No. 993

Title:

Model selection and estimation of the Neyman-Scott type spatial cluster models

Author(s):

Tanaka, Ushio (The Graduate University for Advanced Studies);
Ogata, Yosihiko (The Institute of Statistical Mathematics)

Key words:

Palm intensity function; Palm likelihood function; Thomas model; Inverse-power type model; Stoyan model; AIC.

Abstract:

The Neyman-Scott model for the clustering point pattern is characterized by a set of parameters, i.e., mean number of parent points per unit area, the mean size of offspring cluster and their clustering distribution function relative to their parents. However, it is difficult to write the likelihood function in analytically closed form, due to the combinatorial complexity in specifying the hidden parent points. This paper proposes to make use of a non-homogeneous Poisson likelihood in terms of the Palm intensity function (Palm likelihood) for the Neyman-Scott spatial cluster process. The characterizing parameters can be estimated by maximizing the log Palm likelihood. In order to examine the computational feasibility and the accuracy of the estimates, we apply it to the simulated data of known parameter values. We then consider the data of bramble canes locations and the data of longleaf pine trees locations as the applications, to compare the goodness-of-fit among the Neyman-Scott clustering models with different clustering distribution functions.