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

The paper compares non-parametric (design-based) and parametric (model-base d) approaches to the analysis of data in the form of replicated spatial poi nt patterns in two or more experimental groups. Basic questions for data of this kind concern estimating the properties of the underlying spatial poin t process within each experimental group, and comparing the properties betw een groups. A non-parametric approach, building on work by Diggle et al. (1 991), summarizes each pattern by an estimate of the reduced second moment m easure or K-function (Ripley (1977)) and compares mean K-functions between experimental groups using a bootstrap testing procedure. A parametric appro ach 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 value s 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 .