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 . (In Press)

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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
Divisions:	Faculty of Science > Computer Science Faculty of Science > Statistics
Journal or Publication Title:	Computational Statistics & Data Analysis
Publisher:	Elsevier Science Ltd
ISSN:	0167-9473
Official Date:	2 March 2020
Dates:	Date Event 2 March 2020 Accepted
Date of first compliant deposit:	4 March 2020
Status:	Peer Reviewed
Publication Status:	In Press
Access rights to Published version:	Restricted or Subscription Access
Related URLs:	Publisher

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