Handbook of Bayesian Variable Selection

Bayesian variable selection has experienced substantial developments over the past 30 years with the proliferation of large data sets. Identifying relevant variables to include in a model allows simpler interpretation, avoids overfitting and multicollinearity, and can provide insights into the mechanisms underlying an observed phenomenon. Variable selection is especially important when the number of potential predictors is substantially larger than the sample size and sparsity can reasonably be assumed. The Handbook of Bayesian Variable Selection provides a comprehensive review of theoretical, methodological and computational aspects of Bayesian methods for variable selection. The topics covered include spike-and-slab priors, continuous shrinkage priors, Bayes factors, Bayesian model averaging, partitioning methods, as well as variable selection in decision trees and edge selection in graphical models. The handbook targets graduate students and established researchers who seek to understand the latest developments in the field. It also provides a valuable reference for all interested in applying existing methods and/or pursuing methodological extensions. Features: Provides a comprehensive review of methods and applications of Bayesian variable selection. Divided into four parts: Spike-and-Slab Priors; Continuous Shrinkage Priors; Extensions to various Modeling; Other Approaches to Bayesian Variable Selection. Covers theoretical and methodological aspects, as well as worked out examples with R code provided in the online supplement. Includes contributions by experts in the field. Supported by a website with code, data, and other supplementary material

Table of Contents:
1. Discrete Spike-and-Slab Priors: Models and Computational Aspects 2. Recent Theoretical Advances with the Discrete Spike-and-Slab Priors 3. Theoretical and Computational Aspects of Continuous Spike-and-Slab Priors 4. Spike-and-Slab Meets LASSO: A Review of the Spike-and-Slab LASSO 5. Adaptive Computational Methods for Bayesian Variable Selection 6. Theoretical guarantees for the horseshoe and other global-local shrinkage priors 7. MCMC for Global-Local Shrinkage Priors in High-Dimensional Settings 8. Variable Selection with Shrinkage Priors via Sparse Posterior Summaries 9. Bayesian Model Averaging in Causal Inference 10. Variable Selection for Hierarchically-Related Outcomes: Models and Algorithms 11. Bayesian variable selection in spatial regression models 12. Effect Selection and Regularization in Structured Additive Distributional Regression 13. Sparse Bayesian State-Space and Time-Varying Parameter Models 14. Bayesian estimation of single and multiple graphs 15. Bayes Factors Based on g-Priors for Variable Selection 16. Balancing Sparsity and Power: Likelihoods, Priors, and Misspecification 17. Variable Selection and Interaction Detection with Bayesian Additive Regression Trees 18. Variable Selection for Bayesian Decision Tree Ensembles 19. Stochastic Partitioning for Variable Selection in Multivariate Mixture of Regression Models