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Bayesian Areal Interpolation, Estimation, and Smoothing: An Inferential Approach for Geographic Information Systems

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  • A S Mugglin
  • B P Carlin
  • L Zhu
  • E Conlon

Abstract

Geographic information systems (GISs) offer a powerful tool to geographers, foresters, statisticians, public health officials, and other users of spatially referenced regional data sets. However, as useful as they are for data display and trend detection, they typically feature little ability for statistical inference , leaving the user in doubt as to the significance of the various patterns and ‘hot spots’ identified. Unfortunately, classical statistical methods are often ill suited for this complex inferential task, dealing as it does with data which are multivariate, multilevel, misaligned, and often nonrandomly missing. In this paper we describe a Bayesian approach to this inference problem which simultaneously allows interpolation of missing values, estimation of the effect of relevant covariates, and spatial smoothing of underlying causal patterns. Implemented via Markov-chain Monte Carlo (MCMC) computational methods, the approach automatically produces both point and interval estimates which account for all sources of uncertainty in the data. After describing the approach in the context of a simple, idealized example, we illustrate it with a data set on leukemia rates and potential geographic risk factors in Tompkins County, New York, summarizing our results with numerous maps created by using the popular GIS Arc/INFO.

Suggested Citation

  • A S Mugglin & B P Carlin & L Zhu & E Conlon, 1999. "Bayesian Areal Interpolation, Estimation, and Smoothing: An Inferential Approach for Geographic Information Systems," Environment and Planning A, , vol. 31(8), pages 1337-1352, August.
    • Handle: RePEc:sae:envira:v:31:y:1999:i:8:p:1337-1352
    DOI: 10.1068/a311337
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    References listed on IDEAS

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    1. Robin Flowerdew & Mick Green & Evangelos Kehris, 1991. "Using Areal Interpolation Methods In Geographic Information Systems," Papers in Regional Science, Wiley Blackwell, vol. 70(3), pages 303-315, July.
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    Cited by:

    1. Jonathan R. Bradley & Christopher K. Wikle & Scott H. Holan, 2016. "Bayesian Spatial Change of Support for Count-Valued Survey Data With Application to the American Community Survey," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 111(514), pages 472-487, April.
    2. Groß Marcus & Kreutzmann Ann-Kristin & Rendtel Ulrich & Schmid Timo & Tzavidis Nikos, 2020. "Switching Between Different Non-Hierachical Administrative Areas via Simulated Geo-Coordinates: A Case Study for Student Residents in Berlin," Journal of Official Statistics, Sciendo, vol. 36(2), pages 297-314, June.
    3. Daisuke Murakami & Morito Tsutsumi, 2012. "Practical Spatial Statisics for Areal Interpolation," Environment and Planning B, , vol. 39(6), pages 1016-1033, December.
    4. Groß Marcus & Kreutzmann Ann-Kristin & Rendtel Ulrich & Schmid Timo & Tzavidis Nikos, 2020. "Switching Between Different Non-Hierachical Administrative Areas via Simulated Geo-Coordinates: A Case Study for Student Residents in Berlin," Journal of Official Statistics, Sciendo, vol. 36(2), pages 297-314, June.
    5. Christopher K. Wikle, 2003. "Hierarchical Models in Environmental Science," International Statistical Review, International Statistical Institute, vol. 71(2), pages 181-199, August.

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