Journal articles: 'Rare event probability'

1

Sinha, Ashoke Kumar, and Laurens de Haan. "Estimating the probability of a rare event." Annals of Statistics 27, no. 2 (April 1999): 732–59. http://dx.doi.org/10.1214/aos/1018031214.

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Abbot, Dorian S., Robert J. Webber, Sam Hadden, Darryl Seligman, and Jonathan Weare. "Rare Event Sampling Improves Mercury Instability Statistics." Astrophysical Journal 923, no. 2 (December 1, 2021): 236. http://dx.doi.org/10.3847/1538-4357/ac2fa8.

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Abstract Due to the chaotic nature of planetary dynamics, there is a non-zero probability that Mercury’s orbit will become unstable in the future. Previous efforts have estimated the probability of this happening between 3 and 5 billion years in the future using a large number of direct numerical simulations with an N-body code, but were not able to obtain accurate estimates before 3 billion years in the future because Mercury instability events are too rare. In this paper we use a new rare-event sampling technique, Quantile Diffusion Monte Carlo (QDMC), to estimate that the probability of a Mercury instability event in the next 2 billion years is approximately 10−4 in the REBOUND N-body code. We show that QDMC provides unbiased probability estimates at a computational cost of up to 100 times less than direct numerical simulation. QDMC is easy to implement and could be applied to many problems in planetary dynamics in which it is necessary to estimate the probability of a rare event.

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Ho, Yu-Chi, and Michael E. Larson. "Ordinal optimization approach to rare event probability problems." Discrete Event Dynamic Systems: Theory and Applications 5, no. 2-3 (April 1995): 281–301. http://dx.doi.org/10.1007/bf01439043.

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Chan, Joshua C. C., and Dirk P. Kroese. "Rare-event probability estimation with conditional Monte Carlo." Annals of Operations Research 189, no. 1 (March 24, 2009): 43–61. http://dx.doi.org/10.1007/s10479-009-0539-y.

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Lagnoux, Agnès. "RARE EVENT SIMULATION." Probability in the Engineering and Informational Sciences 20, no. 1 (December 12, 2005): 45–66. http://dx.doi.org/10.1017/s0269964806060025.

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This article deals with estimations of probabilities of rare events using fast simulation based on the splitting method. In this technique, the sample paths are split into multiple copies at various stages in the simulation. Our aim is to optimize the algorithm and to obtain a precise confidence interval of the estimator using branching processes. The numerical results presented suggest that the method is reasonably efficient.

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Picard, Richard R. "Introduction to Rare Event Simulation." Journal of the American Statistical Association 100, no. 471 (September 2005): 1091–92. http://dx.doi.org/10.1198/jasa.2005.s32.

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Pienaar, Elsje. "Multifidelity Analysis for Predicting Rare Events in Stochastic Computational Models of Complex Biological Systems." Biomedical Engineering and Computational Biology 9 (January 2018): 117959721879025. http://dx.doi.org/10.1177/1179597218790253.

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Rare events such as genetic mutations or cell-cell interactions are important contributors to dynamics in complex biological systems, eg, in drug-resistant infections. Computational approaches can help analyze rare events that are difficult to study experimentally. However, analyzing the frequency and dynamics of rare events in computational models can also be challenging due to high computational resource demands, especially for high-fidelity stochastic computational models. To facilitate analysis of rare events in complex biological systems, we present a multifidelity analysis approach that uses medium-fidelity analysis (Monte Carlo simulations) and/or low-fidelity analysis (Markov chain models) to analyze high-fidelity stochastic model results. Medium-fidelity analysis can produce large numbers of possible rare event trajectories for a single high-fidelity model simulation. This allows prediction of both rare event dynamics and probability distributions at much lower frequencies than high-fidelity models. Low-fidelity analysis can calculate probability distributions for rare events over time for any frequency by updating the probabilities of the rare event state space after each discrete event of the high-fidelity model. To validate the approach, we apply multifidelity analysis to a high-fidelity model of tuberculosis disease. We validate the method against high-fidelity model results and illustrate the application of multifidelity analysis in predicting rare event trajectories, performing sensitivity analyses and extrapolating predictions to very low frequencies in complex systems. We believe that our approach will complement ongoing efforts to enable accurate prediction of rare event dynamics in high-fidelity computational models.

