TY - JOUR

T1 - Bayesian spatial monotonic multiple regression

AU - Rohrbeck, Christian

AU - Costain, Deborah Ann

AU - Frigessi, Arnoldo

N1 - This is a pre-copy-editing, author-produced PDF of an article accepted for publication in Biometrika following peer review. The definitive publisher-authenticated versionC Rohrbeck, D A Costain, A Frigessi; Bayesian spatial monotonic multiple regression, Biometrika, Volume 105, Issue 3, 1 September 2018, Pages 691–707, https://doi.org/10.1093/biomet/asy019 is available online at: https://academic.oup.com/biomet/article/105/3/691/5032572

PY - 2018/9/1

Y1 - 2018/9/1

N2 - 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 cross-validation 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 data set, our methodology shows better performance than existing approaches.

AB - 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 cross-validation 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 data set, our methodology shows better performance than existing approaches.

U2 - 10.1093/biomet/asy019

DO - 10.1093/biomet/asy019

M3 - Journal article

VL - 105

SP - 691

EP - 707

JO - Biometrika

JF - Biometrika

SN - 0006-3444

IS - 3

ER -