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

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