Multiset Model Selection

References

• Araki, T., Ikeda, K., and Akaho, S. (2015), “An Efficient Sampling Algorithm With Adaptations for Bayesian Variable Selection,” Neural Networks, 61, 22–31.
   PubMed Web of Science ®Google Scholar
• Beck, T. (2007), The Prediction Tracker, available at http://www.thepredictiontracker.com/basketball.php.
   Google Scholar
• Bottolo, L., and Richardson, S. (2010), “Evolutionary Stochastic Search for Bayesian Model Exploration,” Bayesian Analysis, 5, 583–618.
   Web of Science ®Google Scholar
• Brooks, S. P., Friel, N., and King, R. (2003a), “Classical Model Selection via Simulated Annealing,” Journal of the Royal Statistical Society, Series B, 65, 503–520.
   Google Scholar
• Brooks, S. P., Giudici, P., and Roberts, G. O. (2003b), “Efficient Construction of Reversible Jump Markov Chain Monte Carlo Proposal Distributions,” Journal of the Royal Statistical Society, Series B, 65, 3–55.
   Google Scholar
• Carlin, B. P., and Chib, S. (1995), “Bayesian Model Choice via Markov Chain Monte Carlo methods,” Journal of the Royal Statistical Society, Series B, 57, 473–484.
   Google Scholar
• Clyde, M. (2016), BAS: Bayesian Adaptive Sampling for Bayesian Model Averaging, R package version 1.4.2.
   Google Scholar
• Clyde, M. A., Ghosh, J., and Littman, M. L. (2011), “Bayesian Adaptive Sampling for Variable Selection and Model Averaging,” Journal of Computational and Graphical Statistics, 20, 80–101.
   Web of Science ®Google Scholar
• Dellaportas, P., Forster, J. J., and Ntzoufras, I. (2002), “On Bayesian Model and Variable Selection Using MCMC,” Statistics and Computing, 12, 27–36.
   Web of Science ®Google Scholar
• Fernandez, C., Ley, E., and Steel, M. F. (2001), “Benchmark Priors for Bayesian Model Averaging,” Journal of Econometrics, 100, 381–427.
   Web of Science ®Google Scholar
• Flegal, J. M., Hughes, J., and Vats, D. (2016), mcmcse: Monte Carlo Standard Errors for MCMC, Riverside, CA and Minneapolis, MN. R package version 1.2-1.
   Google Scholar
• George, E., and McCulloch, R. (1993), “Variable Selection via Gibbs Sampling,” Journal of the American Statistical Society, 88, 881–889.
   Web of Science ®Google Scholar
• ——— (1997), “Approaches for Bayesian Variable Selection,” Statistica Sinica, 7, 339–373.
   Web of Science ®Google Scholar
• Geweke, J. (1996), “Variable Selection and Model Comparison in Regression,” in Bayesian Statistics 5, eds. J. M. Bernardo, J. O. Berger, A. P. Dawid, and A. F. M. Smith, University Press, pp. 609–620.
   Google Scholar
• Green, P. J. (1995), “Reversible Jump Markov Chain Monte Carlo Computation and Bayesian Model Determination,” Biometrika, 82, 711–732.
   Web of Science ®Google Scholar
• ——— (2003), “Trans-Dimensional Markov Chain Monte Carlo,” in Highly Structured Stochastic Systems, eds. P. J. Green, N. K. Hjort, and S. Richardson. UK: Oxford University Press, pp. 179–198.
   Google Scholar
• Green, P. J., and Mira, A. (1999), “Delayed Rejection in Reversible Jump Metropolis-Hastings,” Biometrika, 88, 1035–1053.
   Web of Science ®Google Scholar
• Hans, C., Dobra, A., and West, M. (2007), “Shotgun Stochastic Search for “Large p” Regression,” Journal of the American Statistical Association, 102, 507–516.
