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A Uniform Shrinkage Prior in Spatiotemporal Poisson Models for Count Data

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Modern Statistical Methods for Health Research

Part of the book series: Emerging Topics in Statistics and Biostatistics ((ETSB))

Abstract

We consider default Bayesian inference in a Poisson generalized linear mixed model for spatiotemporal data. Normal random effects are used to model the within-area correlation over time, and spatial effects represented with a proper conditional autoregressive (CAR) model are used to model the between-area correlations. We develop a uniform shrinkage prior (USP) for the variance components of the spatiotemporal random effects. We prove that the proposed USP is proper, and the resulting posterior is proper under the proposed USP, an independent flat prior for each fixed effect, and a uniform prior for a spatial parameter, under suitable conditions. Posterior simulation is implemented and inference made using the OpenBUGS, R2OpenBUGS, and RStan software packages. We illustrate the proposed method by applying it to a leptospirosis count dataset with observations from 17 northern provinces of Thailand across four quarters in 2011 to construct the disease maps. According to the deviance information criterion, the proposed USP for the variance components of the spatiotemporal effects yields a better performance than the conventional inverse gamma priors. A simulation study suggests that the estimated fixed-effect parameters are accurate, based on a relative bias criterion. The leptospirosis data analysis indicates that the top ten estimated leptospirosis morbidity rates (per 100,000 population), ranging from the highest to the lowest, are in Nan (Quarter (Q) 3, 9.8060), Chiang Rai (Q3, 3.1010), Nan (Q2, 3.0190), Nan (Q4, 2.2370), Nan (Q1, 2.2330), Phitsanulok (Q3, 2.2240), Lampang (Q3, 1.7890), Uttaradit (Q3, 1.5230), Phrae (Q3, 1.4720), and Phetchabun (Q3, 1.4380) provinces, respectively.

Krisada Lekdee and Chao Yang co-first author.

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Author information

Authors and Affiliations

  1. Faculty of Science and Technology, Department of Mathematics and Statistics, Rajamangala University of Technology Phra Nakhon, Bangkok, Thailand

    Krisada Lekdee

  2. Department of Biostatistics, University of Texas MD Anderson Cancer Center, Houston, TX, USA

    Chao Yang & Yisheng Li

  3. Faculty of Science, Department of Statistics, Kasetsart University, Bangkok, Thailand

    Lily Ingsrisawang

Authors
  1. Krisada Lekdee
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  2. Chao Yang
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  3. Lily Ingsrisawang
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  4. Yisheng Li
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Correspondence to Yisheng Li .

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Editors and Affiliations

  1. Department of Mathematics & Statistics, Georgia State University, Atlanta, GA, USA

    Yichuan Zhao

  2. School of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal, KwaZulu-Natal, South Africa

    (Din) Ding-Geng Chen

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Lekdee, K., Yang, C., Ingsrisawang, L., Li, Y. (2021). A Uniform Shrinkage Prior in Spatiotemporal Poisson Models for Count Data. In: Zhao, Y., Chen, (.DG. (eds) Modern Statistical Methods for Health Research. Emerging Topics in Statistics and Biostatistics . Springer, Cham. https://doi.org/10.1007/978-3-030-72437-5_4

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