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Quadrature methods for Bayesian optimal design of experiments with nonnormal prior distributions

Quadrature methods for Bayesian optimal design of experiments with nonnormal prior distributions
Quadrature methods for Bayesian optimal design of experiments with nonnormal prior distributions

Many optimal experimental designs depend on one or more unknown model parameters. In such cases, it is common to use Bayesian optimal design procedures to seek designs that perform well over an entire prior distribution of the unknown model parameter(s). Generally, Bayesian optimal design procedures are viewed as computationally intensive. This is because they require numerical integration techniques to approximate the Bayesian optimality criterion at hand. The most common numerical integration technique involves pseudo Monte Carlo draws from the prior distribution(s). For a good approximation of the Bayesian optimality criterion, a large number of pseudo Monte Carlo draws is required. This results in long computation times. As an alternative to the pseudo Monte Carlo approach, we propose using computationally efficient Gaussian quadrature techniques. Since, for normal prior distributions, suitable quadrature techniques have already been used in the context of optimal experimental design, we focus on quadrature techniques for nonnormal prior distributions. Such prior distributions are appropriate for variance components, correlation coefficients, and any other parameters that are strictly positive or have upper and lower bounds. In this article, we demonstrate the added value of the quadrature techniques we advocate by means of the Bayesian D-optimality criterion in the context of split-plot experiments, but we want to stress that the techniques can be applied to other optimality criteria and other types of experimental designs as well. Supplementary materials for this article are available online.

Bayesian optimal design, Beta distribution, D-optimality, Gamma distribution, Log-normal distribution, Numerical integration
1061-8600
179-194
Goos, Peter
e85ac472-9312-4a77-ba77-b2f21b64f39e
Mylona, Kalliopi
b44af287-2d9f-4df8-931c-32d8ab117864
Goos, Peter
e85ac472-9312-4a77-ba77-b2f21b64f39e
Mylona, Kalliopi
b44af287-2d9f-4df8-931c-32d8ab117864

Goos, Peter and Mylona, Kalliopi (2018) Quadrature methods for Bayesian optimal design of experiments with nonnormal prior distributions. Journal of Computational and Graphical Statistics, 27 (1), 179-194. (doi:10.1080/10618600.2017.1285778).

Record type: Article

Abstract

Many optimal experimental designs depend on one or more unknown model parameters. In such cases, it is common to use Bayesian optimal design procedures to seek designs that perform well over an entire prior distribution of the unknown model parameter(s). Generally, Bayesian optimal design procedures are viewed as computationally intensive. This is because they require numerical integration techniques to approximate the Bayesian optimality criterion at hand. The most common numerical integration technique involves pseudo Monte Carlo draws from the prior distribution(s). For a good approximation of the Bayesian optimality criterion, a large number of pseudo Monte Carlo draws is required. This results in long computation times. As an alternative to the pseudo Monte Carlo approach, we propose using computationally efficient Gaussian quadrature techniques. Since, for normal prior distributions, suitable quadrature techniques have already been used in the context of optimal experimental design, we focus on quadrature techniques for nonnormal prior distributions. Such prior distributions are appropriate for variance components, correlation coefficients, and any other parameters that are strictly positive or have upper and lower bounds. In this article, we demonstrate the added value of the quadrature techniques we advocate by means of the Bayesian D-optimality criterion in the context of split-plot experiments, but we want to stress that the techniques can be applied to other optimality criteria and other types of experimental designs as well. Supplementary materials for this article are available online.

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More information

e-pub ahead of print date: 19 June 2017
Published date: 2 January 2018
Keywords: Bayesian optimal design, Beta distribution, D-optimality, Gamma distribution, Log-normal distribution, Numerical integration

Identifiers

Local EPrints ID: 420247
URI: https://eprints.soton.ac.uk/id/eprint/420247
ISSN: 1061-8600
PURE UUID: 70893f1d-f4c3-4562-b539-b82188f739db

Catalogue record

Date deposited: 03 May 2018 16:30
Last modified: 16 Jan 2019 17:32

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