Singular prior distributions in Bayesian D-optimal design for nonlinear modelsCitation formats

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Singular prior distributions in Bayesian D-optimal design for nonlinear models. / Waite, Timothy W.

In: Statistica Sinica, Vol. 28, No. 1, 24.08.2015.

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@article{259ad8f78d1b48059ec7c7b0f7d9430b,
title = "Singular prior distributions in Bayesian D-optimal design for nonlinear models",
abstract = "For Bayesian D-optimal design, we define a singular prior distribution for the model parameters as a prior distribution such that the determinant of the Fisher information matrix has a prior geometric mean of zero for all designs. For such a prior distribution, the Bayesian D-optimality criterion fails to select a design. For the exponential decay model, we characterize singularity of the prior distribution in terms of the expectations of a few elementary transformations of the parameter. For a compartmental model and multi-parameter logistic regression, we establish sufficient conditions for singularity of a prior distribution. For logistic regression we also obtain sufficient conditions for non-singularity. In the existing literature, weakly informative prior distributions are commonly recommended as a default choice for inference in logistic regression. Our results show that some of the recommended prior distributions are singular, and hence should not be used for Bayesian D-optimal design. Additionally, methods are developed to derive and assess Bayesian D-efficient designs for logistic regression when numerical evaluation of the objective function fails due to ill-conditioning.",
keywords = "Compartmental model, Exponential decay model, Ill-conditioning, Logistic regression",
author = "Waite, {Timothy W}",
year = "2015",
month = aug,
day = "24",
language = "English",
volume = "28",
journal = "Statistica Sinica",
issn = "1017-0405",
publisher = "Academia Sinica, Institute of Statistical Science",
number = "1",

}

RIS

TY - JOUR

T1 - Singular prior distributions in Bayesian D-optimal design for nonlinear models

AU - Waite, Timothy W

PY - 2015/8/24

Y1 - 2015/8/24

N2 - For Bayesian D-optimal design, we define a singular prior distribution for the model parameters as a prior distribution such that the determinant of the Fisher information matrix has a prior geometric mean of zero for all designs. For such a prior distribution, the Bayesian D-optimality criterion fails to select a design. For the exponential decay model, we characterize singularity of the prior distribution in terms of the expectations of a few elementary transformations of the parameter. For a compartmental model and multi-parameter logistic regression, we establish sufficient conditions for singularity of a prior distribution. For logistic regression we also obtain sufficient conditions for non-singularity. In the existing literature, weakly informative prior distributions are commonly recommended as a default choice for inference in logistic regression. Our results show that some of the recommended prior distributions are singular, and hence should not be used for Bayesian D-optimal design. Additionally, methods are developed to derive and assess Bayesian D-efficient designs for logistic regression when numerical evaluation of the objective function fails due to ill-conditioning.

AB - For Bayesian D-optimal design, we define a singular prior distribution for the model parameters as a prior distribution such that the determinant of the Fisher information matrix has a prior geometric mean of zero for all designs. For such a prior distribution, the Bayesian D-optimality criterion fails to select a design. For the exponential decay model, we characterize singularity of the prior distribution in terms of the expectations of a few elementary transformations of the parameter. For a compartmental model and multi-parameter logistic regression, we establish sufficient conditions for singularity of a prior distribution. For logistic regression we also obtain sufficient conditions for non-singularity. In the existing literature, weakly informative prior distributions are commonly recommended as a default choice for inference in logistic regression. Our results show that some of the recommended prior distributions are singular, and hence should not be used for Bayesian D-optimal design. Additionally, methods are developed to derive and assess Bayesian D-efficient designs for logistic regression when numerical evaluation of the objective function fails due to ill-conditioning.

KW - Compartmental model

KW - Exponential decay model

KW - Ill-conditioning

KW - Logistic regression

M3 - Article

VL - 28

JO - Statistica Sinica

JF - Statistica Sinica

SN - 1017-0405

IS - 1

ER -