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Methods of Model Uncertainty: Bayesian Spatial Predictive Synthesis
Cabel, Danielle
Cabel, Danielle
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Thesis/Dissertation
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2024-05
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Statistics
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http://dx.doi.org/10.34944/dspace/10296
Abstract
This dissertation develops a new method of modeling uncertainty with spatial data called Bayesian spatial predictive synthesis (BSPS) and compares its predictive accuracy to established methods. Spatial data are often non-linear, complex, and difficult to capture with a single model. Existing methods such as model selection or simple model ensembling fail to consider the critical spatially varying model uncertainty problem; different models perform better or worse in different regions. BSPS can capture the model uncertainty by specifying a latent factor coefficient model that varies spatially as a synthesis function. This allows the model coefficients to vary across a region to achieve flexible spatial model ensembling. This method is derived from the theoretically best approximation of the data generating process (DGP), where the predictions are exact minimax. Two Markov chain Monte Carlo (MCMC) based algorithms are implemented in the BSPS framework for full uncertainty quantification, along with a variational Bayes strategy for faster point inference. This method is also extended for general responses. The examples in this dissertation include multiple simulation studies and two real world data applications. Through these examples, the performance and predictive power of BSPS is shown against various standard spatial models, ensemble methods, and machine learning methods. BSPS is able to maintain predictive accuracy as well as maintain interpretability of the prediction mechanisms.
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