“A Theoretical Development and Simulation-Based Comparison of Four Parameter Estimation Methods for the Spatio-Temporal Autologistic Model with Emphasis on Maximum Generalized and Block Generalized Pseudolikelihood”
Document Type
Presentation Abstract
Presentation Date
4-26-2012
Abstract
A regular lattice of spatially dependent binary observations is often modeled using the autologistic model. It is well known that likelihood-based inference methods cannot be employed in the usual way to estimate the parameters of the autologistic model due to the intractability of the normalizing constant for the corresponding joint likelihood. Two popular and vastly contrasting approaches to parameter estimation for the autologistic model are maximum pseudolikelihood (PL) and Markov Chain Monte Carlo Maximum Likelihood (MCMCML). Two newer and less understood approaches are maximum generalized pseudolikelihood (GPL) and maximum block generalized pseudolikelihood (BGPL). Both of these newer methods represent varying degrees of compromise between maximum pseudolikelihood and MCMCML.
In this defense we will establish the strong consistency of the estimators resulting from both GPL and BGPL, and we will additionally present generalizations of GPL and BGPL for use in the space-time domain. The relative performances of all four estimation methods from a large-scale autologistic model simulation study, as well as from a small-scale spatio-temporal autologistic model simulation study, will be presented. Finally, all four estimation methods will be implemented to describe the spread of fire occurrence in a temperate grasslands ecosystem of Oregon and Washington using the autologistic model.
Recommended Citation
Purdy, Jordan Earl, "“A Theoretical Development and Simulation-Based Comparison of Four Parameter Estimation Methods for the Spatio-Temporal Autologistic Model with Emphasis on Maximum Generalized and Block Generalized Pseudolikelihood”" (2012). Colloquia of the Department of Mathematical Sciences. 398.
https://scholarworks.umt.edu/mathcolloquia/398
Additional Details
Doctoral Dissertation Defense. Link to the presenter's dissertation.
Dissertation Committee:Jon Graham, Chair (Mathematical Sciences),
Johnathan M. Bardsley (Mathematical Sciences),
Solomon W. Harrar (Mathematical Sciences),
Jesse V. Johnson (Computer Science),
David Patterson (Mathematical Sciences) Thursday, April 26, 2012
3:10 pm in Math 108