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Journal articles on the topic 'Rare events simulation'

Author: Grafiati

Published: 12 October 2024

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1

Becker, M., and P. L. Douillet. "Hierarchical Simulation For Rare Events." International Journal of Modelling and Simulation 17, no. 2 (January 1997): 66–71. http://dx.doi.org/10.1080/02286203.1997.11760314.

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2

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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3

Kubatur, Shruthi S., and Mary L. Comer. "Simulation of Rare Events in Images." Electronic Imaging 2018, no. 15 (January 28, 2018): 227–1. http://dx.doi.org/10.2352/issn.2470-1173.2018.15.coimg-227.

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4

Asmussen, Søren, Reuven Y. Rubinstein, and Chia-Li Wang. "Regenerative rare events simulation via likelihood ratios." Journal of Applied Probability 31, no. 3 (September 1994): 797–815. http://dx.doi.org/10.2307/3215157.

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In this paper we obtain some new theoretical and numerial results on estimation of small steady-state probabilities in regenerative queueing models by using the likelihood ratio (score function) method, which is based on a change of the probability measure. For simple GI/G/1 queues, this amounts to simulating the regenerative cycles by a suitable change of the interarrival and service time distribution, typically corresponding to a reference traffic intensity ρ0 which is < 1 but larger than the given one ρ. For the M/M/1 queue, the resulting gain of efficiency is calculated explicitly and shown to be considerable. Simulation results are presented indicating that similar conclusions hold for gradient estimates and in more general queueing models like queueing networks.

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5

Asmussen, Søren, Reuven Y. Rubinstein, and Chia-Li Wang. "Regenerative rare events simulation via likelihood ratios." Journal of Applied Probability 31, no. 03 (September 1994): 797–815. http://dx.doi.org/10.1017/s0021900200045356.

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In this paper we obtain some new theoretical and numerial results on estimation of small steady-state probabilities in regenerative queueing models by using the likelihood ratio (score function) method, which is based on a change of the probability measure. For simple GI/G/1 queues, this amounts to simulating the regenerative cycles by a suitable change of the interarrival and service time distribution, typically corresponding to a reference traffic intensity ρ 0 which is < 1 but larger than the given one ρ. For the M/M/1 queue, the resulting gain of efficiency is calculated explicitly and shown to be considerable. Simulation results are presented indicating that similar conclusions hold for gradient estimates and in more general queueing models like queueing networks.

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6

Asmussen, Søren, Klemens Binswanger, Bjarne Højgaard, Soren Asmussen, and Bjarne Hojgaard. "Rare Events Simulation for Heavy-Tailed Distributions." Bernoulli 6, no. 2 (April 2000): 303. http://dx.doi.org/10.2307/3318578.

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7

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.

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8

Townsend, J. K., Z. Haraszti, J. A. Freebersyser, and M. Devetsikiotis. "Simulation of rare events in communications networks." IEEE Communications Magazine 36, no. 8 (1998): 36–41. http://dx.doi.org/10.1109/35.707815.

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9

Chambers, W. G. "Simulation of rare events in Gaussian processes." Electronics Letters 29, no. 15 (1993): 1384. http://dx.doi.org/10.1049/el:19930927.

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10

Bréhier, Charles-Edouard, Maxime Gazeau, Ludovic Goudenège, and Mathias Rousset. "Analysis and simulation of rare events for SPDEs." ESAIM: Proceedings and Surveys 48 (January 2015): 364–84. http://dx.doi.org/10.1051/proc/201448017.

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11

Rubinstein, Reuven Y. "Optimization of computer simulation models with rare events." European Journal of Operational Research 99, no. 1 (May 1997): 89–112. http://dx.doi.org/10.1016/s0377-2217(96)00385-2.

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12

Frater, Michael R., Robert R. Bitmead, Rodney A. Kennedy, and Brian D. O. Anderson. "Fast simulation of rare events using reverse-time models." Computer Networks and ISDN Systems 20, no. 1-5 (December 1990): 315–21. http://dx.doi.org/10.1016/0169-7552(90)90040-y.

