Bayesian Spatial Monotonic Multiple Regression

We consider monotonic, multiple regression for a set of contiguous regions (lattice data). The regression functions permissibly vary between regions and exhibit geographical structure. We develop new Bayesian non-parametric methodology which allows for both continuous and discontinuous functional shapes and which are estimated using marked point processes and reversible jump Markov Chain Monte Carlo techniques. Geographical dependency is incorporated by a flexible prior distribution; the parametrisation allows the dependency to vary with functional level. The approach is tuned using Bayesian global optimization and cross-validation. Estimates enable variable selection, threshold detection and prediction as well as the extrapolation of the regression function. Performance and flexibility of our approach is illustrated by simulation studies and an application to a Norwegian insurance data set.