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国际不确定性的量化期刊

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ISSN 打印: 2152-5080

ISSN 在线: 2152-5099

The Impact Factor measures the average number of citations received in a particular year by papers published in the journal during the two preceding years. 2017 Journal Citation Reports (Clarivate Analytics, 2018) IF: 1.7 To calculate the five year Impact Factor, citations are counted in 2017 to the previous five years and divided by the source items published in the previous five years. 2017 Journal Citation Reports (Clarivate Analytics, 2018) 5-Year IF: 1.9 The Immediacy Index is the average number of times an article is cited in the year it is published. The journal Immediacy Index indicates how quickly articles in a journal are cited. Immediacy Index: 0.5 The Eigenfactor score, developed by Jevin West and Carl Bergstrom at the University of Washington, is a rating of the total importance of a scientific journal. Journals are rated according to the number of incoming citations, with citations from highly ranked journals weighted to make a larger contribution to the eigenfactor than those from poorly ranked journals. Eigenfactor: 0.0007 The Journal Citation Indicator (JCI) is a single measurement of the field-normalized citation impact of journals in the Web of Science Core Collection across disciplines. The key words here are that the metric is normalized and cross-disciplinary. JCI: 0.5 SJR: 0.584 SNIP: 0.676 CiteScore™:: 3 H-Index: 25

Indexed in

A MULTI-INDEX MARKOV CHAIN MONTE CARLO METHOD

卷 8, 册 1, 2018, pp. 61-73
DOI: 10.1615/Int.J.UncertaintyQuantification.2018021551
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摘要

In this paper, we consider computing expectations with respect to probability laws associated with a certain class of stochastic systems. In order to achieve such a task, one must not only resort to numerical approximation of the expectation but also to a biased discretization of the associated probability. We are concerned with the situation for which the discretization is required in multiple dimensions, for instance in space-time. In such contexts, it is known that the multi-index Monte Carlo (MIMC) method of Haji-Ali, Nobile, and Tempone, (Numer. Math., 132, pp. 767– 806, 2016) can improve on independent identically distributed (i.i.d.) sampling from the most accurate approximation of the probability law. Through a nontrivial modification of the multilevel Monte Carlo (MLMC) method, this method can reduce the work to obtain a given level of error, relative to i.i.d. sampling and even to MLMC. In this paper, we consider the case when such probability laws are too complex to be sampled independently, for example a Bayesian inverse problem where evaluation of the likelihood requires solution of a partial differential equation model, which needs to be approximated at finite resolution. We develop a modification of the MIMC method, which allows one to use standard Markov chain Monte Carlo (MCMC) algorithms to replace independent and coupled sampling, in certain contexts. We prove a variance theorem for a simplified estimator that shows that using our MIMCMC method is preferable, in the sense above, to i.i.d. sampling from the most accurate approximation, under appropriate assumptions. The method is numerically illustrated on a Bayesian inverse problem associated to a stochastic partial differential equation, where the path measure is conditioned on some observations.

对本文的引用
  1. Hoang Viet Ha, Quek Jia Hao, Schwab Christoph, Analysis of a multilevel Markov chain Monte Carlo finite element method for Bayesian inversion of log-normal diffusions, Inverse Problems, 36, 3, 2020. Crossref

  2. Zhang Jiaxin, Modern Monte Carlo methods for efficient uncertainty quantification and propagation: A survey, WIREs Computational Statistics, 13, 5, 2021. Crossref

  3. Jasra Ajay, Law Kody J. H., Xu Yaxian, Markov chain simulation for multilevel Monte Carlo, Foundations of Data Science, 3, 1, 2021. Crossref

  4. Chada Neil K., Franks Jordan, Jasra Ajay, Law Kody J., Vihola Matti, Unbiased Inference for Discretely Observed Hidden Markov Model Diffusions, SIAM/ASA Journal on Uncertainty Quantification, 9, 2, 2021. Crossref

  5. Jasra Ajay, Law Kody J. H., Tarakanov Alexander, Yu Fangyuan, Randomized Multilevel Monte Carlo for Embarrassingly Parallel Inference, in Driving Scientific and Engineering Discoveries Through the Integration of Experiment, Big Data, and Modeling and Simulation, 1512, 2022. Crossref

  6. Yang Juntao, Hoang Viet Ha, Multilevel Markov Chain Monte Carlo for Bayesian inverse problem for Navier-Stokes equation, Inverse Problems and Imaging, 2022. Crossref

  7. Davis Andrew D., Marzouk Youssef, Smith Aaron, Pillai Natesh, Rate-optimal refinement strategies for local approximation MCMC, Statistics and Computing, 32, 4, 2022. Crossref

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