Computational Methods and Spatial Models with Intractable Likelihoods
Restricted (Penn State Only)
- Author:
- Kang, Bokgyeong
- Graduate Program:
- Statistics
- Degree:
- Doctor of Philosophy
- Document Type:
- Dissertation
- Date of Defense:
- June 14, 2023
- Committee Members:
- Bing Li, Professor in Charge/Director of Graduate Studies
Matthew Ferrari, Outside Unit & Field Member
Stephen Berg, Major Field Member
Bharath Kumar Sriperumbudur, Major Field Member
John Hughes, Special Member
Murali Haran, Chair & Dissertation Advisor - Keywords:
- Intractable likelihood
Hawkes process
Sample quality measure
Markov chain Monte Carlo
Spatially-varying dispersion
Zero inflation
Conway-Maxwell Poisson - Abstract:
- Advances in data collection and computing have enabled researchers to develop and employ complicated models that better describe complex phenomena in a wide range of disciplines. However, evaluating the likelihood functions of these models is often expensive or intractable. This has motivated the development of a variety of inferential methods that may or may not produce asymptotically exact estimates. My dissertation research focuses on developing computational methods to address important concerns with computationally challenging likelihood functions. I also study novel models for lattice and point process spatial data, and develop new computational methods to fit these models efficiently. My contributions are as follows. (1) Measuring sample quality produced by Monte Carlo algorithms for models with intractable normalizing functions. I develop two new sample quality measures that allow, for the first time, rigorous tuning of approximations, including those based on asymptotically inexact algorithms. I provide theoretical justifications for these methods along with extensive applications to complex models. (2) I develop a new spatial model for large zero-inflated spatial count data with under-and over-dispersion. This model, based on the Conway-Maxwell Poisson model, is potentially useful in disciplines such as ecology, criminology, and public health where such data are common. I also develop an efficient asymptotically exact Monte Carlo algorithm in order to fit this computationally challenging model. (3) Finally, I develop a computationally efficient approach that reliably approximates the intractable likelihood functions of self-exciting spatiotemporal point processes.