Quasi-likelihood for multivariate spatial point processes with semiparametric intensity functions

Quasi-likelihood for Spatial Point Processes.

Fitting regression models for intensity functions of spatial point processes is of great interest in ecological and epidemiological studies of association between spatially referenced events and geographical or environmental covariates. When Cox or cluster process models are used to accommodate clustering not accounted for by the available covariates, likelihood based inference becomes computat...

Bayesian semiparametric intensity estimation for inhomogeneous spatial point processes.

In this work we propose a fully Bayesian semiparametric method to estimate the intensity of an inhomogeneous spatial point process. The basic idea is to first convert intensity estimation into a Poisson regression setting via binning data points on a regular grid, and then model the log intensity semiparametrically using an adaptive version of Gaussian Markov random fields to smooth the corresp...

Supplementary material for ‘ Quasi - likelihood for Spa - tial Point Processes ’

dr ≤ K2. C3 φn,θ(u,β) is differentiable with respect to θ and β, and for |φn,θ(u,β)|, |dφn,θ(u,β)/dβ| and |dφn,θ(u,β)/dθ|, the supremum over u ∈ R ,β ∈ b(β,K3), θ ∈ b(θ ,K3) is bounded for some K3 > 0, where b(x, r) denotes the ball centred at x with radius r > 0. C4 |Wn| (θ̃n − θ ) is bounded in probability. C5 l = lim infn ln > 0, where for each n, ln denotes the minimal eigenvalue of S̄n,θ∗(β ...

Asymptotic Behavior of Multivariate Reward Processes with Nonlinear Reward Functions

COVARIANCE MATRIX OF MULTIVARIATE REWARD PROCESSES WITH NONLINEAR REWARD FUNCTIONS

Multivariate reward processes with reward functions of constant rates, defined on a semi-Markov process, first were studied by Masuda and Sumita, 1991. Reward processes with nonlinear reward functions were introduced in Soltani, 1996. In this work we study a multivariate process , , where are reward processes with nonlinear reward functions respectively. The Laplace transform of the covar...