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13

Tsoucas, Pantelis. "Rare events in series of queues." Journal of Applied Probability 29, no. 1 (March 1992): 168–75. http://dx.doi.org/10.2307/3214800.

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In an ergodic network of K M/M/1 queues in series we consider the rare event that, as N increases, the total population in the network exceeds N during a busy period. By utilizing the contraction principle of large deviation theory, an action functional is obtained for this exit problem. The ensuing minimization is carried out for K = 2 and an indication is given for arbitrary K. It is shown that, asymptotically and for unequal service rates, the ‘most likely' path for this rare event is one where the arrival rate has been interchanged with the smallest service rate. The problem has been posed in Parekh and Walrand [7] in connection with importance sampling simulation methods for queueing networks. Its solution has previously been obtained only heuristically.

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14

Tsoucas, Pantelis. "Rare events in series of queues." Journal of Applied Probability 29, no. 01 (March 1992): 168–75. http://dx.doi.org/10.1017/s0021900200106710.

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In an ergodic network of K M/M/1 queues in series we consider the rare event that, as N increases, the total population in the network exceeds N during a busy period. By utilizing the contraction principle of large deviation theory, an action functional is obtained for this exit problem. The ensuing minimization is carried out for K = 2 and an indication is given for arbitrary K. It is shown that, asymptotically and for unequal service rates, the ‘most likely' path for this rare event is one where the arrival rate has been interchanged with the smallest service rate. The problem has been posed in Parekh and Walrand [7] in connection with importance sampling simulation methods for queueing networks. Its solution has previously been obtained only heuristically.

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15

Chopra, Manan, Rohit Malshe, Allam S. Reddy, and J. J. de Pablo. "Improved transition path sampling methods for simulation of rare events." Journal of Chemical Physics 128, no. 14 (April 14, 2008): 144104. http://dx.doi.org/10.1063/1.2889943.

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16

Heidelberger, Philip. "Fast simulation of rare events in queueing and reliability models." ACM Transactions on Modeling and Computer Simulation 5, no. 1 (January 1995): 43–85. http://dx.doi.org/10.1145/203091.203094.

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17

Rashki, Mohsen. "SESC: A new subset simulation method for rare-events estimation." Mechanical Systems and Signal Processing 150 (March 2021): 107139. http://dx.doi.org/10.1016/j.ymssp.2020.107139.

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18

Estecahandy, M., L. Bordes, S. Collas, and C. Paroissin. "Some acceleration methods for Monte Carlo simulation of rare events." Reliability Engineering & System Safety 144 (December 2015): 296–310. http://dx.doi.org/10.1016/j.ress.2015.07.010.

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19

Carter, E. A., Giovanni Ciccotti, James T. Hynes, and Raymond Kapral. "Constrained reaction coordinate dynamics for the simulation of rare events." Chemical Physics Letters 156, no. 5 (April 1989): 472–77. http://dx.doi.org/10.1016/s0009-2614(89)87314-2.

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20

de Koning, Maurice, Wei Cai, Babak Sadigh, Tomas Oppelstrup, Malvin H. Kalos, and Vasily V. Bulatov. "Adaptive importance sampling Monte Carlo simulation of rare transition events." Journal of Chemical Physics 122, no. 7 (February 15, 2005): 074103. http://dx.doi.org/10.1063/1.1844352.

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21

Kim, Young Jin, Jae Jun Lee, and Julian Lee. "Gillespie Simulation of Rare Events in a Genetic Regulatory Network." Journal of the Korean Physical Society 74, no. 9 (May 2019): 907–11. http://dx.doi.org/10.3938/jkps.74.907.

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22

Borkar, V. S., S. Juneja, and A. A. Kherani. "Peformance Analysis Conditioned on Rare Events: An Adaptive Simulation Scheme." Communications in Information and Systems 3, no. 4 (2003): 259–78. http://dx.doi.org/10.4310/cis.2003.v3.n4.a3.

