Robust Designs for Poisson Regression Models

McGree, James; Eccleston, J. A.

doi:10.1080/00401706.2012.648867

Cited by 12 publications

(7 citation statements)

References 17 publications

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“…Consider the model y i | β ∼ Poisson(λ i ), with µ i = λ i and h(µ) = log µ. Optimal designs for this model were considered by Russell et al (2009) and McGree and Eccleston (2012). Here, w(η) = exp(η) and we have the following results.…”

Section: Poisson Regressionmentioning

confidence: 99%

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

Waite¹

2018

STAT SINICA

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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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Section: Poisson Regressionmentioning

confidence: 99%

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

Waite¹

2018

STAT SINICA

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“…We restrict attention to designs that are minimally supported with respect to the maximal model, that is, where the number, n, of distinct support points is q + 1. For this class of designs, Russell et al (2009) and McGree and Eccleston (2012) presented analytical design construction methods. Atkinson and Woods (2015) showed that for these designs with −1 ≤ x ij ≤ 1 and E(β im ) ≥ 1, for any m = 1, .…”

Section: Minimally-supported Designsmentioning

confidence: 99%

“…Maximisation of (13) defines a (pseudo-) Bayesian D-optimality criterion for the maximal model. A heuristic justification for using this criterion to find model-robust designs was given by McGree and Eccleston (2012) who pointed out that, assuming common prior distributions, the levels included for each variable in the minimally-supported Bayesian D-optimal design for each individual model m are the same. Only the numbers of replications of each variable value differ between the designs.…”

Section: Minimally-supported Designsmentioning

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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“…14) or in environmental and biological experiments where the response is the count of animal numbers or cell growth. Let y( McGree and Eccleston (2012) and Atkinson and Woods (2015) presented theoretical constructions of optimal designs robust to the values of the model parameters for log-linear models with linear predictors of the form…”

Section: Experiments With Discrete Responsesmentioning

confidence: 99%

Bayesian design of experiments for generalised linear models and dimensional analysis with industrial and scientific application

Woods

Overstall

Adamou

et al. 2016

Quality Engineering

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The design of an experiment can always be considered at least implicitly Bayesian, with prior knowledge used informally to aid decisions such as the variables to be studied and the choice of a plausible relationship between the explanatory variables and measured responses. Bayesian methods allow uncertainty in these decisions to be incorporated into design selection through prior distributions that encapsulate information available from scientific knowledge or previous experimentation. Further, a design may be explicitly tailored to the aim of the experiment through a decision-theoretic approach using an appropriate loss function. We review the area of decision-theoretic Bayesian design, with particular emphasis on recent advances in computational methods. For many problems arising in industry and science, experiments result in a discrete response that is well described by a member of the class of generalized linear models. Bayesian design for such nonlinear models is often seen as impractical as the expected loss is analytically intractable and numerical approximations are usually computationally expensive. We describe how Gaussian process emulation, commonly used in computer experiments, can play an important role in facilitating Bayesian design for realistic problems. A main focus is the combination of Gaussian process regression to approximate the expected loss with cyclic descent (coordinate exchange) optimization algorithms to allow optimal designs to be found for previously infeasible problems. We also present the first optimal design results for statistical models formed from dimensional analysis, a methodology widely employed in the engineering and physical sciences to produce parsimonious and interpretable models. Using the famous paper helicopter experiment, we show the potential for the combination of Bayesian design, generalized linear models, and dimensional analysis to produce small but informative experiments.

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Robust Designs for Poisson Regression Models

Cited by 12 publications

References 17 publications

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

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

Model selection via Bayesian information capacity designs for generalised linear models

Bayesian design of experiments for generalised linear models and dimensional analysis with industrial and scientific application

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