AUTHORS: Jinjian Mu, Guanyu Hu, Lynn Kuo

Download as PDF

Poisson regression model is commonly used to model count data. In many scenarios, the data are collected from various locations so spatially varying coefficient Poisson regression model is developed to adjust for spatial dependence. We propose a Bayesian variable selection method for Poisson regression model with spatially varying coefficients. Considering computation efficiency we assign a conjugate multivariate log-gamma (MLG) prior to the regression coefficients and further incorporate the spatial information into the covariance matrix. We apply the horseshoe prior to facilitate a robust variable selection method with computational efficiency and build a MCMC algorithm for the posterior inference.

KEYWORDS: Spatial Poisson Model, Bayesian Variable Selection, MLG Prior, Horseshoe Prior, MCMC

REFERENCES:

[ 1] J. R. Bradley, S. H. Holan, C. K. Wikle, et al. Computationally efficient multivariate spatio-temporal models for high-dimensional count-valued data (with discussion). Bayesian Analysis, 13(1):253–310, 2018.

[2] C. M. Carvalho, N. G. Polson, and J. G. Scott. Handling sparsity via the horseshoe. In International Conference on Artificial Intelligence and Statistics, pages 73–80, 2009.

[3] C. M. Carvalho, N. G. Polson, and J. G. Scott. The horseshoe estimator for sparse signals. Biometrika, 97(2):465–480, 2010.

[4] P. J. Diggle, J. A. Tawn, and R. Moyeed. Modelbased geostatistics. Journal of the Royal Statistical Society: Series C (Applied Statistics), 47(3):299–350, 1998.

[5] A. E. Gelfand, H.-J. Kim, C. Sirmans, and S. Banerjee. Spatial modeling with spatially varying coefficient processes. Journal of the American Statistical Association, 98(462):387–396, 2003.

[6] J. Mu, G. Hu, and L. Kuo. Bayesian variable selection for poisson regression with spatially varying coefficients with applications to connecticut adolescent suicide data. unpublished, N.D.