Purdue University Graduate School
Browse

File(s) under embargo

11

month(s)

8

day(s)

until file(s) become available

ESSAYS ON SCALABLE BAYESIAN NONPARAMETRIC AND SEMIPARAMETRIC MODELS

thesis
posted on 2024-03-29, 20:56 authored by Chenzhong WuChenzhong Wu

In this thesis, we delve into the exploration of several nonparametric and semiparametric econometric models within the Bayesian framework, highlighting their applicability across a broad spectrum of microeconomic and macroeconomic issues. Positioned in the big data era, where data collection and storage expand at an unprecedented rate, the complexity of economic questions we aim to address is similarly escalating. This dual challenge ne- cessitates leveraging increasingly large datasets, thereby underscoring the critical need for designing flexible Bayesian priors and developing scalable, efficient algorithms tailored for high-dimensional datasets.

The initial two chapters, Chapter 2 and 3, are dedicated to crafting Bayesian priors suited for environments laden with a vast array of variables. These priors, alongside their corresponding algorithms, are optimized for computational efficiency, scalability to extensive datasets, and, ideally, distributability. We aim for these priors to accommodate varying levels of dataset sparsity. Chapter 2 assesses nonparametric additive models, employing a smoothing prior alongside a band matrix for each additive component. Utilizing the Bayesian backfitting algorithm significantly alleviates the computational load. In Chapter 3, we address multiple linear regression settings by adopting a flexible scale mixture of normal priors for coefficient parameters, thus allowing data-driven determination of the necessary amount of shrinkage. The use of a conjugate prior enables a closed-form solution for the posterior, markedly enhancing computational speed.

The subsequent chapters, Chapter 4 and 5, pivot towards time series dataset model- ing and Bayesian algorithms. A semiparametric modeling approach dissects the stochastic volatility in macro time series into persistent and transitory components, the latter addi- tional component addressing outliers. Utilizing a Dirichlet process mixture prior for the transitory part and a collapsed Gibbs sampling algorithm, we devise a method capable of efficiently processing over 10,000 observations and 200 variables. Chapter 4 introduces a simple univariate model, while Chapter 5 presents comprehensive Bayesian VARs. Our al- gorithms, more efficient and effective in managing outliers than existing ones, are adept at handling extensive macro datasets with hundreds of variables.

History

Degree Type

  • Doctor of Philosophy

Department

  • Economics

Campus location

  • West Lafayette

Advisor/Supervisor/Committee Chair

Dr. Joshua Chan

Additional Committee Member 2

Dr. Justin Tobias

Additional Committee Member 3

Dr. Mohitosh Kejriwal

Additional Committee Member 4

Dr. Xiao Wang