Evaluating Scalable Markov Chain Monte Carlo Algorithms for Big Data Problems Open Access

Sang, Zhifan (2016)

Permanent URL: https://etd.library.emory.edu/concern/etds/0r9673801?locale=en


Advances in technology have led to generation of enormous amounts of data in many fields including medicine, presenting challenges in data analysis. The reason could be processor, memory, or disk storage bottlenecks in computational environments. These challenges are particularly pronounced for Bayesian analysis, which often entails the use of Markov chain Monte Carlo (MCMC) in computation. As such, a number of scalable MCMC algorithms have been developed to alleviate the computational challenges in three main directions. The first direction is to accelerate expensive gradient computation at each MCMC iteration. The second direction is to parallelize computation at each MCMC iteration, requiring potentially expensive communication within each iteration. The third direction is to divide a data set into small subsets and run independent MCMC for each subset before combining them. This work focuses on scalable MCMC algorithms developed in the third direction. We conduct simulation studies to evaluate and compare several parallel MCMC algorithms. Examples of scalable MCMC are shown for Bayesian linear regression and other regressions.

Table of Contents

1. Introduction

1.1 Background

1.2 Current Approaches

1.2.1 Nonparallel Accelerating Approach

1.2.2 Communication-Intense Parallel Approach

1.2.3 Communication-Free Parallel Approach

1.3 General Comparisons

2. Analysis of MCMC Algorithms and Computational Challenges

2.1 Overview

2.2 Algorithms in Nonparallel Accelerating Approach

2.3 Communication-Intense Parallel Algorithms

2.4 Communication-Free Parallel Algorithms

3. Simulation Study

3.1 Goals

3.2 Simulation Settings

3.3 Performance Metrics

3.4 Results

4. Discussion


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