University of Pennsylvania ScholarlyCommons Publicly Accessible Penn Dissertations 2018 Bayesian Model Selection And Estimation Without Mcmc Sameer Deshpande University of Pennsylvania,
[email protected] Follow this and additional works at: https://repository.upenn.edu/edissertations Part of the Statistics and Probability Commons Recommended Citation Deshpande, Sameer, "Bayesian Model Selection And Estimation Without Mcmc" (2018). Publicly Accessible Penn Dissertations. 2953. https://repository.upenn.edu/edissertations/2953 This paper is posted at ScholarlyCommons. https://repository.upenn.edu/edissertations/2953 For more information, please contact
[email protected]. Bayesian Model Selection And Estimation Without Mcmc Abstract This dissertation explores Bayesian model selection and estimation in settings where the model space is too vast to rely on Markov Chain Monte Carlo for posterior calculation. First, we consider the problem of sparse multivariate linear regression, in which several correlated outcomes are simultaneously regressed onto a large set of covariates, where the goal is to estimate a sparse matrix of covariate effects and the sparse inverse covariance matrix of the residuals. We propose an Expectation-Conditional Maximization algorithm to target a single posterior mode. In simulation studies, we find that our algorithm outperforms other regularization competitors thanks to its adaptive Bayesian penalty mixing. In order to better quantify the posterior model uncertainty, we then describe a particle optimization procedure that targets several high-posterior probability models simultaneously. This procedure can be thought of as running several ``mutually aware'' mode-hunting trajectories that repel one another whenever they approach the same model. We demonstrate the utility of this method for fitting Gaussian mixture models and for identifying several promising partitions of spatially-referenced data.