Nonlocal Priors for High-Dimensional Estimation

References

• Bhattacharya, A., Pati, D., Pillai, N., and Dunson, D. (2012), “Bayesian shrinkage,” Technical Report, arXiv preprint, arXiv:1212.6088.
   Google Scholar
• Calon, A., Espinet, E., Palomo-Ponce, S., Tauriello, D., Iglesias, M., Céspedes, M., Sevillano, M., Nadal, C., Jung, P., Zhang, X.-F., Byrom, D., Riera, A., Rossell, D., Mangues, R., Massague, J., Sancho, E., and Batlle, E. (2012), “Dependency of Colorectal Cancer on a TGF-Beta-Driven Programme in Stromal Cells for Metastasis Initiation,” Cancer Cell, 22, 571–584.
   PubMed Web of Science ®Google Scholar
• Castillo, I., Schmidt-Hieber, J., and van der Vaart, A. (2014), “Bayesian Linear Regression With Sparse Priors,” Technical Report, arXiv preprint, arXiv:1403.0735.
   Google Scholar
• Castillo, I., and Van der Vaart, A. W. (2012), “Needles and Straw in a Haystack: Posterior Concentration for Possibly Sparse Sequences,” The Annals of Statistics, 40, 2069–2101.
   Web of Science ®Google Scholar
• Chen, J., and Chen, Z. (2008), “Extended Bayesian Information Criteria for Model Selection With Large Model Spaces,” Biometrika, 95, 759–771.
   Web of Science ®Google Scholar
• Consonni, G., and La Rocca, L. (2010), “On Moment Priors for Bayesian Model Choice With Applications to Directed Acyclic Graphs,” in Bayesian Statistics 9: Proceedings of the Ninth Valencia International Meeting, eds. J. Bernardo, M. Bayarri, J. Berger, A. Dawid, D. Heckerman, A. Smith, and M. West, Oxford, UK: Oxford University Press, pp. 119–144.
   Google Scholar
• Dawid, A. (1999), “The Trouble With Bayes Factors,” Technical Report, London: University College London.
   Google Scholar
• Fan, J., and Li, R. (2001), “Variable Selection via Nonconcave Penalized Likelihood and Its Oracle Properties,” Journal of the American Statistical Association, 96, 1348–1360.
   Web of Science ®Google Scholar
• Fan, J., and Lv, J. (2010), “A Selective Overview of Variable Selection in High Dimensional Feature Space,” Statistica Sinica, 20, 101–140.
   PubMed Web of Science ®Google Scholar
• Fernández, C., Ley, E., and Steel, M. (2001), “Benchmark Priors for Bayesian Model Averaging,” Journal of Econometrics, 100, 381–427.
   Web of Science ®Google Scholar
• Gelfand, A., and Ghosh, S. (1998), “Model Choice: A Minimum Posterior Predictive Loss Approach,” Biometrika, 85, 1–11.
   Web of Science ®Google Scholar
• Johnson, V., and Rossell, D. (2010), “Prior Densities for Default Bayesian Hypothesis Tests,” Journal of the Royal Statistical Society, Series B, 72, 143–170.
   Google Scholar
• ——— (2012), “Bayesian Model Selection in High-Dimensional Settings,” Journal of the American Statistical Association, 24, 649–660.
   Google Scholar
• Kotecha, J., and Djuric, P. (1999), “Gibbs Sampling Approach for Generation of Truncated Multivariate Gaussian Random Variables,” in Proceedings of the IEEE International Conference on Acoustics, Speech and Signal Processing, IEEE Computer Society, pp. 1757–1760.
   Google Scholar
• Lai, T., Robbins, H., and Wei, C. (1979), “Strong Consistency of Least Squares in Multiple Regression,” Journal of Multivariate Analysis, 9, 343–361.
   Web of Science ®Google Scholar
• Liang, F., Paulo, R., Molina, G., Clyde, M., and Berger, J. (2008), “Mixtures of g-Priors for Bayesian Variable Selection,” Journal of the American Statistical Association, 103, 410–423.
   Web of Science ®Google Scholar
• Liang, F., Song, Q., and Yu, K. (2013), “Bayesian Modeling for High-Dimensional Generalized Linear Models,” Journal of the American Statistical Association, 108, 589–606.
   Web of Science ®Google Scholar
• Martin, R., and Walker, S. (2013), “Asymptotically Minimax Empirical Bayes Estimation of a Sparse Normal Mean Vector,” Technical Report, arXiv preprint, arXiv:1304.7366.
   Google Scholar
• Narisetty, N., and He, X. (2014), “Bayesian Variable Selection With Shrinking and Diffusing Priors,” The Annals of Statistics, 42, 789–817.
   Web of Science ®Google Scholar
• Redner, R. (1981), “Note on the Consistency of the Maximum Likelihood Estimator for Nonidentifiable Distributions,” Annals of Statistics, 9, 225–228.
   Web of Science ®Google Scholar
• Rodriguez-Yam, G., Davis, R., and Scharf, L. (2004), “Efficient Gibbs Sampling of Truncated Multivariate Normal With Application to Constrained Linear Regression,” Ph.D. thesis, Department of Statistics, Colorado State University.
   Google Scholar
• Rossell, D., Telesca, D., and Johnson, V. (2013), “High-Dimensional Bayesian Classifiers Using Non-Local Priors,” in Statistical Models for Data Analysis XV, eds. P. Giudici, S. Ingrassia, and M. Vichi, Switzerland: Springer, pp. 305–314.
   Google Scholar
• Rousseau, J. (2007), “Approximating Interval Hypothesis: P-values and Bayes factors,” in Bayesian Statistics 8, eds. Bernardo, J., Bayarri, M., Berger, J., and Dawid, A., Oxford, UK: Oxford University Press, pp. 417–452.
   Google Scholar
• Shin, M., Bhattacharya, A., and Johnson, V. (2015), “Scalable Bayesian Variable Selection Using Nonlocal Prior Densities in Ultrahigh-Dimensional Settings,” arXiv http://arxiv.org/abs/1507.07106, 1–33.
   Google Scholar
• Springer, M., and Thompson, W. (1970), “The Distribution of Products of Beta, Gamma and Gaussian Random Variables,” SIAM Journal of Applied Mathematics, 18, 721–737.
   Web of Science ®Google Scholar
• Tibshirani, R. (1996), “Regression Shrinkage and Selection via the Lasso,” Journal of the Royal Statistical Society, Series B, 58, 267–288.
   Google Scholar
• Verdinelli, I., and Wasserman, L. (1996), “Bayes Factors, Nuisance Parameters and Imprecise Tests,” in Bayesian Statistics 5, eds. Bernardo, J., Berger, J., Dawid, A., and Smith, A., Oxford, UK: Oxford University Press, pp. 765–771.
   Google Scholar
• Walker, A. (1969), “On the Asymptotic Behaviour of Posterior Distributions,” Journal of the Royal Statistical Society, Series B, 31, 80–88.
   Google Scholar
• Wilhelm, S., and Manjunath, B. (2010), “tmvtnorm: A Package for the Truncated Multivariate Normal Distribution,” The R Journal, 2, 25–29.
   Google Scholar
• Zhou, H. (2006), “The Adaptive LASSO and Its Oracle Properties,” Journal of the American Statistical Association, 101, 1418–1429.
   Web of Science ®Google Scholar