Structured Shrinkage Priors

References

• Bhattacharya, A., Pati, D., Pillai, N. S., and Dunson, D. B. (2015), “Dirichlet – Laplace Priors for Optimal Shrinkage,” Journal of the American Statistical Association, 110, 1479–1490. DOI: 10.1080/01621459.2014.960967.
   PubMed Web of Science ®Google Scholar
• Caron, F., and Doucet, A. (2008), “Sparse Bayesian Nonparametric Regression,” in International Conference on Machine Learning, pp. 88–95. DOI: 10.1145/1390156.1390168.
   Google Scholar
• Carvalho, C. M., Polson, N. G., and Scott, J. G. (2010), “The Horseshoe Estimator for Sparse Signals,” Biometrika, 97, 465–480. DOI: 10.1093/biomet/asq017.
   Web of Science ®Google Scholar
• Daniels, M. J., and Pourahmadi, M. (2002), “Bayesian Analysis of Covariance Matrices and Dynamic Models for Longitudinal Data,” Biometrika, 89, 553–566. DOI: 10.1093/biomet/89.3.553.
   Web of Science ®Google Scholar
• de Brecht, M., and Yamagishi, N. (2012), “Combining Sparseness and Smoothness Improves Classification Accuracy and Interpretability,” NeuroImage, 60, 1550–1561. DOI: 10.1016/j.neuroimage.2011.12.085.
   PubMed Web of Science ®Google Scholar
• Dempster, A. P., Laird, N. M., and Rubin, D. B. (1977), “Maximum Likelihood from Incomplete Data via the EM Algorithm,” Journal of the Royal Statistical Society, Series B, 39, 1–38. DOI: 10.1111/j.2517-6161.1977.tb01600.x.
   Google Scholar
• Devroye, L. (2009), “Random Variate Generation for Exponentially and Polynomially Tilted Stable Distributions,” ACM Transactions on Modeling and Computer Simulation, 19, 1–20. DOI: 10.1145/1596519.1596523.
   Web of Science ®Google Scholar
• Finegold, M., and Drton, M. (2011), “Robust Graphical Modeling of Gene Networks Using Classical and Alternative t-distributions,” Annals of Applied Statistics, 5, 1057–1080.
   Web of Science ®Google Scholar
• Forney, E., Anderson, C., Davies, P., Gavin, W., Taylor, B., and Roll, M. (2013), “A Comparison of EEG Systems for Use in p300 Spellers by Users with Motor Impairments in Real-World Environments,” in Proceedings of the Fifth International Brain-Computer Interface Meeting.
   Google Scholar
• Frank, I. E., and Friedman, J. H. (1993), “A Statistical View of Some Chemometrics Regression Tools,” Technometrics, 35, 109–135. DOI: 10.1080/00401706.1993.10485033.
   Web of Science ®Google Scholar
• Griffin, J. E., and Brown, P. J. (2010), “Inference with Normal-Gamma Prior Distributions in Regression Problems,” Bayesian Analysis, 5, 171–188. DOI: 10.1214/10-BA507.
   Web of Science ®Google Scholar
• Griffin, J. E., and Brown, P. J. (2012a), “Competing Sparsity: A Hierarchical Prior for Sparse Regression with Grouped Effects,” Manuscript.
   Google Scholar
• Griffin, J. E., and Brown, P. J. (2012b), “Structuring Shrinkage: Some Correlated Priors for Regression,” Biometrika, 99, 481–487.
   Web of Science ®Google Scholar
• Hahn, P. R., and Carvalho, C. M. (2015), “Decoupling Shrinkage and Selection in Bayesian Linear Models: A Posterior Summary Perspective,” Journal of the American Statistical Association, 110, 435–448. DOI: 10.1080/01621459.2014.993077.
   Web of Science ®Google Scholar
• Hoff, P. D. (2016), “Equivariant and Scale-Free Tucker Decomposition Models,” Bayesian Analysis, 11, 627–648. DOI: 10.1214/14-BA934.
   Web of Science ®Google Scholar
• Kalli, M., and Griffin, J. E. (2014), “Time-Varying Sparsity in Dynamic Regression Models,” Journal of Econometrics, 178, 779–793. DOI: 10.1016/j.jeconom.2013.10.012.
