Statistical Science

Score, Pseudo-Score and Residual Diagnostics for Spatial Point Process Models

Adrian Baddeley, Ege Rubak, and Jesper Møller

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Abstract

We develop new tools for formal inference and informal model validation in the analysis of spatial point pattern data. The score test is generalized to a “pseudo-score” test derived from Besag’s pseudo-likelihood, and to a class of diagnostics based on point process residuals. The results lend theoretical support to the established practice of using functional summary statistics, such as Ripley’s K-function, when testing for complete spatial randomness; and they provide new tools such as the compensator of the K-function for testing other fitted models. The results also support localization methods such as the scan statistic and smoothed residual plots. Software for computing the diagnostics is provided.

Article information

Source
Statist. Sci., Volume 26, Number 4 (2011), 613-646.

Dates
First available in Project Euclid: 28 February 2012

Permanent link to this document
https://projecteuclid.org/euclid.ss/1330437942

Digital Object Identifier
doi:10.1214/11-STS367

Mathematical Reviews number (MathSciNet)
MR2951394

Zentralblatt MATH identifier
1332.62363

Keywords
Compensator functional summary statistics model validation point process residuals pseudo-likelihood

Citation

Baddeley, Adrian; Rubak, Ege; Møller, Jesper. Score, Pseudo-Score and Residual Diagnostics for Spatial Point Process Models. Statist. Sci. 26 (2011), no. 4, 613--646. doi:10.1214/11-STS367. https://projecteuclid.org/euclid.ss/1330437942


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