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Balesdent, Mathieu, Jérôme Morio, and Julien Marzat. "Recommendations for the tuning of rare event probability estimators." Reliability Engineering & System Safety 133 (January 2015): 68–78. http://dx.doi.org/10.1016/j.ress.2014.09.001.

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Wiorkowski, John. "Finding the probability of a rare real world event." Mathematical Gazette 103, no. 557 (June 6, 2019): 240–47. http://dx.doi.org/10.1017/mag.2019.55.

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One of the nicer things about growing older is that you tend to find a great deal of pleasure in the little rituals of life. Things like morning coffee or tea, a warm bath, or a glass of good wine at the end of the day. There are some rituals, however, that are not at all enjoyable. Take, for example, the monthly ritual of paying bills. I still do this by cheque, so I need to make sure my bank account balance is sufficient to pay the cheque, write the cheque, and subtract the cheque amount from the account balance. Now there is a little pleasure when one actually adds money to the account balance, but the one time that gives me more than a modicum of joy is when the pence portion of the account balance comes out to be exactly zero. This happens very rarely and unpredictably. As a statistician I became intrigued with trying to find the probability of this event occurring. I did an extensive literature search both in traditional hard copy journals and also online, but I could find no reference to this problem.

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Dobson, Ian, Benjamin A. Carreras, and David E. Newman. "How Many Occurrences of Rare Blackout Events Are Needed to Estimate Event Probability?" IEEE Transactions on Power Systems 28, no. 3 (August 2013): 3509–10. http://dx.doi.org/10.1109/tpwrs.2013.2242700.

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Chakraborty, Souvik, and Rajib Chowdhury. "Hybrid Framework for the Estimation of Rare Failure Event Probability." Journal of Engineering Mechanics 143, no. 5 (May 2017): 04017010. http://dx.doi.org/10.1061/(asce)em.1943-7889.0001223.

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Peng, Liang. "Estimating the Probability of a Rare Event via Elliptical Copulas." North American Actuarial Journal 12, no. 2 (April 2008): 116–28. http://dx.doi.org/10.1080/10920277.2008.10597506.

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Bourinet, J. M. "Rare-event probability estimation with adaptive support vector regression surrogates." Reliability Engineering & System Safety 150 (June 2016): 210–21. http://dx.doi.org/10.1016/j.ress.2016.01.023.

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Nguyen, Hoang. "Subjective Risk Estimation of the Rare Event." Journal of KONES 26, no. 1 (March 1, 2019): 103–10. http://dx.doi.org/10.2478/kones-2019-0013.

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Abstract In the safety engineering, the most frequently disadvantage in risk estimation is the lack of data. In such cases, we have to rely on subjective estimations made by persons with practical knowledge in the field of interest, i.e. experts. However, in some realistic situations, they may have uncertainty in the perceiving and evaluation of the problem considered or limited knowledge of the rare events, such as the consequences of the seagoing ship propulsion failures. The probabilistic models of the risk estimation turn out to be insufficient in modelling the subjective uncertainty. The fuzzy methods are viewed to be powerful in dealing with ambiguity and uncertainty that can be used to handle with the subjective estimation. This article addresses the intuitionistic fuzzy method in the subjective estimation of the ship propulsion failure consequences as rare event risk. In the article, a subjective model of the ship propulsion risk is developed as scenarios of the different subsequent consequences of loss of ship propulsion function until a seriously severe accident resulting in loss of seaworthiness. The model proposes an approach combining AHP method and intuitionistic fuzzy method to assess the occurrence probability and severe probability of these rare events based on the expert opinions. In order to show the applicability of the proposed model, a study case of the propulsion risk of the container carrier operating on the North Atlantic lines is conducted.

