Title: Spike and Slab Prior Distributions for Simultaneous Bayesian Hypothesis Testing, Model Selection, and Prediction, of Nonlinear Outcomes Authors: Xun Pang, Jeff Gill Entrydate: 2009-07-13 13:54:37 Keywords: Spike and Slab Prior, Hypothesis Testing, Bayesian Model Selection, Bayesian Model Averaging, Adaptive Rejection Sampling, Generalized Linear Model Abstract: A small body of literature has used the spike and slab prior specification for model selection with strictly linear outcomes. In this setup a two-component mixture distribution is stipulated for coefficients of interest with one part centered at zero with very high precision (the spike) and the other as a distribution diffusely centered at the research hypothesis (the slab). With the selective shrinkage, this setup incorporates the zero coefficient contingency directly into the modeling process to produce posterior probabilities for hypothesized outcomes. We extend the model to qualitative responses by designing a hierarchy of forms over both the parameter and model spaces to achieve variable selection, model averaging, and individual coefficient hypothesis testing. To overcome the technical challenges in estimating the marginal posterior distributions possibly with a dramatic ratio of density heights of the spike to the slab, we develop a hybrid Gibbs sampling algorithm using an adaptive rejection approach for various discrete outcome models, including dichotomous, polychotomous, and count responses. The performance of the models and methods are assessed with both Monte Carlo experiments and empirical applications in political science. http://polmeth.wustl.edu/retrieve.php?id=914 ********************************************************** Political Methodology E-Mail List Editors: Xun Pang <[log in to unmask]> Jon C. Rogowski <[log in to unmask]> ********************************************************** Send messages to [log in to unmask] To join the list, cancel your subscription, or modify your subscription settings visit: http://polmeth.wustl.edu/polmeth.php **********************************************************