10 Gaussian mixture models

To be added.

Bayarri, M. J., J. O. Berger, A. Forte, and G. Garcia-Donato. 2012. “Criteria for Bayesian Model Choice with Application to Variable Selection.” The Annals of Statistics 40: 1550–77.

Bayarri, M. J., and G. Garcia-Donato. 2007. “Extending Conventional Priors for Testing General Hypotheses in Linear Models.” Biometrika 94: 135–52.

Bayarri, M. J., and G. Garcı́a-Donato. 2008. “Generalization of Jeffreys Divergence-Based Priors for Bayesian Hypothesis Testing.” Journal of the Royal Statistical Society B 70 (5): 981–1003.

Berger, J. O., and R. L Pericchi. 1996. “The Intrinsic Bayes Factor for Model Selection and Prediction.” Journal of the American Statistical Association 91: 109–22.

Berger, J. O., and R. L. Pericchi. 2001. “Objective Bayesian Methods for Model Selection: Introduction and Comparison.” In Model Selection, edited by P. Lahiri, 38:135–207. Institute of Mathematical Statistics lecture notes - Monograph series.

Bertsimas, D., A. King, and A. Mazumder. 2016. “Best Subset Selection via a Modern Optimization Lens.” The Annals of Statistics 44 (2): 813–52.

Bertsimas, D., and B. Van Parys. 2020. “Sparse High-Dimensional Regression: Exact Scalable Algorithms and Phase Transitions.” Annals of Statistics 48 (1): 300–323.

Besag, Julian. 1994. “Comments on Representations of Knowledge in Complex Systems by u. Grenander and MI Miller.” Journal of the Royal Statistical Society B 56: 591–92.

Brooks, Steve, Andrew Gelman, Galin Jones, and Xiao-Li Meng. 2011. Handbook of Markov Chain Monte Carlo. CRC press.

Bühlmann, P., and S. van de Geer. 2011. Statistics for High-Dimensional Data. New York: Springer.

Calon, A., E. Espinet, S. Palomo-Ponce, D. V. F. Tauriello, M. Iglesias, M. V. Céspedes, M. Sevillano, et al. 2012. “Dependency of Colorectal Cancer on a TGF-Beta-Driven Programme in Stromal Cells for Metastasis Initiation.” Cancer Cell 22 (5): 571–84.

Carbonetto, Peter, and Matthew Stephens. 2012. “Scalable Variational Inference for Bayesian Variable Selection in Regression, and Its Accuracy in Genetic Association Studies.” Bayesian Analysis 7 (1): 73–108.

Castillo, I., J. Schmidt-Hieber, and A. W. van der Vaart. 2015. “Bayesian Linear Regression with Sparse Priors.” The Annals of Statistics 43 (5): 1986–2018.

Chang, Hyunwoong, and Quan Zhou. 2025. “Dimension-Free Relaxation Times of Informed MCMC Samplers on Discrete Spaces.” Bernoulli (forthcoming): 1–28.

Chen, J., and Z. Chen. 2008. “Extended Bayesian Information Criteria for Model Selection with Large Model Spaces.” Biometrika 95 (3): 759–71.

Clyde, M. 1999. “Bayesian Model Averaging and Model Search Strategies.” In Bayesian Statistics 6, edited by J. M. Bernardo, A. P. Dawid, J. O. Berger, and A. F. M. Smith, 157–85. Oxford University Press.

Consonni, Guido, Dimitris Fouskakis, Brunero Liseo, and Ioannis Ntzoufras. 2018. “Prior Distributions for Objective Bayesian Analysis.” Bayesian Analysis 13 (2): 627–79.

Cover, Thomas M, and Jan M Van Campenhout. 2007. “On the Possible Orderings in the Measurement Selection Problem.” IEEE Transactions on Systems, Man, and Cybernetics 7 (9): 657–61.

Cui, Wen, and Edward I George. 2008. “Empirical Bayes Vs. Fully Bayes Variable Selection.” Journal of Statistical Planning and Inference 138 (4): 888–900.

Fan, J., and R. Li. 2001. “Variable Selection via Nonconcave Penalized Likelihood and Its Oracle Properties.” Journal of the American Statistical Association 96: 1348–60.

Foster, D., H. Karloff, and J. Thaler. 2015. “Variable Selection Is Hard.” In Conference on Learning Theory, 696–709.

Fouskakis, Dimitris, Ioannis Ntzoufras, and Konstantinos Perrakis. 2018. “Power-Expected-Posterior Priors for Generalized Linear Models.” Bayesian Analysis 3 (13): 721–48.

Fúquene, J., M. F. J. Steel, and D. Rossell. 2019. “On Choosing Mixture Components via Non-Local Priors.” Journal of the Royal Statistical Society B 81 (5): 809–37.

Gamerman, Dani, and Hedibert F Lopes. 2006. Markov Chain Monte Carlo: Stochastic Simulation for Bayesian Inference. Chapman; Hall/CRC.