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23

Andersen, Lars Nørvang, Patrick J. Laub, and Leonardo Rojas-Nandayapa. "Efficient Simulation for Dependent Rare Events with Applications to Extremes." Methodology and Computing in Applied Probability 20, no. 1 (April 19, 2017): 385–409. http://dx.doi.org/10.1007/s11009-017-9557-4.

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24

Keller, Bettina G., and Peter G. Bolhuis. "Dynamical Reweighting for Biased Rare Event Simulations." Annual Review of Physical Chemistry 75, no. 1 (June 28, 2024): 137–62. http://dx.doi.org/10.1146/annurev-physchem-083122-124538.

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Dynamical reweighting techniques aim to recover the correct molecular dynamics from a simulation at a modified potential energy surface. They are important for unbiasing enhanced sampling simulations of molecular rare events. Here, we review the theoretical frameworks of dynamical reweighting for modified potentials. Based on an overview of kinetic models with increasing level of detail, we discuss techniques to reweight two-state dynamics, multistate dynamics, and path integrals. We explore the natural link to transition path sampling and how the effect of nonequilibrium forces can be reweighted. We end by providing an outlook on how dynamical reweighting integrates with techniques for optimizing collective variables and with modern potential energy surfaces.

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25

Vats, Shray, Raitis Bobrovs, Pär Söderhjelm, and Soumendranath Bhakat. "AlphaFold-SFA: Accelerated sampling of cryptic pocket opening, protein-ligand binding and allostery by AlphaFold, slow feature analysis and metadynamics." PLOS ONE 19, no. 8 (August 27, 2024): e0307226. http://dx.doi.org/10.1371/journal.pone.0307226.

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Sampling rare events in proteins is crucial for comprehending complex phenomena like cryptic pocket opening, where transient structural changes expose new binding sites. Understanding these rare events also sheds light on protein-ligand binding and allosteric communications, where distant site interactions influence protein function. Traditional unbiased molecular dynamics simulations often fail to sample such rare events, as the free energy barrier between metastable states is large relative to the thermal energy. This renders these events inaccessible on the timescales typically simulated by unbiased molecular dynamics, limiting our understanding of these critical processes. In this paper, we proposed a novel unsupervised learning approach termed as slow feature analysis (SFA) which aims to extract slowly varying features from high-dimensional temporal data. SFA trained on small unbiased molecular dynamics simulations launched from AlphaFold generated conformational ensembles manages to capture rare events governing cryptic pocket opening, protein-ligand binding, and allosteric communications in a kinase. Metadynamics simulations using SFA as collective variables manage to sample ‘deep’ cryptic pocket opening within a few hundreds of nanoseconds which was beyond the reach of microsecond long unbiased molecular dynamics simulations. SFA augmented metadynamics also managed to capture conformational plasticity of protein upon ligand binding/unbinding and provided novel insights into allosteric communication in receptor-interacting protein kinase 2 (RIPK2) which dictates protein-protein interaction. Taken together, our results show how SFA acts as a dimensionality reduction tool which bridges the gap between AlphaFold, molecular dynamics simulation and metadynamics in context of capturing rare events in biomolecules, extending the scope of structure-based drug discovery in the era of AlphaFold.

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26

McLeish, Don L. "Bounded Relative Error Importance Sampling and Rare Event Simulation." ASTIN Bulletin 40, no. 1 (May 2010): 377–98. http://dx.doi.org/10.2143/ast.40.1.2049235.

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AbstractWe consider estimating tail events using exponential families of importance sampling distributions. When the cannonical sufficient statistic for the exponential family mimics the tail behaviour of the underlying cumulative distribution function, we can achieve bounded relative error for estimating tail probabilities. Examples of rare event simulation from various distributions including Tukey's g&h distribution are provided.

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27

Srinivasan, Rajan. "Importance Sampling - the Simulation Theory of Rare Events and its Applications ." Defence Science Journal 49, no. 1 (January 1, 1999): 9–17. http://dx.doi.org/10.14429/dsj.49.3780.

