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Title: Bayesian variable selection in double generalized linear Tweedie spatial process models Authors:  Aritra Halder - University of Virginia (United States) [presenting]
Abstract: Double generalized linear models provide a flexible framework for modeling data by allowing the mean and the dispersion to vary across observations. Common members of the exponential dispersion family including Gaussian, compound Poisson-gamma, Gamma, and inverse-Gaussian, are known to admit such models. However, the lack of their use can be attributed to ambiguities that exist in the model specification under a large number of covariates and complications that arise when data from a chosen application displays dependence. We consider a hierarchical specification for these models with a spatial random effect. The spatial effect is targeted at performing uncertainty quantification by modeling dependence within the data arising from location-based indexing of the response. We focus on a Gaussian process specification for the spatial effect. Simultaneously we tackle the problem of the model specification under such hierarchical spatial process models using Bayesian variable selection, which is effected through a continuous spike and slab prior on the model parameters (or fixed effects). The novelty lies in the Bayesian frameworks developed for such models which have not been explored previously. We perform various synthetic experiments to showcase the accuracy of our frameworks. These developed frameworks are then applied to analyse automobile insurance premiums in Connecticut.