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

Waite, Timothy W.

doi:10.5705/ss.202015.0293

Cited by 3 publications

(4 citation statements)

References 42 publications

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“…We evaluate a design ξ via its Bayesian efficiencies under a given criterion, relative to an appropriate reference design ξ ∗ (see, for example, the work of Waite). Under robust D s ‐optimality, this efficiency is given by

eff (ξ, ξ^{*}) = {(\frac{\exp \int_{B} \log \det [M_{11} (ξ, γ) - M_{12} (ξ, γ) M_{22}^{- 1} (ξ, γ) M_{12}^{T} (ξ, \tilde{γ})] d F (γ)}{\exp \int_{B} \log \det [M_{11} (ξ^{*}, γ) - M_{12} (ξ^{*}, γ) M_{22}^{- 1} (ξ^{*}, γ) M_{12}^{T} (ξ^{*}, γ)] d F (γ)})}^{1 / s} .

We find designs that maximize and numerically using a version of the Fedorov‐Wynn algorithm,) as implemented in R package docopulae…”

Section: Designs For Copula‐based Marginal Modelsmentioning

confidence: 99%

“…This criterion follows as a special case of the D A -criterion with A T = (I s 0 s×(r+l−s) ), where I s is the s × s identity matrix and 0 s×(r+l−s) is the s × (r + l − s) zero matrix. We evaluate a design via its Bayesian efficiencies under a given criterion, relative to an appropriate reference design * (see, for example, the work of Waite 32 ). Under robust D s -optimality, this efficiency is given by…”

Section: Design Of Experiments For Copula Modelsmentioning

confidence: 99%

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Copula‐based robust optimal block designs

Rappold

Müller

Woods

2019

Appl Stoch Models Bus & Ind

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Blocking is often used to reduce known variability in designed experiments by collecting together homogeneous experimental units. A common modeling assumption for such experiments is that responses from units within a block are dependent. Accounting for such dependencies in both the design of the experiment and the modeling of the resulting data when the response is not normally distributed can be challenging, particularly in terms of the computation required to find an optimal design. The application of copulas and marginal modeling provides a computationally efficient approach for estimating population‐average treatment effects. Motivated by an experiment from materials testing, we develop and demonstrate designs with blocks of size two using copula models. Such designs are also important in applications ranging from microarray experiments to experiments on human eyes or limbs with naturally occurring blocks of size two. We present a methodology for design selection, make comparisons to existing approaches in the literature, and assess the robustness of the designs to modeling assumptions.

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eff (ξ, ξ^{*}) = {(\frac{\exp \int_{B} \log \det [M_{11} (ξ, γ) - M_{12} (ξ, γ) M_{22}^{- 1} (ξ, γ) M_{12}^{T} (ξ, \tilde{γ})] d F (γ)}{\exp \int_{B} \log \det [M_{11} (ξ^{*}, γ) - M_{12} (ξ^{*}, γ) M_{22}^{- 1} (ξ^{*}, γ) M_{12}^{T} (ξ^{*}, γ)] d F (γ)})}^{1 / s} .

We find designs that maximize and numerically using a version of the Fedorov‐Wynn algorithm,) as implemented in R package docopulae…”

Section: Designs For Copula‐based Marginal Modelsmentioning

confidence: 99%

Section: Design Of Experiments For Copula Modelsmentioning

confidence: 99%

Copula‐based robust optimal block designs

Rappold

Müller

Woods

2019

Appl Stoch Models Bus & Ind

View full text Add to dashboard Cite

show abstract

“…This criterion follows as a special case of the D A -criterion with A T = (I s 0 s×(r+l−s) ), with I s the s × s identity matrix and 0 s×(r+l−s) the s × (r + l − s) zero matrix. We evaluate a design ξ via its Bayesian efficiencies under a given criterion, relative to an appropriate reference design ξ * (see, for example, Waite, 2018). Under robust D s -optimality, this efficiency is given by:…”

Section: Design Of Experiments For Copula Modelsmentioning

confidence: 99%

Copula-based robust optimal block designs

Mueller¹,

Rappold²,

Woods³

2018

Preprint

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Blocking is often used to reduce known variability in designed experiments by collecting together homogeneous experimental units. A common modelling assumption for such experiments is that responses from units within a block are dependent. Accounting for such dependencies in both the design of the experiment and the modelling of the resulting data when the response is not normally distributed can be challenging, particularly in terms of the computation required to find an optimal design. The application of copulas and marginal modelling provides a computationally efficient approach for estimating population-average treatment effects. Motivated by an experiment from materials testing, we develop and demonstrate designs with blocks of size two using copula models. Such designs are also important in applications ranging from microarray experiments to experiments on human eyes or limbs with naturally occurring blocks of size two. We present methodology for design selection, make comparisons to existing approaches in the literature and assess the robustness of the designs to modelling assumptions.

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“…The adoption of bounded uniform prior distributions prevents the occurrence of parameter vectors in the support of the prior for which no design has a non-singular information matrix (c.f. Waite, 2015).…”

Section: Designs and Model Selection For Binomial Response And Logistmentioning

confidence: 99%

Model selection via Bayesian information capacity designs for generalised linear models

Woods

McGree

Lewis

2017

Computational Statistics & Data Analysis

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The first investigation is made of designs for screening experiments where the response variable is approximated by a generalised linear model. A Bayesian information capacity criterion is defined for the selection of designs that are robust to the form of the linear predictor. For binomial data and logistic regression, the effectiveness of these designs for screening is assessed through simulation studies using all-subsets regression and model selection via maximum penalised likelihood and a generalised information criterion. For Poisson data and log-linear regression, similar assessments are made using maximum likelihood and the Akaike information criterion for minimally-supported designs that are constructed analytically. The results show that effective screening, that is, high power with moderate type I error rate and false discovery rate, can be achieved through suitable choices for the number of design support points and experiment size. Logistic regression is shown to present a more challenging problem than log-linear regression. Some areas for future work are also indicated. This paper will appear in Computational Statistics and Data Analysis.

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

Cited by 3 publications

References 42 publications

Copula‐based robust optimal block designs

Copula‐based robust optimal block designs

Copula-based robust optimal block designs

Model selection via Bayesian information capacity designs for generalised linear models

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