Giannone, Domenico, Michele Lenza, and Giorgio E Primiceri. 2021. “Economic Predictions with Big Data: The Illusion of Sparsity.” Econometrica 89 (5): 2409–37.

Girolami, Mark, and Ben Calderhead. 2011. “Riemann Manifold Langevin and Hamiltonian Monte Carlo Methods.” Journal of the Royal Statistical Society B 73 (2): 123–214.

Gonzalo Garcia-Donato, and Anabel Forte. 2018. “Bayesian Testing, Variable Selection and Model Averaging in Linear Models Using R with BayesVarSel.” The R Journal 10 (1): 329. https://journal.r-project.org/archive/2018/RJ-2018-021/index.html.

Hazimeh, Hussein, Rahul Mazumder, and Tim Nonet. 2023. “L0learn: A Scalable Package for Sparse Learning Using L0 Regularization.” Journal of Machine Learning Research 24 (205): 1–8.

Hoeting, Jennifer A., David Madigan, Adrian E. Raftery, and Chris T. Volinsky. 1999. “Bayesian Model Averaging: A Tutorial.” Statistical Science 14: 382–401.

Hoffman, Matthew D, and Andrew Gelman. 2014. “The No-U-Turn Sampler: Adaptively Setting Path Lengths in Hamiltonian Monte Carlo.” Journal of Machine Learning Research 15 (1): 1593–623.

Jeffreys, H. 1961. Theory of Probability. Third. Oxford, England: Oxford University Press.

Johnson, V. E., and D. Rossell. 2010. “On the Use of Non-Local Prior Densities for Default Bayesian Hypothesis Tests.” Journal of the Royal Statistical Society B 72: 143–70.

———. 2012. “Bayesian Model Selection in High-Dimensional Settings.” Journal of the American Statistical Association 24 (498): 649–60.

Kass, R. E., L. Tierney, and J. B. Kadane. 1990. “The Validity of Posterior Expansions Based on Laplace’s Method.” Bayesian and Likelihood Methods in Statistics and Econometrics 7: 473–88.

Kiefer, Jack, and Jacob Wolfowitz. 1952. “Stochastic Estimation of the Maximum of a Regression Function.” The Annals of Mathematical Statistics 23 (3): 462–66.

Lempers, Fred B. 1971. Rotterdam University Press.

Liang, F., R. Paulo, G. Molina, M. A. Clyde, and J. O. Berger. 2008. “Mixtures of g-Priors for Bayesian Variable Selection.” Journal of the American Statistical Association 103: 410–23.

Liang, Xitong, Samuel Livingstone, and Jim Griffin. 2023. “Adaptive MCMC for Bayesian Variable Selection in Generalised Linear Models and Survival Models.” Entropy 25 (9): 1310.

Lindley, D. V. 1957. “A Statistical Paradox.” Biometrika 44: 187–92.

Linnainmaa, Seppo. 1970. “The Representation of the Cumulative Rounding Error of an Algorithm as a Taylor Expansion of the Local Rounding Errors.” PhD thesis, Master’s Thesis (in Finnish), University of Helsinki.

Madigan, D., and A. E. Raftery. 1994. “Model Selection and Accounting for Model Uncertainty in Graphical Models Using Occam’s Window.” Journal of the American Statistical Association 89 (428): 1535–46.

Moreno, E., F. Bertolino, and W. Racugno. 1998. “An Intrinsic Limiting Procedure for Model Selection and Hypotheses Testing.” Journal of the American Statistical Association 93: 1451–60.

Narisetty, N. N., and X. He. 2014. “Bayesian Variable Selection with Shrinking and Diffusing Priors.” The Annals of Statistics 42 (2): 789–817.

Natarajan, B. K. 1995. “Sparse Approximate Solutions to Linear Systems.” SIAM Journal on Computing 24 (2): 227–34.

Neal, Radford. 2011. “MCMC Using Hamiltonian Dynamics.” In Handbook of Markov Chain Monte Carlo, 113–62. Chapman; Hall/CRC.

O’Hagan, A. 1995. “Fractional Bayes Factors for Model Comparison.” Journal of the Royal Statistical Society B 57: 99–118.

Pérez, J. M., and J. O. Berger. 2002. “Expected Posterior Prior Distributions for Model Selection.” Biometrika 89: 491–512.

Raskutti, G., M. Wainwright, and B. Yu. 2011. “Minimax Rates of Estimation for High-Dimensional Linear Regression over Balls.” Information Theory, IEEE Transactions on 57 (10): 6976–94.

Robbins, Herbert, and Sutton Monro. 1951. “A Stochastic Approximation Method.” The Annals of Mathematical Statistics 22 (9): 400–407.

Roberts, Gareth O, and Jeffrey S Rosenthal. 1998. “Optimal Scaling of Discrete Approximations to Langevin Diffusions.” Journal of the Royal Statistical Society B 60 (1): 255–68.

