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

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
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