Bayesian Variable Selection in Double Generalized Linear Tweedie Spatial Process Models
Volume 1, Issue 2 (2023), pp. 187–199
Pub. online: 19 June 2023
Type: Methodology Article
Open Access
Open Access
Area: Statistical Methodology
1
Equal contribution.
Accepted
31 May 2023
31 May 2023
Published
19 June 2023
19 June 2023
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 the Gaussian, Poisson, compound Poisson-gamma (CP-g), Gamma and inverse-Gaussian are known to admit such models. The lack of their use can be attributed to ambiguities that exist in model specification under a large number of covariates and complications that arise when data display complex spatial dependence. In this work we consider a hierarchical specification for the CP-g model 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 model specification for such models using Bayesian variable selection. It is effected through a continuous spike and slab prior on the model parameters, specifically the fixed effects. The novelty of our contribution lies in the Bayesian frameworks developed for such models. We perform various synthetic experiments to showcase the accuracy of our frameworks. They are then applied to analyze automobile insurance premiums in Connecticut, for the year of 2008.
Supplementary material
Supplementary MaterialSupplementary Material containing further details as described in Section 4 is available online. The R –package is available for installation and deployment at: https://github.com/arh926/sptwdglm.
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