Testing separability in spatial-temporal marked point processes

Nonparametric tests for investigating the separability of a spatial-temporal marked point process are described and compared. It is shown that a Cramer-von Mises-type test is very powerful at detecting gradual departures from separability, and that a residual test based on randomly rescaling the process is powerful at detecting nonseparable clustering or inhibition of the marks. An application to Los Angeles County wildfire data is given, in which it is shown that the separability hypothesis is invalidated largely due to clustering of fires of similar sizes within periods of up to 3.9 years.