Modeling Regular-Clustered Point Patterns: A Generalization of the Neyman-Scott Process

• Activity Number: 313
• Type: Contributed
• Date/Time: Tuesday, August 2, 2011 : 8:30 AM to 10:20 AM
• Sponsor: Section on Statistics and the Environment
• Author(s): Chun Yip Yau*+ and Ji Meng Loh
• Companies: Chinese University of Hong Kong and AT&T Labs Research
• Keywords: Neyman-Scott process ; K-function ; Gibbs process ; Regular point process

Abstract

In this paper we introduce a generalization of Neyman-Scott process that allows for regularity in the parent process. In particular, the parent process is a Strauss process, and the offspring process is uniform on a disc centered at each parent. Such a generalization allows for point realizations that show a mix of regularity and clustering in the points. We work out a closed form expression of the K function for this model and use this to fit the model to data. The approach is illustrated by applications to the locations of a species of trees in a rainforest dataset.