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Balesdent, Mathieu, Jérôme Morio, and Loïc Brevault. "Rare Event Probability Estimation in the Presence of Epistemic Uncertainty on Input Probability Distribution Parameters." Methodology and Computing in Applied Probability 18, no. 1 (May 23, 2014): 197–216. http://dx.doi.org/10.1007/s11009-014-9411-x.

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Piprek, Patrick, Sébastien Gros, and Florian Holzapfel. "Rare Event Chance-Constrained Optimal Control Using Polynomial Chaos and Subset Simulation." Processes 7, no. 4 (March 30, 2019): 185. http://dx.doi.org/10.3390/pr7040185.

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This study develops a ccoc framework capable of handling rare event probabilities. Therefore, the framework uses the gpc method to calculate the probability of fulfilling rare event constraints under uncertainties. Here, the resulting cc evaluation is based on the efficient sampling provided by the gpc expansion. The subsim method is used to estimate the actual probability of the rare event. Additionally, the discontinuous cc is approximated by a differentiable function that is iteratively sharpened using a homotopy strategy. Furthermore, the subsim problem is also iteratively adapted using another homotopy strategy to improve the convergence of the Newton-type optimization algorithm. The applicability of the framework is shown in case studies regarding battery charging and discharging. The results show that the proposed method is indeed capable of incorporating very general cc within an ocp at a low computational cost to calculate optimal results with rare failure probability cc.

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Hassanaly, Malik, and Venkat Raman. "A self-similarity principle for the computation of rare event probability." Journal of Physics A: Mathematical and Theoretical 52, no. 49 (November 14, 2019): 495701. http://dx.doi.org/10.1088/1751-8121/ab5313.

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Jacquemart, Damien, and Jérôme Morio. "Tuning of adaptive interacting particle system for rare event probability estimation." Simulation Modelling Practice and Theory 66 (August 2016): 36–49. http://dx.doi.org/10.1016/j.simpat.2016.02.004.

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Botev, Zdravko I., Pierre L’Ecuyer, and Bruno Tuffin. "Markov chain importance sampling with applications to rare event probability estimation." Statistics and Computing 23, no. 2 (December 17, 2011): 271–85. http://dx.doi.org/10.1007/s11222-011-9308-2.

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Mossel, Elchanan, and Mesrob I. Ohannessian. "On the Impossibility of Learning the Missing Mass." Entropy 21, no. 1 (January 2, 2019): 28. http://dx.doi.org/10.3390/e21010028.

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This paper shows that one cannot learn the probability of rare events without imposing further structural assumptions. The event of interest is that of obtaining an outcome outside the coverage of an i.i.d. sample from a discrete distribution. The probability of this event is referred to as the “missing mass”. The impossibility result can then be stated as: the missing mass is not distribution-free learnable in relative error. The proof is semi-constructive and relies on a coupling argument using a dithered geometric distribution. Via a reduction, this impossibility also extends to both discrete and continuous tail estimation. These results formalize the folklore that in order to predict rare events without restrictive modeling, one necessarily needs distributions with “heavy tails”.

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Gudmundsson, Thorbjörn, and Henrik Hult. "Markov Chain Monte Carlo for Computing Rare-Event Probabilities for a Heavy-Tailed Random Walk." Journal of Applied Probability 51, no. 2 (June 2014): 359–76. http://dx.doi.org/10.1239/jap/1402578630.

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In this paper a method based on a Markov chain Monte Carlo (MCMC) algorithm is proposed to compute the probability of a rare event. The conditional distribution of the underlying process given that the rare event occurs has the probability of the rare event as its normalizing constant. Using the MCMC methodology, a Markov chain is simulated, with the aforementioned conditional distribution as its invariant distribution, and information about the normalizing constant is extracted from its trajectory. The algorithm is described in full generality and applied to the problem of computing the probability that a heavy-tailed random walk exceeds a high threshold. An unbiased estimator of the reciprocal probability is constructed whose normalized variance vanishes asymptotically. The algorithm is extended to random sums and its performance is illustrated numerically and compared to existing importance sampling algorithms.