   Web of Science ®Google Scholar
• Kowal, D. R., Matteson, D. S., and Ruppert, D. (2017), “Dynamic Shrinkage Processes,” ArXiv preprint. arXiv:1707.00763, pp. 1–45.
   Google Scholar
• Kyung, M., Gill, J., Ghosh, M., and Casella, G. (2010), “Penalized Regression, Standard Errors, and Bayesian Lassos,” Bayesian Analysis, 5, 369–412. DOI: 10.1214/10-BA607.
   Web of Science ®Google Scholar
• Li, H., and Pati, D. (2017), “Variable Selection using Shrinkage Priors,” Computational Statistics and Data Analysis, 107, 107–119. DOI: 10.1016/j.csda.2016.10.008.
   Web of Science ®Google Scholar
• Makeig, S., Kothe, C., Mullen, T., Bigdely-Shamlo, N., Zhang, Z., and Kreutz-Delgado, K. (2012), “Evolving Signal Processing for Brain – Computer Interfaces,” Proceedings of the IEEE, 100, 1567–1584. DOI: 10.1109/JPROC.2012.2185009.
   Web of Science ®Google Scholar
• Mulder, J., and Pericchi, L. R. (2018), “The Matrix-f Prior for Estimating and Testing Covariance Matrices,” Bayesian Analysis, 13, 1189–1210. DOI: 10.1214/17-BA1092.
   Web of Science ®Google Scholar
• Murray, I., Adams, R. P., and Mackay, D. J. C. (2010), “Elliptical Slice Sampling,” Journal of Machine Learning Research: WC&P, 9, 541–548.
   Google Scholar
• Natarovskii, V., Rudolf, D., and Sprungk, B. (2021), “Geometric Convergence of Elliptical Slice Sampling,” Proceedings of the 38th International Conference on Machine Learning, 139, 7969–7978.
   Google Scholar
• Ng, B., and Abugharbieh, R. (2011), “Modeling Spatiotemporal Structure in fMRI Brain Decoding Using Generalized Sparse Classifiers,” IEEE International Workshop on Pattern Recognition in NeuroImaging, pp. 65–68.
   Google Scholar
• Nishihara, R., Murray, I., and Adams, R. P. (2014), “Parallel MCMC with Generalized Elliptical Slice Sampling,” Journal of Machine Learning Research, 15, 2087–2112.
   Web of Science ®Google Scholar
• Park, T., and Casella, G. (2008), “The Bayesian Lasso,” Journal of the American Statistical Association, 103, 681–686. DOI: 10.1198/016214508000000337.
   Web of Science ®Google Scholar
• Perry, P. O. (2017), “Fast Moment-based Estimation for Hierarchical Models,” Journal of the Royal Statistical Society, Series B, 79, 267–291. DOI: 10.1111/rssb.12165.
   Google Scholar
• Piironen, J., Paasiniemi, M., and Vehtari, A. (2020), “Projective Inference in High-Dimensional Problems: Prediction and Feature Selection,” Electronic Journal of Statistics, 14, 2155–2197. DOI: 10.1214/20-EJS1711.
   Web of Science ®Google Scholar
• Piironen, J., and Vehtari, A. (2017), “Comparison of Bayesian Predictive Methods for Model Selection,” Statistics and Computing, 27, 711–735. DOI: 10.1007/s11222-016-9649-y.
   Web of Science ®Google Scholar
• Polson, N. G., and Scott, J. G. (2010), “Shrink Globally, Act Locally: Bayesian Sparsity and Regularization,” in Bayesian Statistics 9, eds. J. M. Bernardo, M. J. Bayarri, J. O. Berger, A. P. Dawid, D. Heckerman, A. F. M. Smith, and M. West, pp. 501–538, Oxford: Oxford University Press.
   Google Scholar
• Polson, N. G., Scott, J. G., and Windle, J. (2013), “Bayesian Inference for Logistic Models using pólya-gamma Latent Variables,” Journal of the American Statistical Association, 108, 1339–1349. DOI: 10.1080/01621459.2013.829001.
   Web of Science ®Google Scholar
• Polson, N. G., Scott, J. G., and Windle, J. (2014), “The Bayesian Bridge,” Journal of the Royal Statistical Society, Series B, 76, 713–733.
