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A comparison between parametric and non-parametric approaches to the analysis of replicated spatial point patterns

Part of: Stochastic processes Geometric probability and stochastic geometry Inference from stochastic processes

Published online by Cambridge University Press:  01 July 2016

Peter J. Diggle ,
Jorge Mateu  and
Helen E. Clough
Peter J. Diggle*
Affiliation:
Lancaster University
Jorge Mateu*
Affiliation:
Universitat Jaume I
Helen E. Clough*
Affiliation:
University of Liverpool
*
∗ Postal address: Department of Mathematics and Statistics, Lancaster University, Lancaster LA1 4YF, UK. Email address: p.diggle@lancaster.ac.uk
∗∗ Postal address: Department of Mathematics, Universitat Jaume I, E-12071 Castellón, Spain.
∗∗ Postal address: Department of Mathematical Sciences, University of Liverpool, Liverpool L69 3BX, UK.
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Abstract

The paper compares non-parametric (design-based) and parametric (model-based) approaches to the analysis of data in the form of replicated spatial point patterns in two or more experimental groups. Basic questions for data of this kind concern estimating the properties of the underlying spatial point process within each experimental group, and comparing the properties between groups. A non-parametric approach, building on work by Diggle et. al. (1991), summarizes each pattern by an estimate of the reduced second moment measure or K-function (Ripley (1977)) and compares mean K-functions between experimental groups using a bootstrap testing procedure. A parametric approach fits particular classes of parametric model to the data, uses the model parameter estimates as summaries and tests for differences between groups by comparing fits with and without the assumption of common parameter values across groups. The paper discusses how either approach can be implemented in the specific context of a single-factor replicated experiment and uses simulations to show how the parametric approach can be more efficient when the underlying model assumptions hold, but potentially misleading otherwise.

Keywords

Expected significance levelsK-functionpseudo-likelihood functionreplicated spatial point patternsspatial analysis of variance

MSC classification

Primary: 60D05: Geometric probability and stochastic geometry
Secondary: 60G55: Point processes 62M30: Spatial processes
Type
Stochastic Geometry and Statistical Applications
Information
Advances in Applied Probability , Volume 32 , Issue 2 , June 2000 , pp. 331 - 343
Copyright
Copyright © Applied Probability Trust 2000 

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