An Empirical Bayesian Approach to the Smooth Estimation of Unknown Functions.
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 non-homogeneous Poisson process, the log hazard function for survival data, the logit function in bioassay, and the mean value function in a possibly non-linear time series of the Kalman types or equivalently a regression function for possibly non-normal observations, are considered, and in each case a non-linear 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.
Document Details
- Document Type
- Technical Report
- Publication Date
- Feb 01, 1982
- Accession Number
- ADA114573
Entities
People
- Tom Leonard
Organizations
- University of Wisconsin–Madison