Conditional -minimax prediction with a precautionary loss function in a marked point process model

摘要

A robust Bayesian approach is used to construct optimal predictors of the total size of future marks of a marked point process in the presence of uncertainty regarding the prior distribution. A stochastic marked point process model based on a doubly stochastic Poisson process is considered. The underlying marked point process is assumed to be a two-dimensional non-homogeneous Poisson process with intensity measure , where P is fixed, whereas is treated as a random measure. The prior distribution of is described by an unknown process from a family of gamma processes. Conditional -minimax predictors are constructed under different types of uncertainty about the prior. A precautionary loss function is considered to prevent underestimation. Some properties of the derived predictors are investigated in a simulation study.