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Continuous inference for aggregated point process data

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  • Benjamin M. Taylor
  • Ricardo Andrade‐Pacheco
  • Hugh J. W. Sturrock

Abstract

The paper introduces new methods for inference with count data registered on a set of aggregation units. Such data are omnipresent in epidemiology because of confidentiality issues: it is much more common to know the county in which an individual resides, say, than to know their exact location in space. Inference for aggregated data has traditionally made use of models for discrete spatial variation, e.g. conditional auto‐regressive models. We argue that such discrete models can be improved from both a scientific and an inferential perspective by using spatiotemporally continuous models to model the aggregated counts directly. We introduce methods for delivering (limiting) continuous inference with spatiotemporal aggregated count data in which the aggregation units might change over time and are subject to uncertainty. We illustrate our methods by using two examples: from epidemiology, spatial prediction of malaria incidence in Namibia, and, from politics, forecasting voting under the proposed changes to parliamentary boundaries in the UK.

Suggested Citation

  • Benjamin M. Taylor & Ricardo Andrade‐Pacheco & Hugh J. W. Sturrock, 2018. "Continuous inference for aggregated point process data," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 181(4), pages 1125-1150, October.
  • Handle: RePEc:bla:jorssa:v:181:y:2018:i:4:p:1125-1150
    DOI: 10.1111/rssa.12347
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    File URL: https://doi.org/10.1111/rssa.12347
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    References listed on IDEAS

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    1. Taylor, Benjamin M. & Davies, Tilman M. & Rowlingson, Barry S. & Diggle, Peter J., 2015. "Bayesian Inference and Data Augmentation Schemes for Spatial, Spatiotemporal and Multivariate Log-Gaussian Cox Processes in R," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 63(i07).
    2. Montserrat Fuentes & Adrian E. Raftery, 2005. "Model Evaluation and Spatial Interpolation by Bayesian Combination of Observations with Outputs from Numerical Models," Biometrics, The International Biometric Society, vol. 61(1), pages 36-45, March.
    3. Peter J. Diggle & Raquel Menezes & Ting‐li Su, 2010. "Geostatistical inference under preferential sampling," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 59(2), pages 191-232, March.
    4. Anders Brix & Peter J. Diggle, 2001. "Spatiotemporal prediction for log‐Gaussian Cox processes," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 63(4), pages 823-841.
    5. Zhang, Hao, 2004. "Inconsistent Estimation and Asymptotically Equal Interpolations in Model-Based Geostatistics," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 250-261, January.
    6. Mark Girolami & Ben Calderhead, 2011. "Riemann manifold Langevin and Hamiltonian Monte Carlo methods," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 73(2), pages 123-214, March.
    7. Diggle, Peter J. & Guan, Yongtao & Hart, Anthony C. & Paize, Fauzia & Stanton, Michelle, 2010. "Estimating Individual-Level Risk in Spatial Epidemiology Using Spatially Aggregated Information on the Population at Risk," Journal of the American Statistical Association, American Statistical Association, vol. 105(492), pages 1394-1402.
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