A Total Entropy Criterion for the Dual Problem of Model Discrimination and Parameter Estimation

Borth, David M.

doi:10.1111/j.2517-6161.1975.tb01032.x

Cited by 41 publications

(35 citation statements)

References 17 publications

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“…The optimal design that maximises the utility function is the one that yields the largest information gain, on average, about .Â/ upon observation of the data. Mathematically, the mutual information is the KLD between the joint distribution p.Â; yjd/ and product of marginal distributions of Â and y (Borth, 1975). Ryan (2003) used mutual information to find static designs for efficient parameter estimation.…”

Section: Information-based Utilitiesmentioning

confidence: 99%

“…Conjugate priors have been used to obtain analytic results (e.g. Borth, 1975), and numerical quadrature has also been used (e.g. Cavagnaro et al, 2010).…”

Section: Information-based Utilitiesmentioning

confidence: 99%

“…Model discrimination is an important experimental design problem that has generated a substantial amount of research (for example, Box and Hill, 1967;Hill et al, 1968;Borth, 1975;Cavagnaro et al, 2010;. Much of the design literature has focused on producing designs that offer efficient and precise parameter estimates.…”

Section: Utilities For Model Discriminationmentioning

confidence: 99%

“…Mutual information has commonly been used as the utility function in the Bayesian design literature to design for model discrimination (e.g. Box and Hill, 1967;Borth, 1975;Ng and Chick, 2004;Cavagnaro et al, 2010;McGree et al, 2012a). The optimal design d is the one that maximises the mutual information between the (random variable) model indicator, m, and the future observation y (for example, Cavagnaro et al, 2010).…”

Section: Utilities For Model Discriminationmentioning

confidence: 99%

“…DasGupta et al (1992) gave examples of compromise designs in which one is interested in finding a design that is highly efficient for several design problems. Borth (1975) extended the mutual information utility proposed by Box & Hill (1967), so that fully Bayesian designs could be obtained for the dual goals of model discrimination and parameter estimation. This utility is known as 'total entropy'.…”

Section: Utilities For Several Design Objectivesmentioning

confidence: 99%

See 4 more Smart Citations

A Review of Modern Computational Algorithms for Bayesian Optimal Design

Ryan

Drovandi

McGree

et al. 2015

Int Statistical Rev

241

263

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Bayesian experimental design is a fast growing area of research with many real-world applications. As computational power has increased over the years, so has the development of simulation-based design methods, which involve a number of algorithms, such as Markov chain Monte Carlo, sequential Monte Carlo and approximate Bayes methods, and which have enabled more complex design problems to be solved. TheBayesian framework provides a unified approach for incorporating prior information and/or uncertainties regarding the statistical model with a utility function which describes the experimental aims. In this paper, we provide a general overview on the concepts involved in Bayesian experimental design, and focus on describing some of the more commonly-used Bayesian utility functions and methods for their estimation, as well as a number of algorithms that are used to search over the design space to find the optimal Bayesian design. We also discuss other computational strategies for further research in Bayesian optimal design.

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Section: Information-based Utilitiesmentioning

confidence: 99%

“…Conjugate priors have been used to obtain analytic results (e.g. Borth, 1975), and numerical quadrature has also been used (e.g. Cavagnaro et al, 2010).…”

Section: Information-based Utilitiesmentioning

confidence: 99%

Section: Utilities For Model Discriminationmentioning

confidence: 99%

Section: Utilities For Model Discriminationmentioning

confidence: 99%

Section: Utilities For Several Design Objectivesmentioning

confidence: 99%

See 3 more Smart Citations

A Review of Modern Computational Algorithms for Bayesian Optimal Design

Ryan

Drovandi

McGree

et al. 2015

Int Statistical Rev

241

263

View full text Add to dashboard Cite

show abstract

Bayesian design for minimizing prediction uncertainty in bivariate spatial responses with applications to air quality monitoring

2023

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Model‐based geostatistical design involves the selection of locations to collect data to minimize an expected loss function over a set of all possible locations. The loss function is specified to reflect the aim of data collection, which, for geostatistical studies, could be to minimize the prediction uncertainty at unobserved locations. In this paper, we propose a new approach to design such studies via a loss function derived through considering the entropy about the model predictions and the parameters of the model. The approach includes a multivariate extension to generalized linear spatial models, and thus can be used to design experiments with more than one response. Unfortunately, evaluating our proposed loss function is computationally expensive so we provide an approximation such that our approach can be adopted to design realistically sized geostatistical studies. This is demonstrated through a simulated study and through designing an air quality monitoring program in Queensland, Australia. The results show that our designs remain highly efficient in achieving each experimental objective individually, providing an ideal compromise between the two objectives. Accordingly, we advocate that our approach could be adopted more generally in model‐based geostatistical design.

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Bayesian adaptive N‐of‐1 trials for estimating population and individual treatment effects

Senarathne

Overstall

McGree

2020

Statistics in Medicine

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This article proposes a novel adaptive design algorithm that can be used to find optimal treatment allocations in N-of-1 clinical trials. This new methodology uses two Laplace approximations to provide a computationally efficient estimate of population and individual random effects within a repeated measures, adaptive design framework. Given the efficiency of this approach, it is also adopted for treatment selection to target the collection of data for the precise estimation of treatment effects. To evaluate this approach, we consider both a simulated and motivating N-of-1 clinical trial from the literature. For each trial, our methods were compared with the multiarmed bandit approach and a randomized N-of-1 trial design in terms of identifying the best treatment for each patient and the information gained about the model parameters. The results show that our new approach selects designs that are highly efficient in achieving each of these objectives. As such, we propose our Laplace-based algorithm as an efficient approach for designing adaptive N-of-1 trials.

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A Total Entropy Criterion for the Dual Problem of Model Discrimination and Parameter Estimation

Cited by 41 publications

References 17 publications

A Review of Modern Computational Algorithms for Bayesian Optimal Design

A Review of Modern Computational Algorithms for Bayesian Optimal Design

Bayesian design for minimizing prediction uncertainty in bivariate spatial responses with applications to air quality monitoring

Bayesian adaptive N‐of‐1 trials for estimating population and individual treatment effects

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