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Gudmundsson, Thorbjörn, and Henrik Hult. "Markov Chain Monte Carlo for Computing Rare-Event Probabilities for a Heavy-Tailed Random Walk." Journal of Applied Probability 51, no. 02 (June 2014): 359–76. http://dx.doi.org/10.1017/s0021900200011293.

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In this paper a method based on a Markov chain Monte Carlo (MCMC) algorithm is proposed to compute the probability of a rare event. The conditional distribution of the underlying process given that the rare event occurs has the probability of the rare event as its normalizing constant. Using the MCMC methodology, a Markov chain is simulated, with the aforementioned conditional distribution as its invariant distribution, and information about the normalizing constant is extracted from its trajectory. The algorithm is described in full generality and applied to the problem of computing the probability that a heavy-tailed random walk exceeds a high threshold. An unbiased estimator of the reciprocal probability is constructed whose normalized variance vanishes asymptotically. The algorithm is extended to random sums and its performance is illustrated numerically and compared to existing importance sampling algorithms.

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Липко, И. Ю. "Rare roll event modeling of unmanned catamaran." MORSKIE INTELLEKTUAL`NYE TEHNOLOGII)</msg>, no. 4(54) (December 2, 2021): 219–26. http://dx.doi.org/10.37220/mit.2021.54.4.055.

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Статья посвящена вопросу моделирования редких событий, которые возникают при качке катамарана. Система управления автономного катамарана должна уметь распознавать нежелательные ситуации, которые могут привести к осуществлению редких событий. В данной статье приводится несколько методов, позволяющих проводить моделирование редких событий и делать оценку риска возникновения редкого события. Методы основываются на теории больших уклонений. Первый метод позволяет оценить возможные «ожидаемые потери» при достижении редкого события путём оценки скорости убывания вероятности компонентов вектора состояния в редком состоянии. Оценка осуществляется путём расчёта квазипотенциалов из аттрактора до порогового значения состояния. Второй метод позволяет оценить вероятность движения вдоль наиболее вероятной траектории к редкому событию. Оценка осуществляется путём сравнения вектора состояния с состояниями на наиболее вероятной траектории к редкому событию. Точность оценок зависит от вектора состояния. Приводится сравнение с результатами, полученными с помощью метода Монте-Карло. Указанные методы могут быть использованы для создания систем супервизорного управления и систем поддержки принятия решений при оценке рискованности совершения морских переходов. The article is devoted to the issue of modeling rare events that occur when a catamaran is pitching. The control system of an autonomous catamaran should be able to recognize undesirable situations that can lead to the rare events. This article provides several methods for modeling rare events and making estimation of risk of a rare event occurrence. The methods are based on the large deviations theory for dynamical systems. The first method allows to estimate possible losses via calculation of the probability decreasing rate of the state vector components in a rare state. The estimation is carried out by calculating the quasipotential from the state close to the attractor to the threshold state. The second method allows to estimate the probability of moving along the most likely trajectory to a rare event. The evaluation is carried out by comparing the studied state vector with the states on the most likely trajectory. The accuracy of the estimates depends on the studied state vector. A comparison with the results obtained using the Monte Carlo method. These methods can be used to create supervisory control systems and decision support systems when assessing the riskiness of sea navigation.

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Kuhn, Julia, Michel Mandjes, and Thomas Taimre. "EXACT ASYMPTOTICS OF SAMPLE-MEAN-RELATED RARE-EVENT PROBABILITIES." Probability in the Engineering and Informational Sciences 32, no. 2 (January 16, 2017): 207–28. http://dx.doi.org/10.1017/s0269964816000541.

