Bayesian Analysis

Spatial Product Partition Models

Garritt L. Page and Fernando A. Quintana

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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.

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

First available in Project Euclid: 16 September 2015

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product partition models spatial smoothing spatial clustering spatial prediction


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

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See also

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  • 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.
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