A nonparametric Bayesian method for estimating a response function. (English) Zbl 1326.62016

Brown, Scott; Meeden, Glen

Fourdrinier, Dominique (ed.) et al., Contemporary developments in Bayesian analysis and statistical decision theory. A festschrift for William E. Strawderman. Beachwood, OH: IMS, Institute of Mathematical Statistics (ISBN 978-0-940600-81-2). Institute of Mathematical Statistics Collections 8, 190-199 (2012).

Summary: Consider the problem of estimating a response function which depends upon a non-stochastic independent variable under our control. The data are independent Bernoulli random variables where the probabilities of success are given by the response function at the chosen values of the independent variable. Here we present a nonparametric Bayesian method for estimating the response function. The only prior information assumed is that the response function can be well approximated by a mixture of step functions.
For the entire collection see [Zbl 1319.62003].

MSC:

62C10	Bayesian problems; characterization of Bayes procedures
62C15	Admissibility in statistical decision theory
62G05	Nonparametric estimation
62F15	Bayesian inference

Keywords:

binary regression; nonparametric Bayes; stepwise Bayes