The marginal likelihood is a fundamental statistic for model comparison in a Bayesian framework. Spatial statistics is an area of growing importance as access to large quantities of geographical data is increasing. Bayes factors as a method for model selection is currently rarely used in the area. In this thesis several of the most prominent methods for estimating the marginal likelihood are reviewed, to see which methods would be best applied in a spatial statistics setting. It was found that the Laplace method, method of power posteriors, and steppingstone sampling gave the most promising results in initial testing. These three methods all proved to be highly accurate and precise. Laplace method is clearly the fastest of the methods, but steppingstone sampling and power posteriors should be more generalisable. However when applied to spatial models of the Matérn class specifically, due to the low dimensions of the models, the Laplace method proved to be the most effective as it was dramatically faster than the tempering methods and at least as accurate.
|Date of Award||13 Feb 2019|
|Supervisor||Merrilee Hurn (Supervisor) & Gavin Shaddick (Supervisor)|