Time-varying parameter distributional regression with dynamic global-local shrinkage process priors

Abstract

We consider regression models for exponential family distributions in which all distributional parameters are linked to covariates with time-varying regression coefficients. The coefficients follow dynamic global-local shrinkage process priors, which allow them to stay constant in some periods while moving rapidly or jumping in others. We develop a Gibbs sampling algorithm with three alternative updating steps for the coefficient trajectories. The samplers are based on Gaussian approximations and therefore target a perturbed posterior. Several strategies are proposed to improve sampling speed, robustness and accuracy. The degree of posterior perturbation is assessed by comparing with exact posterior inference from particle Gibbs with ancestor sampling. The coefficient innovations are defined so that they adapt automatically to the model geometry, the link functions, and the scale and covariance of the covariates. The approach is illustrated with a time-varying seasonal Poisson regression for UK bike rental demand and a Beta regression for US layoff proportions, with time-varying effects on both the mean and the precision. The algorithms will be made available in an open-source Julia package.