COMPUTATIONAL METHODS FOR MODELS WITH INTRACTABLE NORMALIZING FUNCTIONS

Open Access
- Author:
- Park, Jaewoo
- Graduate Program:
- Statistics
- Degree:
- Doctor of Philosophy
- Document Type:
- Dissertation
- Date of Defense:
- May 14, 2019
- Committee Members:
- Murali Haran, Dissertation Advisor/Co-Advisor
Murali Haran, Committee Chair/Co-Chair
Le Bao, Committee Member
Benjamin Adam Shaby, Committee Member
Matthew Joseph Ferrari, Outside Member - Keywords:
- Markov chain Monte Carlo
doubly intractable distributions
exponen- tial random graph models
Markov point processes
importance sampling
Gaussian processes
non-Gaussian spatial data
dimension reduction
Monte Carlo maximum likelihood - Abstract:
- My dissertation research focuses on computational methods for intractable likelihoods, and modeling high-dimensional and non-Gaussian spatial data. The models I consider are important for a wide variety of applications, from studying the spread of infectious diseases to modeling social networks, to analyzing environmental data like satellite images of ice sheets. My dissertation consists of three projects: (1) Studying Bayesian approaches for models with intractable normalizing functions. This involves comparing the statistical and computational efficiency of recently developed algorithms, and providing a framework for understanding and contrasting the approaches. (2) A function emulation approach for models with intractable normalizing functions. This involves developing a fast two-stage approximation for intractable normalizing functions which enables Bayesian inference for large data sets. (3) A projection-based Monte Carlo maximum likelihood approach for high-dimensional non-Gaussian spatial data. The computational methods developed here are of broad interest, for example by providing general insights into practical and theoretical issues with the implementation of Monte Carlo maximum likelihood methods for latent variable models, and by developing general function approximation strategies that may be useful for computationally expensive likelihood functions.