Conditional Γ-minimax prediction with a precautionary loss function in a marked point process model
Daniel A. Lazar · Statistics · 2016
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 P×Θ, where P is fixed, whereas Θ is treated as a random measure. The prior distribution of Θ is described by an unknown process from a family Γ of gamma processes. Conditional Γ-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.