Optimal Bayesian Design by Inhomogeneous Markov Chain Simulation

Müller, Peter; Sansó, Bruno; Iorio, Maria De

doi:10.1198/016214504000001123

Cited by 140 publications

(152 citation statements)

References 20 publications

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“…However exponentiating this function to a power of 50 concentrates most of the probability mass on the major mode, so that samples distributed proportional to this function provide a good basis for estimating π * . When using a single MCMC chain using the approach of [10], the chain often gets trapped in the minor modes, as can be seen in Figure 2(c). The interaction between multiple particles in the SMC samplers algorithm we proposed in [8] helps avoid this and yields a much better estimate as shown in Figure 2(d).…”

Section: Active Sensing Examplementioning

confidence: 99%

“…The corresponding expected utility U (π) for the maximum entropy criterion from Equation 1.1 is shown as a dashed blue line in (b) while U (π) 50 is displayed in solid red. Plot (c) presents a histogram of the final samples of 100 independent MCMC chains using the approach of [10] when annealing to U (π) 50 , while (d) shows the result achieved using 100 interacting particles using our SMC samplers algorithm proposed in [8].…”

Section: Active Sensing Examplementioning

confidence: 99%

“…In the context of control this seems to have originated with [4], although only immediate rewards are considered, thus making it perhaps more applicable to the setting of myopic experimental design. In this section we will focus on a promising sample-based technique originating in the experimental design literature [10].…”

Section: A Common Solution Frameworkmentioning

confidence: 99%

“…However, these approaches are expensive and inadequate for high dimensional spaces. To eliminate the need for discretization, Müller et al [10] proposed a Markov chain Monte Carlo annealing technique for simultaneous maximization and integration. They define the following artificial target distribution For large exponents J, the probability mass of this distribution will concentrate on the global maximum for π * .…”

Section: A Common Solution Frameworkmentioning

confidence: 99%

See 3 more Smart Citations

Inference and Learning for Active Sensing, Experimental Design and Control

Kueck

Hoffman

Doucet

et al. 2009

Pattern Recognition and Image Analysis

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Abstract. In this paper we argue that maximum expected utility is a suitable framework for modeling a broad range of decision problems arising in pattern recognition and related fields. Examples include, among others, gaze planning and other active vision problems, active learning, sensor and actuator placement and coordination, intelligent humancomputer interfaces, and optimal control. Following this remark, we present a common inference and learning framework for attacking these problems. We demonstrate this approach on three examples: (i) active sensing with nonlinear, non-Gaussian, continuous models, (ii) optimal experimental design to discriminate among competing scientific models, and (iii) nonlinear optimal control. The Principle of Maximum Expected Utility

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Section: Active Sensing Examplementioning

confidence: 99%

Section: Active Sensing Examplementioning

confidence: 99%

Section: A Common Solution Frameworkmentioning

confidence: 99%

Section: A Common Solution Frameworkmentioning

confidence: 99%

See 2 more Smart Citations

Inference and Learning for Active Sensing, Experimental Design and Control

Kueck

Hoffman

Doucet

et al. 2009

Pattern Recognition and Image Analysis

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show abstract

“…We design a Markov chain Monte Carlo (MCMC) algorithm with a corresponding marginal distribution on the decision that collapses on the optimal first-stage decision. Our approach builds on previous literature; see Bielza et al (1999), Müller et al (2004), and Jacquier et al (2007).…”

Section: Introductionmentioning

confidence: 99%

Augmented Markov Chain Monte Carlo Simulation for Two-Stage Stochastic Programs with Recourse

2014

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I n this paper, we develop a simulation-based approach for two-stage stochastic programs with recourse.We construct an augmented probability model with stochastic shocks and decision variables. Simulating from the augmented probability model solves for the expected recourse function and the optimal first-stage decision. Markov chain Monte Carlo methods, together with ergodic averaging, provide a framework to compute the optimal solution. We illustrate our methodology via the two-stage newsvendor problem with unimodal and bimodal continuous uncertainty. Finally, we present performance comparisons of our algorithm and the sample average approximation method.

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Decision Search via Simulation

De Iorio

2007

Encyclopedia of Statistics in Quality and Reliability

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This entry provides an overview of simulation‐based methods in decision theory and optimal design problems. We consider decision problems defined by a utility function and an underlying probability model for all unknowns. The search for the optimal design requires the maximization of the expected utility with respect to some design parameter, where the expectation is taken with respect to all the unknowns. In many applications the solution to the optimal design problem is not analytically tractable, as neither the maximization nor the integration have a closed‐form solution requiring approximation and/or simulation‐based methods. We present four related simulation‐based strategies: prior simulations, curve fitting of Monte Carlo experiments, Markov chain Monte Carlo simulations in an augmented probability model, and inhomogeneous Markov chain simulations.

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Optimal Bayesian Design by Inhomogeneous Markov Chain Simulation

Cited by 140 publications

References 20 publications

Inference and Learning for Active Sensing, Experimental Design and Control

Inference and Learning for Active Sensing, Experimental Design and Control

Augmented Markov Chain Monte Carlo Simulation for Two-Stage Stochastic Programs with Recourse

Decision Search via Simulation

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