Bayesian Models for Response Surfaces. II. Estimating the Response Surface.

Abstract

We analyze a Bayesian model for response surfaces. This model augments a simple graduating function with a bias term that represents the difference between the true, but unknown, response function and the graduating function. The model is a straightforward extension of Blight and Ott's (1975) Bayesian model for polynomial regression. The bias term is defined in terms of prior distributions and we show how estimates of the response surface and measures of precision depend on the form of the prior distribution. Estimates and measures of precision are given for strictly proper prior distributions and also when improper priors are assigned to the coefficients of the graduating function, in which case the model leads to generalized spline estimates. (Author)

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Document Details

Document Type
Technical Report
Publication Date
Apr 01, 1984
Accession Number
ADA142768

Entities

People

  • D. M. Steinberg

Organizations

  • University of Wisconsin–Madison

Tags

Communities of Interest

  • Air Platforms

DTIC Thesaurus Topics

  • Bayesian Networks
  • Data Science
  • Estimators
  • Experimental Design
  • Information Science
  • Numerical Analysis
  • Polynomials
  • Probability
  • Probability Distributions
  • Regression Analysis
  • Standards
  • Statistical Algorithms
  • Statistical Analysis
  • Statistical Inference
  • Statistics
  • Two Dimensional
  • United States

Fields of Study

  • Mathematics

Readers

  • Approximation Theory.
  • Computational Modeling and Simulation

Technology Areas

  • AI & ML
  • AI & ML - Bayesian Inference