Conducting Inference on Ripley's K-Function for Spatial Point Processes

• Activity Number: 296
• Type: Topic Contributed
• Date/Time: Tuesday, August 6, 2013 : 8:30 AM to 10:20 AM
• Sponsor: ENAR
• Author(s): Michael Hyman*+

Abstract

Spatial point processes are random processes used in a variety of disciplines to model and analyze point data. Spatial point patterns are observed realizations of a spatial point process. Typically, inference of point patterns is parametric in nature and based on simulation envelopes generated from a model fit to the data. It is often of interest to compare multiple point patterns observed at different locations or times to determine whether they may be realizations from the same process. However, statistical properties of the statistics related to point processes are relatively unknown and nonparametric hypothesis tests to compare patterns are underdeveloped. Ripley's K-function is a common statistic used to assess the spatial dependence observed in a pattern. Here, confidence intervals for the K-function are determined using a new spatial bootstrapping procedure. Using these intervals, the groundwork for a more powerful statistical test to compare multiple patterns is laid. Applications of point process models are also discussed.