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|a (DE-627)JST140205136
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|a (JST)26384251
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|a DE-627
|b ger
|c DE-627
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|a eng
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|a Waite, Timothy W.
|e verfasserin
|4 aut
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|a SINGULAR PRIOR DISTRIBUTIONS AND ILL-CONDITIONING IN BAYESIAN D-OPTIMAL DESIGN FOR SEVERAL NONLINEAR MODELS
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|c 2018
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|a Text
|b txt
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|a Computermedien
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|a 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 several multi-parameter generalized linear models, we establish sufficient conditions for singularity of a prior distribution. For the generalized linear models 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. Here it is shown 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 when numerical evaluation of the objective function fails due to ill-conditioning, as often occurs for heavy-tailed prior distributions. These numerical methods are illustrated for logistic regression.
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|a © 2018 STATISTICA SINICA
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|a Philosophy
|x Applied philosophy
|x Philosophy of science
|x Scientific method
|x Experimentation
|x Experiment design
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|a Information science
|x Information analysis
|x Data analysis
|x Regression analysis
|x Logistic regression
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|a Arts
|x Applied arts
|x Design
|x Design engineering
|x Design efficiency
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| 650 |
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|a Information science
|x Information analysis
|x Data analysis
|x Regression analysis
|x Linear regression
|x Linear models
|x Generalized linear model
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| 650 |
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|a Philosophy
|x Applied philosophy
|x Philosophy of science
|x Scientific method
|x Experimentation
|x Experiment design
|x Factorial design
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| 650 |
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|a Applied sciences
|x Computer science
|x Computer programming
|x Mathematical programming
|x Nonlinear programming
|x Objective functions
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|a Information science
|x Information analysis
|x Data analysis
|x Regression analysis
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| 650 |
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|a Physical sciences
|x Physics
|x Mathematical physics
|x Numerical quadratures
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| 650 |
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|a Mathematics
|x Mathematical procedures
|x Approximation
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| 650 |
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|a Mathematics
|x Pure mathematics
|x Linear algebra
|x Vector analysis
|x Mathematical vectors
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|a research-article
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|i Enthalten in
|t Statistica Sinica. in
|d Institute of Statistical Science, Academia Sinica and International Chinese Statistical Association, 1991
|g 28(2018), 1, Seite 505-525
|w (DE-627)JST098920278
|x 19968507
|7 nnns
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|g volume:28
|g year:2018
|g number:1
|g pages:505-525
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|u https://www.jstor.org/stable/26384251
|3 Volltext
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|d 28
|j 2018
|e 1
|h 505-525
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