Bayesian Analysis

Spatial Product Partition Models

Garritt L. Page and Fernando A. Quintana

Full-text: Open access

Abstract

When modeling geostatistical or areal data, spatial structure is commonly accommodated via a covariance function for the former and a neighborhood structure for the latter. In both cases the resulting spatial structure is a consequence of implicit spatial grouping in that observations near in space are assumed to behave similarly. It would be desirable to develop spatial methods that explicitly model the partitioning of spatial locations providing more control over resulting spatial structures and be able to better balance local and global spatial dependence. To this end, we extend product partition models to a spatial setting so that the partitioning of locations into spatially dependent clusters is explicitly modeled. We explore the resulting spatial structure and demonstrate its flexibility in accommodating many types of spatial dependencies. We illustrate the method’s utility through simulation studies and two applications. Computational techniques with additional simulations are provided in a Supplementary Material file available online.

Article information

Source
Bayesian Anal., Volume 11, Number 1 (2016), 265-298.

Dates
First available in Project Euclid: 16 September 2015

Permanent link to this document
https://projecteuclid.org/euclid.ba/1442363925

Digital Object Identifier
doi:10.1214/15-BA971

Mathematical Reviews number (MathSciNet)
MR3465813

Zentralblatt MATH identifier
1359.62401

Keywords
product partition models spatial smoothing spatial clustering spatial prediction

Citation

Page, Garritt L.; Quintana, Fernando A. Spatial Product Partition Models. Bayesian Anal. 11 (2016), no. 1, 265--298. doi:10.1214/15-BA971. https://projecteuclid.org/euclid.ba/1442363925


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See also

  • Related item: Robert B. Gramacy, Herbert K. H. Lee (2016). Comment on Article by Page and Quintana. Bayesian Anal. Vol. 11, Iss. 1, 299–302.
  • Related item: Brian J. Reich, Montserrat Fuentes (2016). Comment on Article by Page and Quintana. Bayesian Anal. Vol. 11, Iss. 1, 303–305.
  • Related item: Carlo Gaetan, Simone A. Padoan, Igor Prünster (2016). Comment on Article by Page and Quintana. Bayesian Anal. Vol. 11, Iss. 1, 307–314.
  • Related item: Garrit L. Page, Fernando A. Quintana (2016). Rejoinder. Bayesian Anal. Vol. 11, Iss. 1, 315–323.

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