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Relying only on the classical Bahadur–Rao approximation for large deviations (LDs) of univariate sample means, we derive strong LD approximations for probabilities involving two sets of sample means. The main result concerns the exact asymptotics (asn→∞) of$$ {\open P}\left({\max_{i\in\{1,\ldots,d_x\}}\bar X_{i,n} \les \min_{i\in\{1,\ldots,d_y\}}\bar Y_{i,n}}\right),$$with the${\bar X}_{i,n}{\rm s}$(${\bar Y}_{i,n}{\rm s}$, respectively) denotingdx(dy) independent copies of sample means associated with the random variableX(Y). Assuming${\open E}X \gt {\open E}Y$, this is a rare event probability that vanishes essentially exponentially, but with an additional polynomial term. We also point out how the probability of interest can be estimated using importance sampling in a logarithmically efficient way. To demonstrate the usefulness of the result, we show how it can be applied to compare the order statistics of the sample means of the two populations. This has various applications, for instance in queuing or packing problems.

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Srinivasan, Palanivel, and Manivannan Doraipandian. "Framework for rare event detection using Artificial Neural Network based context free grammar." Journal of Intelligent & Fuzzy Systems 39, no. 6 (December 4, 2020): 8463–75. http://dx.doi.org/10.3233/jifs-189164.

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Rare event detections are performed using spatial domain and frequency domain-based procedures. Omnipresent surveillance camera footages are increasing exponentially due course the time. Monitoring all the events manually is an insignificant and more time-consuming process. Therefore, an automated rare event detection contrivance is required to make this process manageable. In this work, a Context-Free Grammar (CFG) is developed for detecting rare events from a video stream and Artificial Neural Network (ANN) is used to train CFG. A set of dedicated algorithms are used to perform frame split process, edge detection, background subtraction and convert the processed data into CFG. The developed CFG is converted into nodes and edges to form a graph. The graph is given to the input layer of an ANN to classify normal and rare event classes. Graph derived from CFG using input video stream is used to train ANN Further the performance of developed Artificial Neural Network Based Context-Free Grammar – Rare Event Detection (ACFG-RED) is compared with other existing techniques and performance metrics such as accuracy, precision, sensitivity, recall, average processing time and average processing power are used for performance estimation and analyzed. Better performance metrics values have been observed for the ANN-CFG model compared with other techniques. The developed model will provide a better solution in detecting rare events using video streams.

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Krystul, Jaroslav, and Henk A. P. Blom. "SEQUENTIAL MONTE CARLO SIMULATION OF RARE EVENT PROBABILITY IN STOCHASTIC HYBRID SYSTEMS." IFAC Proceedings Volumes 38, no. 1 (2005): 176–81. http://dx.doi.org/10.3182/20050703-6-cz-1902.00382.

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Jeon, Seung-Joon. "A Strategy for Searching a Rare Event 21: Probability Distribution of Bindings." Bulletin of the Korean Chemical Society 35, no. 3 (March 20, 2014): 701–2. http://dx.doi.org/10.5012/bkcs.2014.35.3.701.

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Homem-de-Mello, Tito. "A Study on the Cross-Entropy Method for Rare-Event Probability Estimation." INFORMS Journal on Computing 19, no. 3 (August 2007): 381–94. http://dx.doi.org/10.1287/ijoc.1060.0176.

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Botev, Zdravko I., and Dirk P. Kroese. "An Efficient Algorithm for Rare-event Probability Estimation, Combinatorial Optimization, and Counting." Methodology and Computing in Applied Probability 10, no. 4 (May 20, 2008): 471–505. http://dx.doi.org/10.1007/s11009-008-9073-7.

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Hartmann, Carsten, and Christof Schütte. "Efficient rare event simulation by optimal nonequilibrium forcing." Journal of Statistical Mechanics: Theory and Experiment 2012, no. 11 (November 2, 2012): P11004. http://dx.doi.org/10.1088/1742-5468/2012/11/p11004.

