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    Rights statement: 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

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Bayesian spatial monotonic multiple regression

Research output: Contribution to journalJournal articlepeer-review

Published
<mark>Journal publication date</mark>1/09/2018
<mark>Journal</mark>Biometrika
Issue number3
Volume105
Number of pages17
Pages (from-to)691-707
Publication StatusPublished
Early online date3/06/18
<mark>Original language</mark>English

Abstract

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.

Bibliographic note

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