A Bayesian latent process spatiotemporal regression model for areal count data.

Model-based approaches for the analysis of areal count data are commonplace in spatiotemporal analysis. In Bayesian hierarchical models, a latent process is incorporated in the mean function to account for dependence in space and time. Typically, the latent process is modelled using a conditional autoregressive (CAR) prior. The aim of this paper is to offer an alternative approach to CAR-based priors for modelling the latent process. The proposed approach is based on a spatiotemporal generalization of a latent process Poisson regression model developed in a time series setting. Spatiotemporal dependence in the autoregressive model for the latent process is modelled through its transition matrix, with a structured covariance matrix specified for its error term. The proposed model and its parameterizations are fitted in a Bayesian framework implemented via MCMC techniques. Our findings based on real-life examples show that the proposed approach is at least as effective as CAR-based models.

[1]  W. Wong,et al.  The calculation of posterior distributions by data augmentation , 1987 .

[2]  Bradley P. Carlin,et al.  Hierarchical Spatio-Temporal Mapping of Disease Rates , 1997 .

[3]  Duncan Lee,et al.  A spatio-temporal model for estimating the long-term effects of air pollution on respiratory hospital admissions in Greater London. , 2014, Spatial and spatio-temporal epidemiology.

[4]  S. Zeger.  A regression model for time series of counts , 1988 .

[5]  D. Clayton,et al.  Bayesian analysis of space-time variation in disease risk. , 1995, Statistics in medicine.

[6]  John Geweke,et al.  Evaluating the accuracy of sampling-based approaches to the calculation of posterior moments , 1991 .

[7]  P. Pfeifer,et al.  A Three-Stage Iterative Procedure for Space-Time Modeling , 1980 .

[8]  P. Moran.  Notes on continuous stochastic phenomena. , 1950, Biometrika.

[9]  Aki Vehtari,et al.  Practical Bayesian model evaluation using leave-one-out cross-validation and WAIC , 2015, Statistics and Computing.

[10]  M. Cameletti,et al.  Spatial and Spatio-temporal Bayesian Models with R - INLA , 2015 .

[11]  Duncan Lee,et al.  A comparison of conditional autoregressive models used in Bayesian disease mapping. , 2011, Spatial and spatio-temporal epidemiology.

[12]  Duncan Lee,et al.  CARBayes: An R Package for Bayesian Spatial Modeling with Conditional Autoregressive Priors , 2013 .

[13]  P. Pfeifer,et al.  A Three-Stage Iterative Procedure for Space-Time Modeling Phillip , 2012 .

[14]  B P Carlin,et al.  Spatio-temporal models with errors in covariates: mapping Ohio lung cancer mortality. , 1998, Statistics in medicine.

[15]  A. Lawson,et al.  Cluster detection and risk estimation for spatio-temporal health data , 2014, 1408.1191.

[16]  L. M. Berliner,et al.  Hierarchical Bayesian space-time models , 1998, Environmental and Ecological Statistics.

[17]  Christopher K. Wikle,et al.  Estimation of Parameterized Spatio-Temporal Dynamic Models , 2007 .

[18]  Renato M. Assunção,et al.  Space varying coefficient models for small area data , 2003 .

[19]  C Pascutto,et al.  Statistical issues in the analysis of disease mapping data. , 2000, Statistics in medicine.

[20]  David S. Stoffer,et al.  Estimation and Identification of Space-Time ARMAX Models in the Presence of Missing Data , 1986 .

[21]  Sumio Watanabe,et al.  Asymptotic Equivalence of Bayes Cross Validation and Widely Applicable Information Criterion in Singular Learning Theory , 2010, J. Mach. Learn. Res..

[22]  Aki Vehtari,et al.  Understanding predictive information criteria for Bayesian models , 2013, Statistics and Computing.

[23]  J. Besag,et al.  Bayesian image restoration, with two applications in spatial statistics , 1991 .

[24]  A. Lawson,et al.  Spatio-temporal patterning of small area low birth weight incidence and its correlates: a latent spatial structure approach. , 2011, Spatial and spatio-temporal epidemiology.

[25]  Duncan Lee,et al.  Quantifying the Spatial Inequality and Temporal Trends in Maternal Smoking Rates in Glasgow. , 2016, The annals of applied statistics.

[26]  W. Dunsmuir,et al.  On autocorrelation in a Poisson regression model , 2000 .

[27]  Bradley P. Carlin,et al.  Hierarchical models for mapping Ohio lung cancer rates , 1997 .

[28]  Craig Anderson,et al.  A Comparison of Spatio-Temporal Disease Mapping Approaches Including an Application to Ischaemic Heart Disease in New South Wales, Australia , 2017, International journal of environmental research and public health.

[29]  L Knorr-Held,et al.  Modelling risk from a disease in time and space. , 1998, Statistics in medicine.

[30]  Richard A. Davis,et al.  Sparse Vector Autoregressive Modeling , 2012, 1207.0520.

[31]  Bradley P. Carlin,et al.  Bayesian measures of model complexity and fit , 2002 .

[32]  Sw. Banerjee,et al.  Hierarchical Modeling and Analysis for Spatial Data , 2003 .

[33]  Helmut Ltkepohl,et al.  New Introduction to Multiple Time Series Analysis , 2007 .

[34]  Duncan Lee,et al.  An adaptive spatiotemporal smoothing model for estimating trends and step changes in disease risk , 2014, 1411.0924.

[35]  Jon Wakefield,et al.  Disease mapping and spatial regression with count data. , 2007, Biostatistics.

[36]  Andrew B. Lawson,et al.  Bayesian disease mapping , 2013 .

[37]  Bayesian Single Changepoint Estimation in a Parameter‐driven Model , 2017 .

[38]  P S Albert,et al.  A latent process regression model for spatially correlated count data. , 1997, Biometrics.

[39]  Noel A Cressie,et al.  Statistics for Spatio-Temporal Data , 2011 .

[40]  R Core Team,et al.  R: A language and environment for statistical computing. , 2014 .

[41]  Dongmei Chen,et al.  A spatial–temporal analysis of low birth weight prevalence in Georgia, USA , 2013 .

[42]  Sylvia Richardson,et al.  A comparison of Bayesian spatial models for disease mapping , 2005, Statistical methods in medical research.

[43]  L Knorr-Held,et al.  Bayesian modelling of inseparable space-time variation in disease risk. , 2000, Statistics in medicine.

[44]  Norman E. Breslow,et al.  Estimation of Disease Rates in Small Areas: A new Mixed Model for Spatial Dependence , 2000 .