Likelihood based tests for spatial randomness.

Many different methods have been proposed to test the spatial randomness of a point pattern adjusting for an inhomogeneous background population. These tests can be classified into cluster detection tests, concerned with the detection and inference of local clusters, and global clustering tests, which collect evidence for clustering throughout the study region. This paper is mainly concerned about global clustering tests. Some tests for spatial randomness are based on likelihoods, which include the spatial and space-time scan statistics with variable window size and Gangnon and Clayton's weighted average likelihood ratio tests. Both of these tests perform well compared to other tests for cluster detection and global clustering, respectively. In this study, we develop other likelihood based tests for global clustering and we explore the use of different weight functions with these tests. The power of these tests is evaluated using simulated data set and compared with existing methods.