Decision-theoretic sensitivity analysis for reservoir development under uncertainty using multilevel quasi-Monte Carlo methods

Goda, Takashi; Murakami, Daisuke; Tanaka, Kei; Satô, Kôzô

doi:10.1007/s10596-018-9735-7

Cited by 10 publications

(17 citation statements)

References 23 publications

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“…The idea behind QMC sampling is that by distributing samples more uniformly or evenly over the domain, i.e., by generating "lowdiscrepancy" points or sequences, the rate of convergence for estimating expectations is to be improved. There are some works which combine QMC sampling with MLMC, see for instance [10,11]. It is expected to achieve additional computational savings also in the current application.…”

Section: Discussionmentioning

confidence: 99%

Multilevel Monte Carlo estimation of expected information gains

Goda

Hironaka

Iwamoto

2019

Stochastic Analysis and Applications

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The expected information gain is an important quality criterion of Bayesian experimental designs, which measures how much the information entropy about uncertain quantity of interest θ is reduced on average by collecting relevant data Y . However, estimating the expected information gain has been considered computationally challenging since it is defined as a nested expectation with an outer expectation with respect to Y and an inner expectation with respect to θ. In fact, the standard, nested Monte Carlo method requires a total computational cost of O(ε −3 ) to achieve a root-mean-square accuracy of ε. In this paper we develop an efficient algorithm to estimate the expected information gain by applying a multilevel Monte Carlo (MLMC) method. To be precise, we introduce an antithetic MLMC estimator for the expected information gain and provide a sufficient condition on the data model under which the antithetic property of the MLMC estimator is well exploited such that optimal complexity of O(ε −2 ) is achieved. Furthermore, we discuss how to incorporate importance sampling techniques within the MLMC estimator to avoid arithmetic underflow. Numerical experiments show the considerable computational cost savings compared to the nested Monte Carlo method for a simple test case and a more realistic pharmacokinetic model.

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Section: Discussionmentioning

confidence: 99%

Multilevel Monte Carlo estimation of expected information gains

Goda

Hironaka

Iwamoto

2019

Stochastic Analysis and Applications

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“…Looking only at the variability (or, the variance) of the output from a single model is not enough, however, if we are faced with a decision-making problem 15 , 16 . Let D be a finite set of possible alternative options for decision, and consider that each option is associated with its model described by an utility function .…”

Section: Introductionmentioning

confidence: 99%

“…In fact, the equality is equivalent to that happens almost surely (up to uniqueness of the argument), that is, the perfect knowledge on does not change the choice of the optimal option. This is how probabilistic sensitivity analysis can be performed for a decision model, and a strong interest in such decision-theoretic probabilistic sensitivity analysis can be found not only in health economic evaluations 21 – 24 but also in petroleum engineering 16 , 25 , 26 . Here we emphasize that EVPPI is not the only measure for evaluating the relative importance of each input variable, and we shall introduce a new sensitivity measure called decision switching probability in this paper.…”

Section: Introductionmentioning

confidence: 99%

Probabilistic threshold analysis by pairwise stochastic approximation for decision-making under uncertainty

Goda

Yamada

2021

Sci Rep

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The concept of probabilistic parameter threshold analysis has recently been introduced as a way of probabilistic sensitivity analysis for decision-making under uncertainty, in particular, for health economic evaluations which compare two or more alternative treatments with consideration of uncertainty on outcomes and costs. In this paper we formulate the probabilistic threshold analysis as a root-finding problem involving the conditional expectations, and propose a pairwise stochastic approximation algorithm to search for the threshold value below and above which the choice of conditionally optimal decision options changes. Numerical experiments for both a simple synthetic testcase and a chemotherapy Markov model illustrate the effectiveness of our proposed algorithm, without any need for accurate estimation or approximation of conditional expectations which the existing approaches rely upon. Moreover we introduce a new measure called decision switching probability for probabilistic sensitivity analysis in this paper.

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“…This method is computationally very expensive as it requires building a posterior ensemble of realizations for every possible dataset. Goda et al (2018) used multilevel quasi-Monte Carlo methods to estimate the Expected Value of Partial Perfect Information (EVPPI), but their model too is parameterized using a few parameters, and thus might not capture the complex spatial heterogeneity of petroleum reservoirs.…”

Section: Introductionmentioning

confidence: 99%

Value of information of time-lapse seismic data by simulation-regression: comparison with double-loop Monte Carlo

Dutta

Mukerji

Eidsvik³

2019

Comput Geosci

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Simulation-regression is a computationally efficient methodology to estimate the value of information (VOI), as it involves directly estimating the value outcomes corresponding to different data realizations by building a statistical relationship between the prospect values and the data, rather than estimating the model parameters from the data and then estimating the value outcomes given the model parameters. The simulation-regression workflow is applied to estimate the VOI of time-lapse seismic data in a 2D reservoir case using Partial Least Squares Regression (PLSR) and Principal Components Regression (PCR), and the variance in the VOI result is estimated using bootstrapping for varying number of realizations. The VOI results from the two regression techniques are found to be consistent, and it is seen from the bootstrap results that the variance in the VOI decreases with increasing number of realizations and the VOI ranges obtained by higher number of realizations are captured by those obtained by fewer realizations. The VOI results from simulation-regression are then compared with those obtained by a rigorous Monte Carlo method, where the posterior model realizations are sampled using rejection sampling for each possible data realization, and then the prospect values are estimated for each model realization using flow simulation. Finally, the simulation-regression method is applied to estimate the VOI of timelapse seismic data in a complex production optimization case involving sequential well placement and control decisions.

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Decision-theoretic sensitivity analysis for reservoir development under uncertainty using multilevel quasi-Monte Carlo methods

Cited by 10 publications

References 23 publications

Multilevel Monte Carlo estimation of expected information gains

Multilevel Monte Carlo estimation of expected information gains

Probabilistic threshold analysis by pairwise stochastic approximation for decision-making under uncertainty

Value of information of time-lapse seismic data by simulation-regression: comparison with double-loop Monte Carlo

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