   Web of Science ®Google Scholar
• Hastie, D. (2005), Towards Automatic Reversible Jump Markov Chain Monte Carlo, unpublished doctoral thesis, University of Bristol.
   Google Scholar
• Hoegh, A., Carzolio, M., Crandell, I., Hu, X., Roberts, L., Song, Y., and Leman, S. C. (2015), “Nearest-Neighbor Matchup Effects: Accounting for Team Matchups for Predicting March Madness,” Journal of Quantitative Analysis in Sports, 11, 29–37.
   Google Scholar
• Hoeting, J. A., Madigan, D., Raftery, A. E., and Volinsky, C. T. (1999), “Bayesian Model Averaging: A Tutorial,” Statistical Science, 14, 382–417.
   Web of Science ®Google Scholar
• Jasra, A., Stephens, D. A., and Holmes, C. C. (2007), “Population-Based Reversible Jump Markov Chain Monte Carlo,” Biometrika, 94, 787–807.
   Web of Science ®Google Scholar
• Ji, C., and Schmidler, S. C. (2013), “Adaptive Markov Chain Monte Carlo for Bayesian Variable Selection,” Journal of Computational and Graphical Statistics, 22, 708–728.
   Web of Science ®Google Scholar
• Kim, H. J., and MacEachern, S. N. (2015), “The Generalized Multiset Sampler,” Journal of Computational and Graphical Statistics, 24, 1134–1154.
   Web of Science ®Google Scholar
• Kuo, L., and Mallick, B. (1998), “Variable Selection for Regression Models,” Sankhya: The Indian Journal of Statistics, 60B, 65–81.
   Google Scholar
• Leman, S. C., Chen, Y., and Lavine, M. (2009), “The Multiset Sampler,” Journal of the American Statistical Association, 104, 1029–1041.
   Web of Science ®Google Scholar
• Li, Y., and Clyde, M. A. (2015), “Mixtures of g-Priors in Generalized Linear Models,” arXiv:1503.06913.
   Google Scholar
• Liang, F., Paulo, R., Molina, G., Clyde, M. A., and Berger, J. O. (2012), “Mixtures of g Priors for Bayesian Variable Selection,” Journal of the American Statistical Association, 103, 410–423.
   Google Scholar
• Liu, J. S. (2008), Monte Carlo Strategies in Scientific Computing, New York: Springer Science & Business Media.
   Google Scholar
• Liu, J. S., and Chen, R. (1998), “Sequential Monte Carlo Methods for Dynamic Systems,” Journal of the American Statistical Association, 93, 1032–1044.
   Web of Science ®Google Scholar
• Madigan, D., York, J., and Allard, D. (1995), “Bayesian Graphical Models for Discrete Data,” International Statistical Review, 63, 215–232.
   Web of Science ®Google Scholar
• Nott, D. J., and Green, P. J. (2004), “Bayesian Variable Selection and the Swendsen–Wang Algorithm,” Journal of Computational and Graphical Statistics, 13, 141–157.
   Web of Science ®Google Scholar
• Petralias, A., and Dellaportas, P. (2013), “An MCMC Model Search Algorithm for Regression Problems,” Journal of Statistical Computation and Simulation, 83, 1722–1740.
   Web of Science ®Google Scholar
• Robert, C., and Casella, G. (2013), Monte Carlo Statistical Methods, New York: Springer Science & Business Media.
   Google Scholar
• Ročková, V., and George, E. (2014), “EMVS: The EM Approach to Bayesian Variable Selection,” Journal of the American Statistical Association, 109, 828–846.
   Web of Science ®Google Scholar
• Yuan, L.-H., Liu, A., Yeh, A., Kaufman, A., Reece, A., Bull, P., Franks, A., Wang, S., Illushin, D., and Bornn, L. (2015), “A Mixture-of-Modelers Approach to Forecasting NCAA Tournament Outcomes,” Journal of Quantitative Analysis in Sports, 11, 13–27.
   Web of Science ®Google Scholar