for a direct comparison of pairs of half-$t$ and inverse-gamma priors. Estimation of very small values of the random effect standard deviation led to convergence issues especially for the half-$t$ priors. For most settings, we found that the posterior distribution of the standard deviation had smaller bias under half-$t$ priors than under their

Author

Brehm, Zachary; Wagner, Aaron; VonKaenel, Erik; Burton, David; Weisenthal, Samuel J.; Cole, Martin; Pang, Yiping; Thurston, Sally W.

Published

2021

Language

EN