Detecting Clustering in Inhomogeneous Point Processes with Applications to Duck Nesting Locations

• Activity Number: 195
• Type: Contributed
• Date/Time: Monday, August 5, 2013 : 10:30 AM to 12:20 PM
• Sponsor: Section on Statistics and the Environment
• Author(s): Daniel Fortin*+ and Philip Dixon and William Clark and Nicholas Michaud
• Companies: Iowa State University and Iowa State Univ and Iowa State University and Iowa State University
• Keywords: Inhomogeneous point process

Abstract

For homogeneous Poisson point processes it is common practice to compute Ripley's L-function to test for complete spatial randomness (CSR). Under CSR, the expected L-function is a horizontal line. Large peeks in the empirical L-function are interpreted as indicating clustering, where 'large' is typically determined by computing simulation envelopes of the L-function under the assumption of CSR. We investigate duck nest locations, where nesting intensity depends on known habitat types as well as bodies of water which have zero nesting intensity, forming holes in the region of interest. We propose a test for clustering based on the L-function for regions with this type of inhomogeneity and demonstrate, through a simulation study, that our method has greater power than standard methods in the literature for detecting clustering in inhomogeneous point processes.