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Dynamically updated spatially varying parameterizations of hierarchical Bayesian models for spatial data

Dynamically updated spatially varying parameterizations of hierarchical Bayesian models for spatial data
Dynamically updated spatially varying parameterizations of hierarchical Bayesian models for spatial data
Fitting hierarchical Bayesian models to spatially correlated data sets using Markov chain Monte Carlo (MCMC) techniques is computationally expensive. Complicated covariance structures of the underlying spatial processes, together with high dimensional parameter space, mean that the number of calculations required grows cubically with the number of spatial locations at each MCMC iteration. This necessitates the need for efficient model parameterisations that hasten the convergence and improve the mixing of the associated algorithms. We consider partially centred parameterisations (PCPs) which lie on a continuum between what are known as the centred (CP) and noncentered parameterisations (NCP). By introducing a weight matrix we remove the conditional posterior correlation between the fixed and the random effects, and hence construct a PCP which achieves immediate convergence for a three stage model, based on multiple Gaussian processes with known covariance parameters. When the covariance parameters are unknown we dynamically update the parameterisation within the sampler. The PCP outperforms both the CP and the NCP and leads to a fully automated algorithm which has been demonstrated in two simulation examples. The effectiveness of the spatially varying PCP is illustrated with a practical data set of nitrogen dioxide concentration levels. Supplemental materials consisting of appendices, data sets and computer code to reproduce the results are available online.
1061-8600
105-116
Bass, Mark
53ed9f53-65a0-41bf-904b-1f4e73cc8365
Sahu, Sujit
33f1386d-6d73-4b60-a796-d626721f72bf
Bass, Mark
53ed9f53-65a0-41bf-904b-1f4e73cc8365
Sahu, Sujit
33f1386d-6d73-4b60-a796-d626721f72bf

Bass, Mark and Sahu, Sujit (2019) Dynamically updated spatially varying parameterizations of hierarchical Bayesian models for spatial data. Journal of Computational and Graphical Statistics, 28 (1), 105-116. (doi:10.1080/10618600.2018.1482761).

Record type: Article

Abstract

Fitting hierarchical Bayesian models to spatially correlated data sets using Markov chain Monte Carlo (MCMC) techniques is computationally expensive. Complicated covariance structures of the underlying spatial processes, together with high dimensional parameter space, mean that the number of calculations required grows cubically with the number of spatial locations at each MCMC iteration. This necessitates the need for efficient model parameterisations that hasten the convergence and improve the mixing of the associated algorithms. We consider partially centred parameterisations (PCPs) which lie on a continuum between what are known as the centred (CP) and noncentered parameterisations (NCP). By introducing a weight matrix we remove the conditional posterior correlation between the fixed and the random effects, and hence construct a PCP which achieves immediate convergence for a three stage model, based on multiple Gaussian processes with known covariance parameters. When the covariance parameters are unknown we dynamically update the parameterisation within the sampler. The PCP outperforms both the CP and the NCP and leads to a fully automated algorithm which has been demonstrated in two simulation examples. The effectiveness of the spatially varying PCP is illustrated with a practical data set of nitrogen dioxide concentration levels. Supplemental materials consisting of appendices, data sets and computer code to reproduce the results are available online.

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Accepted/In Press date: 17 May 2018
e-pub ahead of print date: 19 September 2018
Published date: January 2019

Identifiers

Local EPrints ID: 421012
URI: http://eprints.soton.ac.uk/id/eprint/421012
ISSN: 1061-8600
PURE UUID: 6066da81-c02a-4b73-94b4-8f1a95d2e5b2
ORCID for Sujit Sahu: ORCID iD orcid.org/0000-0003-2315-3598

Catalogue record

Date deposited: 21 May 2018 16:30
Last modified: 27 Jan 2020 13:38

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