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Bayesian Modeling of Discrete-Time Point-Referenced Spatio-Temporal Data

  • Review Article
  • Published:
Journal of the Indian Institute of Science Aims and scope

Abstract

Discrete-time point-referenced spatio-temporal data are obtained by collecting observations at arbitrary but fixed spatial locations \(\varvec{s}_{1},\varvec{s}_{2},\ldots ,\varvec{s}_{n}\) at regular intervals of time \(t := 1,2,\ldots ,T\). They are encountered routinely in meteorological and environmental studies. Gaussian linear dynamic spatio-temporal models (LDSTMs) are the most widely used models for fitting and prediction with them. While Gaussian LDSTMs demonstrate good predictive performance at a wide range of scenarios, discrete-time point-referenced spatio-temporal data, often being the end product of complex interactions among environmental processes, are better modeled by nonlinear dynamic spatio-temporal models (NLDSTMs). Several such nonlinear models have been proposed in the context of precipitation, deposition, and sea-surface temperature modeling. Some of the above-mentioned models, although are fitted classically, dynamic spatio-temporal models with their complex dependence structure, are more naturally accommodated within the fully Bayesian framework. In this article, we review many such linear and nonlinear Bayesian models for discrete-time point-referenced spatio-temporal data. As we go along, we also review some nonparametric spatio-temporal models as well as some recently proposed Bayesian models for massive spatio-temporal data.

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Notes

  1. Cressie and Wikle17 covered a wide range of materials on spatio-temporal modeling that serves as the main resource for many of the models that we cite subsequently.

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Acknowledgements

We would like to thank an anonymous referee whose suggestions lead to an improvement of the review article.

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Authors and Affiliations

  1. Department of Statistics, Presidency University Kolkata, 86/1 College Street, Kolkata, 700073, India

    Suman Guha

  2. Interdisciplinary Statistical Research Unit, Indian Statistical Institute, Kolkata, 203, B. T. Road, Kolkata, 700108, India

    Sourabh Bhattacharya

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  1. Suman Guha
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Correspondence to Suman Guha.

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Guha, S., Bhattacharya, S. Bayesian Modeling of Discrete-Time Point-Referenced Spatio-Temporal Data. J Indian Inst Sci 102, 1189–1204 (2022). https://doi.org/10.1007/s41745-022-00298-w

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