Bayesian spatial monotonic multiple regression

• 成果类型: Article
• 署名作者: Rohrbeck, C.; Costain, D. A.; Frigessi, A.
• 署名单位: Lancaster University; University of Oslo
• 刊物名称: BIOMETRIKA
• ISSN/ISSBN: 0006-3444
• DOI: 10.1093/biomet/asy019
• 发表日期: 2018
• 页码: 691707
• 关键词: geographically weighted regression; isotonic regression; testing monotonicity; MODEL; distributions; optimization; computation; Consistency; statistics; Lasso

摘要

We consider monotonic, multiple regression for contiguous regions. The regression functions vary regionally and may exhibit spatial structure. We develop Bayesian nonparametric methodology that permits estimation of both continuous and discontinuous functional shapes using marked point process and reversible jump Markov chain Monte Carlo techniques. Spatial dependence is incorporated by a flexible prior distribution which is tuned using crossvalidation and Bayesian optimization. We derive the mean and variance of the prior induced by the marked point process approach. Asymptotic results show consistency of the estimated functions. Posterior realizations enable variable selection, the detection of discontinuities and prediction. In simulations and in an application to a Norwegian insurance dataset, our method shows better performance than existing approaches.