
Accession Number : ADA114573
Title : An Empirical Bayesian Approach to the Smooth Estimation of Unknown Functions.
Descriptive Note : Technical summary rept.,
Corporate Author : WISCONSIN UNIVMADISON MATHEMATICS RESEARCH CENTER
Personal Author(s) : Leonard,Tom
PDF Url : ADA114573
Report Date : Feb 1982
Pagination or Media Count : 22
Abstract : A Bayesian procedure is described for smoothly estimating unknown functions, given a finite set of observations. It is assumed that a suitable transformation of the function can be taken to possess a Gaussian prior distribution across function space. The five special cases estimation of a logistic density transform, the log intensity function of a nonhomogeneous Poisson process, the log hazard function for survival data, the logit function in bioassay, and the mean value function in a possibly nonlinear time series of the Kalman types or equivalently a regression function for possibly nonnormal observations, are considered, and in each case a nonlinear Fredholm equation is described for the posterior estimate. In two cases this reduces to a finite dimensional system. In all five cases an approximate procedure is developed which is particularly useful when the sample size is large. This approximates the function space prior by a multivariate normal prior on the coefficients in a linear approximation, and then proceeds by conventional Bayesian techniques.
Descriptors : *Bayes theorem, *Estimates, *Methodology, Regression analysis, Poisson equation, Poisson density functions, Approach, Set theory, Nonlinear systems, Mean, Value, Time series analysis, Bioassay, Approximation(Mathematics)
Subject Categories : Statistics and Probability
Distribution Statement : APPROVED FOR PUBLIC RELEASE