Large-Scale Quasi-Bayesian Inference with Spike-and-Slab Priors
Anwesha Bhattacharyya · Deep Blue (University of Michigan) · 2020
This dissertation studies a general framework using spike-and-slab prior distributions to facilitate the development of high-dimensional Bayesian inference. Our framework allows inference with a general quasi-likelihood function to address scenarios where likelihood based inference are infeasible or the underlying optimization problems are not the same as the data generating mechanisms. We show that highly efficient and scalable Markov Chain Monte Carlo (MCMC) algorithms can be easily constructed to sample from the resulting quasi-posterior distributions. We study the large scale behavior of the resulting quasi-posterior distributions as the dimension of the parameter space grows, and we establish several convergence results. In large-scale applications where computational speed is important, variational approximation methods are often used to approximate posterior distributions. We show that the contraction behaviors of the quasi-posterior distributions can be exploited to provide theoretical guarantees for their variational approximations. We illustrate the theory with several examples. Finally we develop a quasi-likelihood based algorithm for estimation of Ising/Potts models that incorporates inbuilt mechanism for parallel computation. We illustrate the usability of the method by analyzing 16 Personality Factors data under the setup of Five-level Potts Model. The data analysis recovers known clusters of personality traits and also indicates plausible novel clusters.