Bayesian semiparametric regression analysis of multicategorical time-space data. (English) Zbl 0995.62098

Fahrmeir, Ludwig; Lang, Stefan

Ann. Inst. Stat. Math. 53, No. 1, 11-30 (2001).

Summary: We present a unified semiparametric Bayesian approach based on Markov random field priors for analyzing the dependence of multicategorical response variables on time, space and further covariates. The general model extends dynamic, or state space, models for categorical time series and longitudinal data by including spatial effects as well as nonlinear effects of metrical covariates in flexible semiparametric form.
Trend and seasonal components, different types of covariates and spatial effects are all treated within the same general framework by assigning appropriate priors with different forms and degrees of smoothness. Inference is fully Bayesian and uses MCMC techniques for posterior analysis. The approach in this paper is based on latent semiparametric utility models and is particularly useful for probit models. The methods are illustrated by applications to unemployment data and a forest damage survey.

MSC:

62M40	Random fields; image analysis
62F15	Bayesian inference
62M10	Time series, auto-correlation, regression, etc. in statistics (GARCH)
62M30	Inference from spatial processes

Keywords:

categorical time-space data; forest damage; latent utility models; Markov random fields; MCMC probit models; unemployment