B1503
Title: Functional estimation of log-Gaussian Cox process for prediction of risk maps in disease mapping
Authors: Antoni Torres - University of Granada (Spain)
Maria Pilar Frias Bustamante - University of Granada (Spain) [presenting]
Maria Dolores Ruiz-Medina - University of Granada (Spain)
Abstract: The aim is to present new results on classical and Bayesian estimation and prediction of log-Gaussian Cox processes, whose stochastic intensity is defined by an autoregressive Hilbertian process of order one (ARH(1) process). The functional parameter estimation of the stochastic Hilbert-valued intensity is performed in terms of classical and Bayesian componentwise estimators. Their asymptotic efficiency and equivalence is proved under certain conditions on the class of ARH(1) processes considered. The prediction of the functional values of the random intensity is achieved by the implementation of Kalman filtering in terms of the componentwise parameter estimators formulated. Conditional prediction of the log-Gaussian Cox process is then derived. A conditional simulation study is performed from different types of risk cancer data. EOF-based nonparametric, and nonlinear parametric estimation of the trend of the random intensity, is undertaken to illustrate the properties of the formulated functional parameter estimators, and associated plug-in predictors, comparing results and evaluating the relative performance, in terms of efficiency. Their application to the estimation and prediction of risk maps in disease mapping is contemplated as well, comparing both estimators in terms of the associated functional analysis of variance, and the correlation analysis of the associated functional residuals
Journal