Bayesian spatial monotonic multiple regression
提出一种贝叶斯非参数方法，利用标记点过程和可逆跳跃马尔可夫链蒙特卡洛技术，估计具有空间结构的连续和不连续单调回归函数，并通过挪威保险数据验证其优于现有方法。
SummaryWe 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.