PICAR: An Efficient Extendable Approach for Fitting Hierarchical Spatial Models

Hierarchical spatial models are very flexible and popular for a vast array of applications in areas such as ecology, social science, public health, and atmospheric science. It is common to carry out Bayesian inference for these models via Markov chain Monte Carlo (MCMC). Each iteration of the MCMC a...

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Published in:Technometrics Vol. 64; no. 2; pp. 187 - 198
Main Authors: Lee, Ben Seiyon, Haran, Murali
Format: Journal Article
Language:English
Published: Alexandria Taylor & Francis 03.04.2022
American Society for Quality
Subjects:
Algorithms
Arrays
Atmospheric models
Basis functions
Basis representation
Bayesian analysis
Cloud cover
Computational efficiency
Computing costs
Cross correlation
Fields (mathematics)
Finite element method
Gaussian random field
Iterative methods
Markov analysis
Markov chain Monte Carlo
Markov chains
Monte Carlo simulation
Non-Gaussian spatial data
Ordinal spatial data
Predictions
Programming languages
Public health
Spatial data
Spatially varying coefficients
Statistical inference
ISSN:0040-1706, 1537-2723
Online Access:Get full text
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Summary:Hierarchical spatial models are very flexible and popular for a vast array of applications in areas such as ecology, social science, public health, and atmospheric science. It is common to carry out Bayesian inference for these models via Markov chain Monte Carlo (MCMC). Each iteration of the MCMC algorithm is computationally expensive due to costly matrix operations. In addition, the MCMC algorithm needs to be run for more iterations because the strong cross-correlations among the spatial latent variables result in slow mixing Markov chains. To address these computational challenges, we propose a projection-based intrinsic conditional autoregression (PICAR) approach, which is a discretized and dimension-reduced representation of the underlying spatial random field using empirical basis functions on a triangular mesh. Our approach exhibits fast mixing as well as a considerable reduction in computational cost per iteration. PICAR is computationally efficient and scales well to high dimensions. It is also automated and easy to implement for a wide array of user-specified hierarchical spatial models. We show, via simulation studies, that our approach performs well in terms of parameter inference and prediction. We provide several examples to illustrate the applicability of our method, including (i) a high-dimensional cloud cover dataset that showcases its computational efficiency, (ii) a spatially varying coefficient model that demonstrates the ease of implementation of PICAR in the probabilistic programming languages stan and nimble, and (iii) a watershed survey example that illustrates how PICAR applies to models that are not amenable to efficient inference via existing methods.
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ISSN:0040-1706
1537-2723
DOI:10.1080/00401706.2021.1933596