Shotgun stochastic search for “Large p” regression Model search in regression with very large numbers of candidate predictors raises challenges for both model specification and computation, for which standard approaches such as Markov chain Monte Carlo (MCMC) methods are often infeasible or ineffective. We describe a novel shotgun stochastic search (SSS) approach that explores ”interesting” regions of the resulting high-dimensional model spaces and quickly identifies regions of high posterior probability over models. We describe algorithmic and modeling aspects, priors over the model space that induce sparsity and parsimony over and above the traditional dimension penalization implicit in Bayesian and likelihood analyses, and parallel computation using cluster computers. We discuss an example from gene expression cancer genomics, comparisons with MCMC and other methods, and theoretical and simulation-based aspects of performance characteristics in large-scale regression model searches. We also provide software implementing the methods.

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  1. Ghosh, Satyajit; Khare, Kshitij; Michailidis, George: Strong selection consistency of Bayesian vector autoregressive models based on a pseudo-likelihood approach (2021)
  2. Jin, Shiqiang; Goh, Gyuhyeong: Bayesian selection of best subsets via hybrid search (2021)
  3. Staerk, Christian; Kateri, Maria; Ntzoufras, Ioannis: High-dimensional variable selection via low-dimensional adaptive learning (2021)
  4. Andrade, Daniel; Takeda, Akiko; Fukumizu, Kenji: Robust Bayesian model selection for variable clustering with the Gaussian graphical model (2020)
  5. Kim, Youngseok; Gao, Chao: Bayesian model selection with graph structured sparsity (2020)
  6. Kirsner, Daniel; Sansó, Bruno: Multi-scale shotgun stochastic search for large spatial datasets (2020)
  7. Yang, Xinming; Narisetty, Naveen N.: Consistent group selection with Bayesian high dimensional modeling (2020)
  8. Dobra, Adrian; Valdes, Camilo; Ajdic, Dragana; Clarke, Bertrand; Clarke, Jennifer: Modeling association in microbial communities with clique loglinear models (2019)
  9. Narisetty, Naveen N.; Shen, Juan; He, Xuming: Skinny Gibbs: a consistent and scalable Gibbs sampler for model selection (2019)
  10. Kim, Joungyoun; Lim, Johan; Kim, Yongdai; Jang, Woncheol: Bayesian variable selection with strong heredity constraints (2018)
  11. Ročková, Veronika: Particle EM for variable selection (2018)
  12. Papathomas, Michail; Richardson, Sylvia: Exploring dependence between categorical variables: benefits and limitations of using variable selection within Bayesian clustering in relation to log-linear modelling with interaction terms (2016)
  13. Castillo, Ismaël; Schmidt-Hieber, Johannes; van der Vaart, Aad: Bayesian linear regression with sparse priors (2015)
  14. Elliott, Graham; Gargano, Antonio; Timmermann, Allan: Complete subset regressions with large-dimensional sets of predictors (2015)
  15. Ghosh, Joyee; Tan, Aixin: Sandwich algorithms for Bayesian variable selection (2015)
  16. Pungpapong, Vitara; Zhang, Min; Zhang, Dabao: Selecting massive variables using an iterated conditional modes/medians algorithm (2015)
  17. Bleich, Justin; Kapelner, Adam; George, Edward I.; Jensen, Shane T.: Variable selection for BART: an application to gene regulation (2014)
  18. Elliott, Graham; Gargano, Antonio; Timmermann, Allan: Complete subset regressions (2013)
  19. García-Donato, G.; Martínez-Beneito, M. A.: On sampling strategies in Bayesian variable selection problems with large model spaces (2013)
  20. Guedj, Benjamin; Alquier, Pierre: PAC-Bayesian estimation and prediction in sparse additive models (2013)

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