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. Kim, Joungyoun; Lim, Johan; Kim, Yongdai; Jang, Woncheol: Bayesian variable selection with strong heredity constraints (2018)
  2. 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)
  3. Castillo, Ismaël; Schmidt-Hieber, Johannes; van der Vaart, Aad: Bayesian linear regression with sparse priors (2015)
  4. Elliott, Graham; Gargano, Antonio; Timmermann, Allan: Complete subset regressions with large-dimensional sets of predictors (2015)
  5. Pungpapong, Vitara; Zhang, Min; Zhang, Dabao: Selecting massive variables using an iterated conditional modes/medians algorithm (2015)
  6. Bleich, Justin; Kapelner, Adam; George, Edward I.; Jensen, Shane T.: Variable selection for BART: an application to gene regulation (2014)
  7. Elliott, Graham; Gargano, Antonio; Timmermann, Allan: Complete subset regressions (2013)
  8. García-Donato, G.; Martínez-Beneito, M. A.: On sampling strategies in Bayesian variable selection problems with large model spaces (2013)
  9. Guedj, Benjamin; Alquier, Pierre: PAC-Bayesian estimation and prediction in sparse additive models (2013)
  10. Turnbull, Bradley; Ghosal, Subhashis; Zhang, Hao Helen: Iterative selection using orthogonal regression techniques (2013)
  11. Woodard, Dawn B.; Rosenthal, Jeffrey S.: Convergence rate of Markov chain methods for genomic motif discovery (2013)
  12. Dellaportas, Petros; Forster, Jonathan J.; Ntzoufras, Ioannis: Joint specification of model space and parameter space prior distributions (2012)
  13. Oates, Chris. J.; Mukherjee, Sach: Network inference and biological dynamics (2012)
  14. Liu, Fei; Dunson, David; Zou, Fei: High-dimensional variable selection in meta-analysis for censored data (2011)
  15. Sabanés Bové, Daniel; Held, Leonhard: Bayesian fractional polynomials (2011)
  16. Speed, Doug; Tavaré, Simon: Sparse partitioning: nonlinear regression with binary or tertiary predictors, with application to association studies (2011)
  17. Chen, Ming-Hui (ed.); Dey, Dipak K. (ed.); Müller, Peter (ed.); Sun, Dongchu (ed.); Ye, Keying (ed.): Frontiers of statistical decision making and Bayesian analysis. In honor of James O. Berger (2010)
  18. Dobra, Adrian; Massam, Héléne: The mode oriented stochastic search (MOSS) algorithm for log-linear models with conjugate priors (2010)
  19. Lucas, Joseph; Carvalho, Carlos; West, Mike: A Bayesian analysis strategy for cross-study translation of gene expression biomarkers (2009)
  20. Wang, Hao; West, Mike: Bayesian analysis of matrix normal graphical models (2009)

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