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Cahen, Ewan Jacov, Michel Mandjes, and Bert Zwart. "RARE EVENT ANALYSIS AND EFFICIENT SIMULATION FOR A MULTI-DIMENSIONAL RUIN PROBLEM." Probability in the Engineering and Informational Sciences 31, no. 3 (January 23, 2017): 265–83. http://dx.doi.org/10.1017/s0269964816000553.

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This paper focuses on the evaluation of the probability that both components of a bivariate stochastic process ever simultaneously exceed some large level; a leading example is that of two Markov fluid queues driven by the same background process ever reaching the set (u, ∞)×(u, ∞), for u>0. Exact analysis being prohibitive, we resort to asymptotic techniques and efficient simulation, focusing on large values of u. The first contribution concerns various expressions for the decay rate of the probability of interest, which are valid under Gärtner–Ellis-type conditions. The second contribution is an importance-sampling-based rare-event simulation technique for the bivariate Markov modulated fluid model, which is capable of asymptotically efficiently estimating the probability of interest; the efficiency of this procedure is assessed in a series of numerical experiments.

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Buijsrogge, Anne, Paul Dupuis, and Michael Snarski. "Splitting algorithms for rare event simulation over long time intervals." Annals of Applied Probability 30, no. 6 (December 2020): 2963–98. http://dx.doi.org/10.1214/20-aap1578.

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Chan, Hock Peng, Shaojie Deng, and Tze-Leung Lai. "Rare-Event Simulation of Heavy-Tailed Random Walks by Sequential Importance Sampling and Resampling." Advances in Applied Probability 44, no. 4 (December 2012): 1173–96. http://dx.doi.org/10.1239/aap/1354716593.

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We introduce a new approach to simulating rare events for Markov random walks with heavy-tailed increments. This approach involves sequential importance sampling and resampling, and uses a martingale representation of the corresponding estimate of the rare-event probability to show that it is unbiased and to bound its variance. By choosing the importance measures and resampling weights suitably, it is shown how this approach can yield asymptotically efficient Monte Carlo estimates.

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Chan, Hock Peng, Shaojie Deng, and Tze-Leung Lai. "Rare-Event Simulation of Heavy-Tailed Random Walks by Sequential Importance Sampling and Resampling." Advances in Applied Probability 44, no. 04 (December 2012): 1173–96. http://dx.doi.org/10.1017/s000186780000608x.

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We introduce a new approach to simulating rare events for Markov random walks with heavy-tailed increments. This approach involves sequential importance sampling and resampling, and uses a martingale representation of the corresponding estimate of the rare-event probability to show that it is unbiased and to bound its variance. By choosing the importance measures and resampling weights suitably, it is shown how this approach can yield asymptotically efficient Monte Carlo estimates.

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Ferro, Christopher A. T. "A Probability Model for Verifying Deterministic Forecasts of Extreme Events." Weather and Forecasting 22, no. 5 (October 1, 2007): 1089–100. http://dx.doi.org/10.1175/waf1036.1.

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Abstract This article proposes a method for verifying deterministic forecasts of rare, extreme events defined by exceedance above a high threshold. A probability model for the joint distribution of forecasts and observations, and based on extreme-value theory, characterizes the quality of forecasting systems with two key parameters. This enables verification measures to be estimated for any event rarity and helps to reduce the uncertainty associated with direct estimation. Confidence regions are obtained and the method is used to compare daily precipitation forecasts from two operational numerical weather prediction models.

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Haraszti, Zsolt, and J. Keith Townsend. "The theory of direct probability redistribution and its application to rare event simulation." ACM Transactions on Modeling and Computer Simulation 9, no. 2 (April 1999): 105–40. http://dx.doi.org/10.1145/333296.333349.

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Munoz Zuniga, M., J. Garnier, E. Remy, and E. de Rocquigny. "Adaptive directional stratification for controlled estimation of the probability of a rare event." Reliability Engineering & System Safety 96, no. 12 (December 2011): 1691–712. http://dx.doi.org/10.1016/j.ress.2011.06.016.

