The Annals of Statistics

Asymptotic Bayes Criteria for Nonparametric Response Surface Design

Toby Mitchell, Jerome Sacks, and Donald Ylvisaker

Full-text: Open access

Abstract

This paper deals with Bayesian design for response surface prediction when the prior may be finite or infinite dimensional, the design space arbitrary. In order that the resulting problems be manageable, we resort to asymptotic versions of D-, G- and A-optimality. Here the asymptotics stem from allowing the error variance to be large. The problems thus elicited have strong game-like characteristics. Examples of theoretical solutions are brought forward, especially when the priors are stationary processes on an interval, and we give numerical evidence that the asymptotics work well in the finite domain.

Article information

Source
Ann. Statist., Volume 22, Number 2 (1994), 634-651.

Dates
First available in Project Euclid: 11 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176325488

Digital Object Identifier
doi:10.1214/aos/1176325488

Mathematical Reviews number (MathSciNet)
MR1292533

Zentralblatt MATH identifier
0815.62050

JSTOR
links.jstor.org

Subjects
Primary: 62K05: Optimal designs
Secondary: 62J02: General nonlinear regression

Keywords
Bayesian design asymptotics D-, G- and A-optimality stationary processes

Citation

Mitchell, Toby; Sacks, Jerome; Ylvisaker, Donald. Asymptotic Bayes Criteria for Nonparametric Response Surface Design. Ann. Statist. 22 (1994), no. 2, 634--651. doi:10.1214/aos/1176325488. https://projecteuclid.org/euclid.aos/1176325488


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