Bayesian design of experiments for generalised linear models and dimensional analysis with industrial and scientific application: rejoinder to discussion

Woods, David C.; Overstall, Antony M.; Adamou, Maria; Waite, Timothy W.

doi:10.1080/08982112.2016.1246051

Cited by 5 publications

(5 citation statements)

References 12 publications

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“…For example, under SIG and NSEL, the utility function is not available in closed form, not to mention the expected SIG and NSEL utilities. Even with the ongoing development of new methodology (see, for example, Ryan et al, 2016;Woods et al, 2017) to approximate and maximise the expected utility, finding designs in practice is a computationally expensive task. Under standard regularity conditions (see, for example, Schervish, 1995, page 111), it can be shown (Walker, 2016) that the expected FIG utility can be written…”

Section: Bayesian Decision-theoretic Design Of Experimentsmentioning

confidence: 99%

Properties of Fisher information gain for Bayesian design of experiments

Overstall

2022

Journal of Statistical Planning and Inference

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Section: Bayesian Decision-theoretic Design Of Experimentsmentioning

confidence: 99%

Properties of Fisher information gain for Bayesian design of experiments

Overstall

2022

Journal of Statistical Planning and Inference

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“…We describe this novel approach for the logistic model case and provide a simulation to show how it compares to the myopic approach. This approach takes averages over simulated values of the covariates for subjects i + 1 up to n. Optimization based on Monte Carlo simulations of unknown quantities is typically conducted in a Bayesian setting for design of experiments [26], where values of the unknown parameters may be simulated from a prior distribution. See Gentle [27] for an overview of Monte Carlo methods and Ryan [28] for an application to Bayesian design of experiments.…”

Section: Pseudo-nonmyopic Approachmentioning

confidence: 99%

Nonmyopic and pseudo-nonmyopic approaches to optimal sequential design in the presence of covariates

Tackney¹,

Woods²,

Shpitser³

2022

Journal of Statistical Computation and Simulation

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In sequential experiments, subjects become available for the study over a period of time, and covariates are often measured at the time of arrival. We consider the setting where the sample size is fixed but covariate values are unknown until subjects enrol. Given a model for the outcome, a sequential optimal design approach can be used to allocate treatments to minimize the variance of the estimator of the treatment effect. We extend existing optimal design methodology so it can be used within a nonmyopic framework, where treatment allocation for the current subject depends not only on the treatments and covariates of the subjects already enrolled in the study, but also the impact of possible future treatment assignments within a specified horizon. The nonmyopic approach requires recursive formulae and suffers from the curse of dimensionality. We propose a pseudo-nonmyopic approach which has a similar aim to the nonmyopic approach, but does not involve recursion and instead relies on simulating trajectories of future possible decisions. Our simulation studies show that, for the simple case of a logistic regression with a single binary covariate and a binary treatment, and a more realistic case with four binary covariates, binary treatment and treatment-covariate interactions, the nonmyopic and pseudo-nonmyopic approaches provide no competitive advantage over the myopic approach, both in terms of the size of the estimated treatment effect and also the efficiency of the designs. Results are robust to the size of the horizon used in the nonmyopic approach, and the number of simulated trajectories used in the pseudo-nonmyopic approach.

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“…However, the results would often be highly sensitive to the value chosen for M , which is arbitrary and typically has no objective justification. For further discussion on the role of prior information in design of experiments, see Woods et al (2016).…”

Section: Alternative Prior Distributionsmentioning

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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Bayesian design of experiments for generalised linear models and dimensional analysis with industrial and scientific application: rejoinder to discussion

Cited by 5 publications

References 12 publications

Properties of Fisher information gain for Bayesian design of experiments

Properties of Fisher information gain for Bayesian design of experiments

Nonmyopic and pseudo-nonmyopic approaches to optimal sequential design in the presence of covariates

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

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