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Schuurmans, Dale; Southey, Finnegan

doi:10.1023/a:1013947519741

Cited by 25 publications

(2 citation statements)

References 38 publications

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“…Other adaptations include considerations of scaling (Beskos, Roberts, & Stuart, 2009), Gibbs sampling (Graves, 2011;Walsh, 2004), adaptive methods and step size selection (Graves, 2011) (Atchade & Rosenthal, 2005) (Burda & Maheu, 2011) (Atchade, 2006a) (Cui, Fox, & O'Sullivan, 2011), (Haario, Saksman, & Tamminen, 1999) (Haario, Saksman, & Tamminen, 2001) (Karawatzki, Leydold, & Potzelberger, 2005) (Vihola, 2012) (Roberts & Rosenthal, 2009), hyperdynamic sampling (Sminchisescu & Triggs, 2002), multi modal sampling (Rudoy & Wolfe, 2006), reversible jump (Fronk, 2002), hit and run (Belisle, Romeijn, H., & Smith, 1993), and others (Schuurmans & Southey, 2000) (Brockwell, 2006) (Graves, 2007) (Neal, 2012) (Sanz-Serna, 2013) (Casella, Roberts, & Stramer, 2011).…”

Section: Monte Carlo Techniquesmentioning

confidence: 99%

Bridging the Gap Between Deterministic and Probabilistic Uncertainty Quantification Using Advanced Proxy Based Methods

Goodwin

2015

SPE Reservoir Simulation Symposium

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The use of proxy models for optimisation of expensive functions has demonstrated its value since the 1990's in many industries. Within reservoir engineering, similar techniques have been used for over a decade for history matching, both in commercial tools and in-house software.In addition to efficient history matching, proxy models have a distinct advantage when performing uncertainty quantification of probabilistic forecasts. Markov Chain Monte Carlo (MCMC) methods cannot realistically be applied directly with reservoir simulations, and even fast proxy models can fail dramatically to adequately represent the range of uncertainty if implemented without due care.A pitfall of the use of proxy models is that they are considered 'black box' and their quality is difficult to measure. Engineers prefer to deal with deterministic simulation models which they can evaluate and understand.The main pitfall of simple random walk MCMC techniques, which have begun to appear within reservoir engineering workflows, is a focus on theoretical properties which are not observed in practical implementations. This gives rise to potential gross errors, which are not generally appreciated by practitioners. Advances in recent years within the field of Bayesian statistics have significantly improved this situation, but have not yet been disseminated within the oil and gas industry. This paper describes the limitations of random walk MCMC techniques which are currently used for reservoir prediction studies, and shows how Hamiltonian MCMC techniques, together with an efficient implementation of proxy models, can lead to a more reliable and validated probabilistic uncertainty quantification, whilst also generating a suitable ensemble of deterministic reservoir models. Scientific comparison studies are performed for both an analytical case and a realistic reservoir simulation case to demonstrate the validity of the approach.The benefit of this methodology is to allow asset teams to effectively manage reservoir decisions using a robust and validated understanding of uncertainty. It lays the scientific foundations for the next generation of uncertainty tools and workflows.

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Section: Monte Carlo Techniquesmentioning

confidence: 99%

Bridging the Gap Between Deterministic and Probabilistic Uncertainty Quantification Using Advanced Proxy Based Methods

Goodwin

2015

SPE Reservoir Simulation Symposium

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“…Adaptive importance sampling appears to have originated in the structural safety literature (Bucher, 1988), and has been extensively applied in the communications literature (Al-Qaq, Devetsikiotis, & Townsend, 1995;Remondo et al, 2000). This technique has also been exploited recently in the machine learning community Cheng & Druzdzel, 2000;Ortiz & Kaelbling, 2000;Schuurmans & Southey, 2000). A popular adaptive strategy involves computing the derivative of the first term on the right hand side of Eq.…”

Section: Importance Samplingmentioning

confidence: 99%

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et al. 2003

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Generalization Error Bounds Using Unlabeled Data

Kääriäinen

2005

Learning Theory

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Abstract. We present two new methods for obtaining generalization error bounds in a semi-supervised setting. Both methods are based on approximating the disagreement probability of pairs of classifiers using unlabeled data. The first method works in the realizable case. It suggests how the ERM principle can be refined using unlabeled data and has provable optimality guarantees when the number of unlabeled examples is large. Furthermore, the technique extends easily to cover active learning. A downside is that the method is of little use in practice due to its limitation to the realizable case.The idea in our second method is to use unlabeled data to transform bounds for randomized classifiers into bounds for simpler deterministic classifiers. As a concrete example of how the general method works in practice, we apply it to a bound based on cross-validation. The result is a semi-supervised bound for classifiers learned based on all the labeled data. The bound is easy to implement and apply and should be tight whenever cross-validation makes sense. Applying the bound to SVMs on the MNIST benchmark data set gives results that suggest that the bound may be tight enough to be useful in practice.

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Cited by 25 publications

References 38 publications

Bridging the Gap Between Deterministic and Probabilistic Uncertainty Quantification Using Advanced Proxy Based Methods

Bridging the Gap Between Deterministic and Probabilistic Uncertainty Quantification Using Advanced Proxy Based Methods

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Generalization Error Bounds Using Unlabeled Data

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