Posterior inference for sparse hierarchical non-stationary models

Karla Monterrubio-Gómez, Lassi Roininen, Sara Wade, Theodoros Damoulas and Mark Girolami

Computational Statistics & Data Analysis, 2020, vol. 148, issue C

Abstract: Gaussian processes are valuable tools for non-parametric modelling, where typically an assumption of stationarity is employed. While removing this assumption can improve prediction, fitting such models is challenging. 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. Three adaptive MCMC schemes are developed and compared making 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 methods in nonstationary settings is presented for both simulated experiments and a computer emulation problem.

Keywords: Gaussian process; Multilevel models; Gaussian Markov random fields; MCMC; SPDE (search for similar items in EconPapers)
Date: 2020
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Persistent link: https://EconPapers.repec.org/RePEc:eee:csdana:v:148:y:2020:i:c:s0167947320300451

DOI: 10.1016/j.csda.2020.106954

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