Journal ArticleDOI
A Bayesian approach to model inadequacy for polynomial regression
B. J. N. Blight,L. Ott +1 more
TLDR
In this paper, a model is constructed in which its properties are represented in terms of a Bayesian prior distribution, and the model is analyzed to give parameter estimates and predictions of further observations.Abstract:
A method is presented which, in many cases, appears to be an improvement over the standard approach to the polynomial regression problem. This improvement is achieved by focusing attention on the deviation of the polynomial representation from the true underlying function. By fully utilizing the nature of this deviation, a model is constructed in which its properties are represented in terms of a Bayesian prior distribution. The model is analyzed to give parameter estimates and predictions of further observations. Comparisons are made with standard least squares procedures when the true underlying model is (a) quadratic and (b) linear and quadratic with a superimposed sine wave.read more
Citations
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Book
Gaussian Processes for Machine Learning
TL;DR: The treatment is comprehensive and self-contained, targeted at researchers and students in machine learning and applied statistics, and deals with the supervised learning problem for both regression and classification.
Journal ArticleDOI
The design and analysis of computer experiments
TL;DR: This paper presents a meta-modelling framework for estimating Output from Computer Experiments-Predicting Output from Training Data and Criteria Based Designs for computer Experiments.
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A gentle tutorial of the em algorithm and its application to parameter estimation for Gaussian mixture and hidden Markov models
TL;DR: In this paper, the authors describe the EM algorithm for finding the parameters of a mixture of Gaussian densities and a hidden Markov model (HMM) for both discrete and Gaussian mixture observation models.
Journal ArticleDOI
Predicting the output from a complex computer code when fast approximations are available
Marc C. Kennedy,Anthony O'Hagan +1 more
TL;DR: The purpose of the current paper is to explore ways in which runs from several levels of a code can be used to make inference about the output from the most complex code.
Journal ArticleDOI
Bayesian Prediction of Deterministic Functions, with Applications to the Design and Analysis of Computer Experiments
TL;DR: This article is concerned with prediction of a function y(t) over a (multidimensional) domain T, given the function values at a set of “sites” in T, and with the design, that is, with the selection of those sites.
References
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Journal ArticleDOI
Remarks on Some Nonparametric Estimates of a Density Function
TL;DR: In this article, some aspects of the estimation of the density function of a univariate probability distribution are discussed, and the asymptotic mean square error of a particular class of estimates is evaluated.
Journal ArticleDOI
A Basis for the Selection of a Response Surface Design
TL;DR: In this paper, the problem of choosing a design such that the polynomial f(ξ) = f (ξ1, ξ2, · · ·, ξ k ) fitted by the method of least squares most closely represents the true function over some region of interest R in the ξ space, no restrictions being introduced that the experimental points should necessarily lie inside R, is considered.
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The Choice of the Degree of a Polynomial Regression as a Multiple Decision Problem
TL;DR: In this article, the problem of determining the appropriate degree of a polynomial in the index, say time, to represent the regression of the observable variable is formulated in terms used in the theory of testing hypotheses and the optimal procedure is to test in sequence whether coefficients are 0, starting with the highest (specified) degree.