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Approximate methods in Bayesian point process spatial models

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  • Hossain, Md. Monir
  • Lawson, Andrew B.

Abstract

A range of point process models which are commonly used in spatial epidemiology applications for the increased incidence of disease are compared. The models considered vary from approximate methods to an exact method. The approximate methods include the Poisson process model and methods that are based on discretization of the study window. The exact method includes a marked point process model, i.e., the conditional logistic model. Apart from analyzing a real dataset (Lancashire larynx cancer data), a small simulation study is also carried out to examine the ability of these methods to recover known parameter values. The main results are as follows. In estimating the distance effect of larynx cancer incidences from the incinerator, the conditional logistic model and the binomial model for the discretized window perform relatively well. In explaining the spatial heterogeneity, the Poisson model (or the log Gaussian Cox process model) for the discretized window produces the best estimate.

Suggested Citation

  • Hossain, Md. Monir & Lawson, Andrew B., 2009. "Approximate methods in Bayesian point process spatial models," Computational Statistics & Data Analysis, Elsevier, vol. 53(8), pages 2831-2842, June.
    • Handle: RePEc:eee:csdana:v:53:y:2009:i:8:p:2831-2842
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    1. Julian Besag & Jeremy York & Annie Mollié, 1991. "Bayesian image restoration, with two applications in spatial statistics," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 43(1), pages 1-20, March.
    2. Mark Berman & T. Rolf Turner, 1992. "Approximating Point Process Likelihoods with Glim," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 41(1), pages 31-38, March.
    3. Fuentes, Montserrat, 2007. "Approximate Likelihood for Large Irregularly Spaced Spatial Data," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 321-331, March.
    4. Peter J. Diggle & Barry S. Rowlingson, 1994. "A Conditional Approach to Point Process Modelling of Elevated Risk," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 157(3), pages 433-440, May.
    5. Lawson, A. B., 1992. "GLIM and normalising constant models in spatial and directional data analysis," Computational Statistics & Data Analysis, Elsevier, vol. 13(3), pages 331-348, April.
    6. David J. Spiegelhalter & Nicola G. Best & Bradley P. Carlin & Angelika Van Der Linde, 2002. "Bayesian measures of model complexity and fit," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(4), pages 583-639, October.
    7. Peter J. Diggle, 1990. "A Point Process Modelling Approach to Raised Incidence of a Rare Phenomenon in the Vicinity of a Prespecified Point," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 153(3), pages 349-362, May.
    8. Peter Diggle & Sara Morris & Paul Elliott & Gavin Shaddick, 1997. "Regression Modelling of Disease Risk in Relation to Point Sources," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 160(3), pages 491-505, September.
    9. E. E. Kammann & M. P. Wand, 2003. "Geoadditive models," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 52(1), pages 1-18, January.
    10. Baddeley, Adrian & Turner, Rolf, 2005. "spatstat: An R Package for Analyzing Spatial Point Patterns," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 12(i06).
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    1. Athanasios Christou Micheas, 2014. "Hierarchical Bayesian modeling of marked non-homogeneous Poisson processes with finite mixtures and inclusion of covariate information," Journal of Applied Statistics, Taylor & Francis Journals, vol. 41(12), pages 2596-2615, December.
    2. Fernández-Alcalá, R.M. & Navarro-Moreno, J. & Ruiz-Molina, J.C., 2009. "Statistical inference for doubly stochastic multichannel Poisson processes: A PCA approach," Computational Statistics & Data Analysis, Elsevier, vol. 53(12), pages 4322-4331, October.
    3. Su Yun Kang & James McGree & Kerrie Mengersen, 2013. "The Impact of Spatial Scales and Spatial Smoothing on the Outcome of Bayesian Spatial Model," PLOS ONE, Public Library of Science, vol. 8(10), pages 1-14, October.
    4. LeSage, James & Banerjee, Sudipto & Fischer, Manfred M. & Congdon, Peter, 2009. "Spatial statistics: Methods, models & computation," Computational Statistics & Data Analysis, Elsevier, vol. 53(8), pages 2781-2785, June.
    5. Shengde Liang & Sudipto Banerjee & Bradley P. Carlin, 2009. "Bayesian Wombling for Spatial Point Processes," Biometrics, The International Biometric Society, vol. 65(4), pages 1243-1253, December.
    6. Bivand, Roger & Gómez-Rubio, Virgilio & Rue, Håvard, 2015. "Spatial Data Analysis with R-INLA with Some Extensions," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 63(i20).
    7. Athanasios C. Micheas & Jiaxun Chen, 2018. "sppmix: Poisson point process modeling using normal mixture models," Computational Statistics, Springer, vol. 33(4), pages 1767-1798, December.

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