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Smith, Peter J. "Introduction to Rare Event Simulation." Biometrics 62, no. 2 (June 2006): 632–33. http://dx.doi.org/10.1111/j.1541-0420.2006.00589_11.x.

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Wagner, Fabian, I. Papaioannou, and E. Ullmann. "The Ensemble Kalman Filter for Rare Event Estimation." SIAM/ASA Journal on Uncertainty Quantification 10, no. 1 (February 28, 2022): 317–49. http://dx.doi.org/10.1137/21m1404119.

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Wang, Liping, and Wenhui Fan. "A multi-level splitting algorithm based on differential evolution." International Journal of Modeling, Simulation, and Scientific Computing 09, no. 02 (March 20, 2018): 1850021. http://dx.doi.org/10.1142/s1793962318500216.

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Multi-level splitting algorithm is a famous rare event simulation (RES) method which reaches rare set through splitting samples during simulation. Since choosing sample paths is a key factor of the method, this paper embeds differential evolution in multi-level splitting mechanism to improve the sampling strategy and precision, so as to improve the algorithm efficiency. Examples of rare event probability estimation demonstrate that the new proposed algorithm performs well in convergence rate and precision for a set of benchmark cases.

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Saidi, Mohamed El Mehdi, Tarik Saouabe, Abdelhafid El Alaoui El Fels, El Mahdi El Khalki, and Abdessamad Hadri. "Hydro-meteorological characteristics and occurrence probability of extreme flood events in Moroccan High Atlas." Journal of Water and Climate Change 11, S1 (July 23, 2020): 310–21. http://dx.doi.org/10.2166/wcc.2020.069.

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Abstract Flood frequency analysis could be a tool to help decision-makers to size hydraulic structures. To this end, this article aims to compare two analysis methods to see how rare an extreme hydrometeorological event is, and what could be its return period. This event caused many deadly floods in southwestern Morocco. It was the result of unusual atmospheric conditions, characterized by a very low atmospheric pressure off the Moroccan coast and the passage of the jet stream further south. Assessment of frequency and return period of this extreme event is performed in a High Atlas watershed (the Ghdat Wadi) using historical floods. We took into account, on the one hand, flood peak flows and, on the other hand, flood water volumes. Statistically, both parameters are better adjusted respectively to Gamma and Log Normal distributions. However, the peak flow approach underestimates the return period of long-duration hydrographs that do not have a high peak flow, like the 2014 event. The latter is indeed better evaluated, as a rare event, by taking into account the flood water volumes. Therefore, this parameter should not be omitted in the calculation of flood probabilities for watershed management and the sizing of flood protection infrastructure.

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Lestang, Thibault, Francesco Ragone, Charles-Edouard Bréhier, Corentin Herbert, and Freddy Bouchet. "Computing return times or return periods with rare event algorithms." Journal of Statistical Mechanics: Theory and Experiment 2018, no. 4 (April 25, 2018): 043213. http://dx.doi.org/10.1088/1742-5468/aab856.

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Abbot, Dorian S., J. D. Laurence-Chasen, Robert J. Webber, David M. Hernandez, and Jonathan Weare. "AI Can Identify Solar System Instability Billions of Years in Advance." Research Notes of the AAS 8, no. 1 (January 3, 2024): 3. http://dx.doi.org/10.3847/2515-5172/ad18a6.

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Abstract Rare event schemes require an approximation of the probability of the rare event as a function of system state. Finding an appropriate reaction coordinate is typically the most challenging aspect of applying a rare event scheme. Here we develop an artificial intelligence (AI) based reaction coordinate that effectively predicts which of a limited number of simulations of the solar system will go unstable using a convolutional neural network classifier. The performance of the algorithm does not degrade significantly even 3.5 billion years before the instability. We overcome the class imbalance intrinsic to rare event problems using a combination of minority class oversampling, increased minority class weighting, and pulling multiple non-overlapping training sequences from simulations. Our success suggests that AI may provide a promising avenue for developing reaction coordinates without detailed theoretical knowledge of the system.

