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Posterior inference for sparse hierarchical non-stationary models

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Monterrubio-Gomez, Karla, Roininen, Lassi, Wade, Sara, Damoulas, Theodoros and Girolami, Mark (2020) Posterior inference for sparse hierarchical non-stationary models. Computational Statistics & Data Analysis, 148 . 106954. doi:10.1016/j.csda.2020.106954

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Official URL: https://doi.org/10.1016/j.csda.2020.106954

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Abstract

Gaussian processes are valuable tools for non-parametric modelling, where typ- ically an assumption of stationarity is employed. While removing this assump- tion can improve prediction, fitting such models is challenging. In this work, hierarchical models are constructed based on Gaussian Markov random fields with stochastic spatially varying parameters. Importantly, this allows for non- stationarity while also addressing the computational burden through a sparse banded representation of the precision matrix. In this setting, efficient Markov chain Monte Carlo (MCMC) sampling is challenging due to the strong coupling a posteriori of the parameters and hyperparameters. We develop and compare three adaptive MCMC schemes and make use of banded matrix operations for faster inference. Furthermore, a novel extension to higher dimensional input spaces is proposed through an additive structure that retains the flexibility and scalability of the model, while also inheriting interpretability from the additive approach. A thorough assessment of the efficiency and accuracy of the meth- ods in nonstationary settings is presented for both simulated experiments and a computer emulation problem.

Item Type: Journal Article
Subjects: Q Science > QA Mathematics
Divisions: Faculty of Science > Computer Science
Faculty of Science > Statistics
Library of Congress Subject Headings (LCSH): Gaussian processes, Multilevel models (Statistics), Gaussian Markov random fields, Bayesian statistical decision theory, Machine learning
Journal or Publication Title: Computational Statistics & Data Analysis
Publisher: Elsevier Science Ltd
ISSN: 0167-9473
Official Date: August 2020
Dates:
DateEvent
August 2020Published
19 March 2020Available
8 March 2020Accepted
Volume: 148
Article Number: 106954
DOI: 10.1016/j.csda.2020.106954
Status: Peer Reviewed
Publication Status: Published
Access rights to Published version: Restricted or Subscription Access
Copyright Holders: © 2020 Elsevier B.V. All rights reserved
RIOXX Funder/Project Grant:
Project/Grant IDRIOXX Funder NameFunder ID
CVU609843Consejo Nacional de Ciencia y Tecnologíahttp://dx.doi.org/10.13039/501100003141
EP/K034154/1[EPSRC] Engineering and Physical Sciences Research Councilhttp://dx.doi.org/10.13039/501100000266
326240Academy of Finlandhttp://dx.doi.org/10.13039/501100002341
326341Academy of Finlandhttp://dx.doi.org/10.13039/501100002341
Lloyds Register Foundation programme on data-centric engineeringAlan Turing Institutehttp://dx.doi.org/10.13039/100012338
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