Learning Functions and Approximate Bayesian Computation Design: ABCD

Hainy, Markus; Müller, Werner G.; Wynn, Henry P.

doi:10.3390/e16084353

Cited by 11 publications

(9 citation statements)

References 28 publications

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“…To discuss this connection more precisely in our particular setting, let us consider the following definition. Then it is easy to see that any functional of the form H(ν) = H ′ (ν β ) is DoA, where H ′ denotes a DoA functional defined on some appropriate subset of the set of all probability measures on R p ; the reader is referred to [30] for a variety of examples of such functionals. Section 4.2 provides an example of this construction, with p = 1 and H ′ the variance functional.…”

Section: Uncertainty Functionals and Uncertainty Reductionmentioning

confidence: 99%

A supermartingale approach to Gaussian process based sequential design of experiments

Bect¹,

Bachoc²,

Ginsbourger³

2019

Bernoulli

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Gaussian process (GP) models have become a well-established framework for the adaptive design of costly experiments, and notably of computer experiments. GP-based sequential designs have been found practically efficient for various objectives, such as global optimization (estimating the global maximum or maximizer(s) of a function), reliability analysis (estimating a probability of failure) or the estimation of level sets and excursion sets. In this paper, we study the consistency of an important class of sequential designs, known as stepwise uncertainty reduction (SUR) strategies. Our approach relies on the key observation that the sequence of residual uncertainty measures, in SUR strategies, is generally a supermartingale with respect to the filtration generated by the observations. This observation enables us to establish generic consistency results for a broad class of SUR strategies. The consistency of several popular sequential design strategies is then obtained by means of this general result. Notably, we establish the consistency of two SUR strategies proposed by Bect, Ginsbourger, Li, Picheny and Vazquez (Stat. Comp., 2012)-to the best of our knowledge, these are the first proofs of consistency for GP-based sequential design algorithms dedicated to the estimation of excursion sets and their measure. We also establish a new, more general proof of consistency for the expected improvement algorithm for global optimization which, unlike previous results in the literature, applies to any GP with continuous sample paths.MSC 2010 subject classifications: Primary 60G15, 62L05; secondary 68T05.

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Section: Uncertainty Functionals and Uncertainty Reductionmentioning

confidence: 99%

A supermartingale approach to Gaussian process based sequential design of experiments

Bect¹,

Bachoc²,

Ginsbourger³

2019

Bernoulli

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show abstract

“…We agree that the consideration of the expected performance (or worst‐case performance as in ) for a set of possible ν would be more robust and could be more or less straightforwardly implemented in our framework. Another possibility would be to take a fully Bayesian approach and apply a simulation‐based technique such as ABCD (see and ).…”

Section: Dependence Upon Parameter Valuesmentioning

confidence: 99%

Rejoinder to ‘Efficient Prediction Designs for Random Fields’

Müller

Pronzato

Rendas

et al. 2015

Appl Stoch Models Bus & Ind

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“…Hainy et al. 2014 ), which is also called the expected utility. As utility function one would typically use convex functionals of the posterior distribution, such as the Kullback-Leibler divergence between the (uninformative) prior and the posterior distribution, to measure the additional information gained by conducting the experiment (Chaloner and Verdinelli 1995 ).…”

Section: Introductionmentioning

confidence: 99%

Likelihood-free simulation-based optimal design with an application to spatial extremes

Hainy

Müller

Wagner

2015

Stoch Environ Res Risk Assess

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In this paper we employ a novel method to find the optimal design for problems where the likelihood is not available analytically, but simulation from the likelihood is feasible. To approximate the expected utility we make use of approximate Bayesian computation methods. We detail the approach for a model on spatial extremes, where the goal is to find the optimal design for efficiently estimating the parameters determining the dependence structure. The method is applied to determine the optimal design of weather stations for modeling maximum annual summer temperatures.Electronic supplementary materialThe online version of this article (doi:10.1007/s00477-015-1067-8) contains supplementary material, which is available to authorized users.

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Learning Functions and Approximate Bayesian Computation Design: ABCD

Cited by 11 publications

References 28 publications

A supermartingale approach to Gaussian process based sequential design of experiments

A supermartingale approach to Gaussian process based sequential design of experiments

Rejoinder to ‘Efficient Prediction Designs for Random Fields’

Likelihood-free simulation-based optimal design with an application to spatial extremes

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