Multitype Markov point processes: some approximations

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.

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Statistical Analysis and Modelling of Spatial Point Patterns by ILLIAN, J., PENTTINEN, A., STOYAN, H., and STOYAN, D.

Biometrics ◽

10.1111/j.1541-0420.2009.01315_8.x ◽

2009 ◽

Vol 65 (3) ◽

pp. 995-995

Author(s):

Jesper Møller

Keyword(s):

Statistical Analysis ◽

Point Patterns ◽

Spatial Point ◽

Spatial Point Patterns

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

Advances in Applied Probability ◽

10.1017/s0001867800009952 ◽

2000 ◽

Vol 32 (02) ◽

pp. 331-343 ◽

Cited By ~ 14

Author(s):

Peter J. Diggle ◽

Jorge Mateu ◽

Helen E. Clough

Keyword(s):

Parametric Design ◽

Testing Procedure ◽

Parametric Model ◽

Parameter Estimates ◽

Parametric Approach ◽

Point Patterns ◽

Spatial Point ◽

Spatial Point Patterns ◽

Reduced Second Moment Measure ◽

Non Parametric

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.

Download Full-text