Estimating Expected Information Gains for Experimental Designs With Application to the Random Fatigue-Limit Model

Ryan, Kenneth J.

doi:10.1198/1061860032012

Cited by 134 publications

(149 citation statements)

References 14 publications

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“…Ryan () used mutual information to find static designs for efficient parameter estimation. Kim et al () used the mutual information utility to find sequential designs to efficiently estimate parameters, which was of the form:

U (d_{(t)}) = \int_{normalΘ} \int_{Y} [\log (\frac{p (φ (θ) | d_{(t)}, y_{(1 : t)})}{p (φ (θ) | y_{(1 : t - 1)})})] p (y_{(t)} | d_{(t)}, φ (θ)) p (φ (θ) | y_{(1 : t - 1)}) d y_{(t)} d θ,

where y (1: t ) are the data that were observed from the first to the t ‐th trial, y ( t ) are the data that were observed at the current, t ‐th trial, using design d ( t ) , y (1: t − 1) are the data that were measured from the first to the ( t − 1)‐th trials using the designs d (1: t − 1) .…”

Section: Bayesian Utility Functions and Methods For Their Estimationmentioning

confidence: 99%

A Review of Modern Computational Algorithms for Bayesian Optimal Design

Ryan

Drovandi

McGree

et al. 2015

Int Statistical Rev

228

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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U (d_{(t)}) = \int_{normalΘ} \int_{Y} [\log (\frac{p (φ (θ) | d_{(t)}, y_{(1 : t)})}{p (φ (θ) | y_{(1 : t - 1)})})] p (y_{(t)} | d_{(t)}, φ (θ)) p (φ (θ) | y_{(1 : t - 1)}) d y_{(t)} d θ,

Section: Bayesian Utility Functions and Methods For Their Estimationmentioning

confidence: 99%

A Review of Modern Computational Algorithms for Bayesian Optimal Design

Ryan

Drovandi

McGree

et al. 2015

Int Statistical Rev

228

263

View full text Add to dashboard Cite

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“…As suggested in [6], the most used utility function ( , , ) is the Kullbach-Leibler divergence, i.e., the increase in Shannon information between the prior probability distribution and the posterior probability distribution:…”

Section: Methodsmentioning

confidence: 99%

Optimal Sensor Placement through Bayesian Experimental Design: Effect of Measurement Noise and Number of Sensors

Capellari

Chatzi

Mariani

2016

Proceedings of the 3rd International Electronic Conference on Sensors and Applications, 15–30 November 2016; Available Online:

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Sensors networks for the health monitoring of structural systems ought to be designed to render both accurate estimations of the relevant mechanical parameters and an affordable experimental setup. Therefore, the number, type and location of the sensors have to be chosen so that the uncertainties related to the estimated health are minimized. Several deterministic methods based on the sensitivity of measures with respect to the parameters to be tuned are widely used. Despite their low computational cost, these methods do not take into account the uncertainties related to the measurement process. In former studies, a method based on the maximization of the information associated with the available measurements has been proposed and the use of approximate solutions has been extensively discussed. Here we propose a robust numerical procedure to solve the optimization problem: in order to reduce the computational cost of the overall procedure, Polynomial Chaos Expansion and a stochastic optimization method are employed. The method is applied to a flexible plate. First of all, we investigate how the information changes with the number of sensors; then we analyze the effect of choosing different types of sensors (with their relevant accuracy) on the information provided by the structural health monitoring system.

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“…The computational expense of evaluating the utility function has been a major challenge in deploying Bayesian design to determine the optimal experiment as most of the real world models are complex and cannot be analytically evaluated (Ryan, 2003;Terejanu et al, 2012). In effect, most of the reported work on Bayesian experimental design have been using linear models and in the few studies having non-linear models, approximations of the utility function or Gaussian approximations of the posterior distributions are used (Russi et al, 2008;Mosbach et al, 2012).…”

Section: Introductionmentioning

confidence: 98%

Bayesian estimation of parametric uncertainties, quantification and reduction using optimal design of experiments for CO2 adsorption on amine sorbents

Kalyanaraman

Fan

Labreche

et al. 2015

Computers & Chemical Engineering

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Please cite this article in press as: Kalyanaraman J, et al. Bayesian estimation of parametric uncertainties, quantification and reduction using optimal design of experiments for CO 2 adsorption on amine sorbents. Computers and Chemical Engineering (2015), http://dx. a b s t r a c tUncertainty quantification plays a significant role in establishing reliability of mathematical models, while applying to process optimization or technology feasibility studies. Uncertainties, in general, could occur either in mathematical model or in model parameters. In this work, process of CO 2 adsorption on amine sorbents, which are loaded in hollow fibers is studied to quantify the impact of uncertainties in the adsorption isotherm parameters on the model prediction. The process design variable that is most closely related to the process economics is the CO 2 sorption capacity, whose uncertainty is investigated. We apply Bayesian analysis and determine a utility function surface corresponding to the value of information gained by the respective experimental design point. It is demonstrated that performing an experiment at a condition with a higher utility has a higher reduction of design variable prediction uncertainty compared to choosing a design point at a lower utility.

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Estimating Expected Information Gains for Experimental Designs With Application to the Random Fatigue-Limit Model

Cited by 134 publications

References 14 publications

A Review of Modern Computational Algorithms for Bayesian Optimal Design

A Review of Modern Computational Algorithms for Bayesian Optimal Design

Optimal Sensor Placement through Bayesian Experimental Design: Effect of Measurement Noise and Number of Sensors

Bayesian estimation of parametric uncertainties, quantification and reduction using optimal design of experiments for CO2 adsorption on amine sorbents

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