Abstract
A simple Bayesian approach to nonparametric regression is described using fuzzy sets and membership functions. Membership functions are interpreted as likelihood functions for the unknown regression function, so that with the help of a reference prior they can be transformed to prior density functions. The unknown regression function is decomposed into wavelets and a hierarchical Bayesian approach is employed for making inferences on the resulting wavelet coefficients.
Information
Published: 1 January 2008
First available in Project Euclid: 28 April 2008
MathSciNet: MR2459219
Digital Object Identifier: 10.1214/074921708000000084
Subjects:
Primary:
62G08
Secondary:
62A15
,
62F15
Keywords:
Function estimation
,
hierarchical Bayes
,
membership function
,
model choice
,
wavelet
Rights: Copyright © 2008, Institute of Mathematical Statistics