Rognon-Vael, Paul, and David Rossell. 2025. “Empirical Bayes for Data Integration.” arXiv 2508.08336: 1–51.

Rognon-Vael, Paul, David Rossell, and Piotr Zwiernik. 2025. “Improving Variable Selection Properties by Leveraging External Data.” arXiv 2502.15584: 1–75.

Rosenblatt, Frank. 1958. “The Perceptron: A Probabilistic Model for Information Storage and Organization in the Brain.” Psychological Review 65 (6): 386–408.

Rossell, D., O. Abril, and A. Bhattacharya. 2021. “Approximate Laplace Approximations for Scalable Model Selection.” Journal of the Royal Statistical Society B 83 (4): 853–79.

Rossell, David. 2022. “Concentration of Posterior Model Probabilities and Normalized L0 Criteria.” Bayesian Analysis 17 (2): 565–91.

Rossell, D., and F. J. Rubio. 2018. “Tractable Bayesian Variable Selection: Beyond Normality.” Journal of the American Statistical Association 113 (524): 1742–58.

———. 2021. “Additive Bayesian Variable Selection Under Censoring and Misspecification.” Statistical Science 38 (1): 13–29.

Rossell, D., and D. Telesca. 2017. “Non-Local Priors for High-Dimensional Estimation.” Journal of the American Statistical Association 112: 254–65.

Rumelhart, David E, Geoffrey E Hinton, and Ronald J Williams. 1986. “Learning Representations by Back-Propagating Errors.” Nature 323 (6088): 533–36.

Schwarz, G. 1978. “Estimating the Dimension of a Model.” The Annals of Statistics 6: 461–64.

Scott, J. G., and J. O Berger. 2010. “Bayes and Empirical Bayes Multiplicity Adjustment in the Variable Selection Problem.” The Annals of Statistics 38 (5): 2587–2619.

Stone, M. 1977. “An Asymptotic Equivalence of Choice of Model by Cross-Validation and Akaike’s Criterion.” Journal of the Royal Statistical Society B 39: 44–47.

Sulem, Déborah, Jack Jewson, and David Rossell. 2025. “Bayesian Computation for High-Dimensional Gaussian Graphical Models with Spike-and-Slab Priors.” arXiv 2511.01875: 1–139.

Tibshirani, R. 1996. “Regression Shrinkage and Selection via the Lasso.” Journal of the Royal Statistical Society, B 58: 267–88.

Wainwright, Martin J. 2009. “Information-Theoretic Limits on Sparsity Recovery in the High-Dimensional and Noisy Setting.” IEEE Transactions on Information Theory 55 (12): 5728–41.

Xu, Maoran, and Leo L Duan. 2023. “Bayesian Inference with the L1-Ball Prior: Solving Combinatorial Problems with Exact Zeros.” Journal of the Royal Statistical Society B 85 (5): 1538–60.

Xu, X., P. Lu, S. N. MacEachern, and R. Xu. 2019. “Calibrated Bayes Factors for Model Comparison.” Journal of Statistical Computation and Simulation (in press): 1–24.

Yang, Y., M. J. Wainwright, and M. I. Jordan. 2016. “On the Computational Complexity of High-Dimensional Bayesian Variable Selection.” The Annals of Statistics 44 (6): 2497–2532.

Zanella, Giacomo. 2020. “Informed Proposals for Local MCMC in Discrete Spaces.” Journal of the American Statistical Association 115 (530): 852–65.

Zellner, A. 1986. “On Assessing Prior Distributions and Bayesian Regression Analysis with g-Prior Distributions.” In Bayesian Inference and Decision Techniques: Essays in Honor of Bruno de Finetti. Amsterdam; New York: North-Holland/Elsevier.

Zellner, A., and A. Siow. 1980. “Posterior Odds Ratios for Selected Regression Hypotheses.” In Bayesian Statistics: Proceedings of the First International Meeting Held in Valencia (Spain), edited by J. M. Bernardo, M. H. DeGroot, D. V. Lindley, and A. F. M. Smith. Vol. 1. Valencia: University Press.

———. 1984. Basic Issues in Econometrics. Chicago: University of Chicago Press.

Zhang, Y., M. J. Wainwright, and M. I. Jordan. 2014. “Lower Bounds on the Performance of Polynomial-Time Algorithms for Sparse Linear Regression.” JMLR: Workshop and Conference Proceedings 35: 1–28.

Zhou, Quan, Jun Yang, Dootika Vats, Gareth O Roberts, and Jeffrey S Rosenthal. 2022. “Dimension-Free Mixing for High-Dimensional Bayesian Variable Selection.” Journal of the Royal Statistical Society B 84 (5): 1751–84.

Zou, H. 2006. “The Adaptive LASSO and Its Oracle Properties.” Journal of the American Statistical Association 101 (476): 1418–29.