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Fast covariance estimation for innovations computed from a spatial Gibbs point process

By Jean-François Coeurjolly and Ege Rubak
CSGB Research Reports
No. 03, April 2012

In this paper, we derive an exact formula for the covariance of two innovations computed from a spatial Gibbs point process and suggest a fast method for estimating this covariance. We show how this methodology can be used to estimate the asymptotic covariance matrix of the maximum pseudo-likelihood estimate of the parameters of a spatial Gibbs point process model. This allows us to construct asymptotic confidence intervals for the parameters. We illustrate the efficiency of our procedure in a simulation study for several classical parametric models. The procedure is implemented in the statistical software R and it is included in spatstat, which is an R package for analyzing spatial point patterns.

Keywords: innovation process, maximum pseudo-likelihood, confidence intervals, exponential family models, Georgii-Nguyen-Zessin formula

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