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Radaelli, Giovanni. "Detection of an unknown increase in the rate of a rare event." Journal of Applied Statistics 23, no. 1 (February 1996): 105–14. http://dx.doi.org/10.1080/02664769624396.

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Blanchet, Jose, and Peter Glynn. "Efficient rare-event simulation for the maximum of heavy-tailed random walks." Annals of Applied Probability 18, no. 4 (August 2008): 1351–78. http://dx.doi.org/10.1214/07-aap485.

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Garvels, M. J. J. "A combined splitting—cross entropy method for rare-event probability estimation of queueing networks." Annals of Operations Research 189, no. 1 (August 27, 2009): 167–85. http://dx.doi.org/10.1007/s10479-009-0608-2.

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Dang, Chao, Marcos A. Valdebenito, Pengfei Wei, Jingwen Song, and Michael Beer. "Bayesian active learning line sampling with log-normal process for rare-event probability estimation." Reliability Engineering & System Safety 246 (June 2024): 110053. http://dx.doi.org/10.1016/j.ress.2024.110053.

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Gong, Xianliang, and Yulin Pan. "Multifidelity Bayesian Experimental Design to Quantify Rare-Event Statistics." SIAM/ASA Journal on Uncertainty Quantification 12, no. 1 (February 29, 2024): 101–27. http://dx.doi.org/10.1137/22m1503956.

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Lucente, Dario, Joran Rolland, Corentin Herbert, and Freddy Bouchet. "Coupling rare event algorithms with data-based learned committor functions using the analogue Markov chain." Journal of Statistical Mechanics: Theory and Experiment 2022, no. 8 (August 1, 2022): 083201. http://dx.doi.org/10.1088/1742-5468/ac7aa7.

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Abstract Rare events play a crucial role in many physics, chemistry, and biology phenomena, when they change the structure of the system, for instance in the case of multistability, or when they have a huge impact. Rare event algorithms have been devised to simulate them efficiently, avoiding the computation of long periods of typical fluctuations. We consider here the family of splitting or cloning algorithms, which are versatile and specifically suited for far-from-equilibrium dynamics. To be efficient, these algorithms need to use a smart score function during the selection stage. Committor functions are the optimal score functions. In this work we propose a new approach, based on the analogue Markov chain, for a data-based learning of approximate committor functions. We demonstrate that such learned committor functions are extremely efficient score functions when used with the adaptive multilevel splitting algorithm. We illustrate our approach for a gradient dynamics in a three-well potential, and for the Charney–DeVore model, which is a paradigmatic toy model of multistability for atmospheric dynamics. For these two dynamics, we show that having observed a few transitions is enough to have a very efficient data-based score function for the rare event algorithm. This new approach is promising for use for complex dynamics: the rare events can be simulated with a minimal prior knowledge and the results are much more precise than those obtained with a user-designed score function.

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Kabanov, A. A., and S. A. Dubovik. "Simulation of Rare Events in Stochastic Systems." Journal of Physics: Conference Series 2096, no. 1 (November 1, 2021): 012151. http://dx.doi.org/10.1088/1742-6596/2096/1/012151.

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Abstract The paper presents algorithms for simulation rare events in stochastic systems based on the theory of large deviations. Here, this approach is used in conjunction with the tools of optimal control theory to estimate the probability that some observed states in a stochastic system will exceed a given threshold by some upcoming time instant. Algorithms for obtaining controlled extremal trajectory (A-profile) of the system, along which the transition to a rare event (threshold) occurs most likely under the influence of disturbances that minimize the action functional, are presented. It is also shown how this minimization can be efficiently performed using numerical-analytical methods of optimal control for linear and nonlinear systems. These results are illustrated by an example for a precipitation-measured monsoon intraseasonal oscillation (MISO) described by a low-order nonlinear stochastic model.

Journal articles on the topic 'Rare event probability'

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