   Google Scholar
• Roos, M., and Held, L. (2011), “Sensitivity Analysis in Bayesian Generalized Linear Mixed Models for Binary Data,” Bayesian Analysis, 6, 259–278. DOI: 10.1214/11-BA609.
   Web of Science ®Google Scholar
• Roy, A., Reich, B. J., Guinness, J., Shinohara, R. T., and Staicu, A.-M. (2021), “Spatial Shrinkage via the Product Independent Gaussian Process Prior,” Journal of Computational and Graphical Statistics, 30, 1068–1080. DOI: 10.1080/10618600.2021.1923512.
   Web of Science ®Google Scholar
• Roy, V., and Chakraborty, S. (2016), “Selection of Tuning Parameters, Solution Paths and Standard Errors for Bayesian Lassos,” Bayesian Analysis, 12, 753–778. DOI: 10.1214/16-BA1025.
   Web of Science ®Google Scholar
• Schuurman, N. K., Grasman, R. P., and Hamaker, E. L. (2016), “A Comparison of Inverse-Wishart Prior Specifications for Covariance Matrices in Multilevel Autoregressive Models,” Multivariate Behavioral Research, 51, 185–206. DOI: 10.1080/00273171.2015.1065398.
   PubMed Web of Science ®Google Scholar
• Simon, N., Friedman, J., Hastie, T., and Tibshirani, R. (2013), “A Sparse-Group Lasso,” Journal of Computational and Graphical Statistics, 22, 231–245. DOI: 10.1080/10618600.2012.681250.
   Web of Science ®Google Scholar
• Styan, P. H. (1973), “Hadamard Products and Multivariate Statistical Analysis,” Linear Algebra and Its Applications, 6, 217–240. DOI: 10.1016/0024-3795(73)90023-2.
   Google Scholar
• Tibshirani, R. (1996), “Regression Shrinkage and Selection via the Lasso,” Journal of the Royal Statistical Society, Series B, 58, 267–288. DOI: 10.1111/j.2517-6161.1996.tb02080.x.
   Google Scholar
• van Gerven, M., Cseke, B., Oostenveld, R., and Heskes, T. (2009), “Bayesian Source Localization with the Multivariate Laplace Prior,” Advances in Neural Information Processing Systems, 22, 1–9.
   Google Scholar
• van Gerven, M. A. J., Cseke, B., de Lange, F. P., and Heskes, T. (2010), “Efficient Bayesian Multivariate fMRI Analysis Using a Sparsifying Spatio-Temporal Prior,” Neuroimage 50, 150–161. DOI: 10.1016/j.neuroimage.2009.11.064.
   PubMed Web of Science ®Google Scholar
• Vehtari, A., Gelman, A., and Gabry, J. (2017), “Practical Bayesian Model Evaluation using Leave-One-Out Cross-Validation and waic,” Statistics and Computing, 27, 1413–1432. DOI: 10.1007/s11222-016-9696-4.
   Web of Science ®Google Scholar
• Wolpaw, J., and Wolpaw, E. W. (2012), Brain-Computer Interfaces: Principles and Practice, Oxford: Oxford University Press.
   Google Scholar
• Woody, S., Carvalho, C. M., and Murray, J. S. (2021), “Model Interpretation through Lower-Dimensional Posterior Summarization,” Journal of Computational and Graphical Statistics, 30, 144–161. DOI: 10.1080/10618600.2020.1796684.
   Web of Science ®Google Scholar
• Wu, A., Park, M., Koyejo, O., and Pillow, J. W. (2014), “Sparse Bayesian Structure Learning with Dependent Relevance Determination Prior,” in Advances in Neural Information Processing Systems, pp. 1628–1636.
   Google Scholar
• Yuan, M., and Lin, Y. (2006), “Model Selection and Estimation in Regression with Grouped Variables,” Journal of the Royal Statistical Society, Series B, 68, 49–67. DOI: 10.1111/j.1467-9868.2005.00532.x.
   Google Scholar
• Zhao, S., Gao, C., Mukherjee, S., and Engelhardt, B. E. (2016), “Bayesian Group Factor Analysis with Structured Sparsity,” Journal of Machine Learning Research, 17, 1–47.
   Web of Science ®Google Scholar