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28

Melnik-Melnikov, P. G., and E. S. Dekhtyaruk. "Rare events probabilities estimation by “ Russian Roulette and Splitting ” simulation technique." Probabilistic Engineering Mechanics 15, no. 2 (April 2000): 125–29. http://dx.doi.org/10.1016/s0266-8920(97)00016-7.

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29

Freitas, Ana Cristina Moreira, Jorge Milhazes Freitas, Mike Todd, and Sandro Vaienti. "Rare events for the Manneville–Pomeau map." Stochastic Processes and their Applications 126, no. 11 (November 2016): 3463–79. http://dx.doi.org/10.1016/j.spa.2016.05.001.

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30

Hodkinson, Alexander, and Evangelos Kontopantelis. "Applications of simple and accessible methods for meta-analysis involving rare events: A simulation study." Statistical Methods in Medical Research 30, no. 7 (June 17, 2021): 1589–608. http://dx.doi.org/10.1177/09622802211022385.

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Meta-analysis of clinical trials targeting rare events face particular challenges when the data lack adequate number of events and are susceptible to high levels of heterogeneity. The standard meta-analysis methods (DerSimonian Laird (DL) and Mantel–Haenszel (MH)) often lead to serious distortions because of such data sparsity. Applications of the methods suited to specific incidence and heterogeneity characteristics are lacking, thus we compared nine available methods in a simulation study. We generated 360 meta-analysis scenarios where each considered different incidences, sample sizes, between-study variance (heterogeneity) and treatment allocation. We include globally recommended methods such as inverse-variance fixed/random-effect (IV-FE/RE), classical-MH, MH-FE, MH-DL, Peto, Peto-DL and the two extensions for MH bootstrapped-DL (bDL) and Peto-bDL. Performance was assessed on mean bias, mean error, coverage and power. In the absence of heterogeneity, the coverage and power when combined revealed small differences in meta-analysis involving rare and very rare events. The Peto-bDL method performed best, but only in smaller sample sizes involving rare events. For medium-to-larger sample sizes, MH-bDL was preferred. For meta-analysis involving very rare events, Peto-bDL was the best performing method which was sustained across all sample sizes. However, in meta-analysis with 20% or more heterogeneity, the coverage and power were insufficient. Performance based on mean bias and mean error was almost identical across methods. To conclude, in meta-analysis of rare binary outcomes, our results suggest that Peto-bDL is better in both rare and very rare event settings in meta-analysis with limited sample sizes. However, when heterogeneity is large, the coverage and power to detect rare events are insufficient. Whilst this study shows that some of the less studied methods appear to have good properties under sparse data scenarios, further work is needed to assess them against the more complex distributional-based methods to understand their overall performances.

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31

Asch, Anna, Ethan J. Brady, Hugo Gallardo, John Hood, Bryan Chu, and Mohammad Farazmand. "Model-assisted deep learning of rare extreme events from partial observations." Chaos: An Interdisciplinary Journal of Nonlinear Science 32, no. 4 (April 2022): 043112. http://dx.doi.org/10.1063/5.0077646.

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To predict rare extreme events using deep neural networks, one encounters the so-called small data problem because even long-term observations often contain few extreme events. Here, we investigate a model-assisted framework where the training data are obtained from numerical simulations, as opposed to observations, with adequate samples from extreme events. However, to ensure the trained networks are applicable in practice, the training is not performed on the full simulation data; instead, we only use a small subset of observable quantities, which can be measured in practice. We investigate the feasibility of this model-assisted framework on three different dynamical systems (Rössler attractor, FitzHugh–Nagumo model, and a turbulent fluid flow) and three different deep neural network architectures (feedforward, long short-term memory, and reservoir computing). In each case, we study the prediction accuracy, robustness to noise, reproducibility under repeated training, and sensitivity to the type of input data. In particular, we find long short-term memory networks to be most robust to noise and to yield relatively accurate predictions, while requiring minimal fine-tuning of the hyperparameters.

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32

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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33

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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34

Freitas, Ana Cristina Moreira, Jorge Milhazes Freitas, and Jorge Valentim Soares. "Rare events for product fractal sets *." Journal of Physics A: Mathematical and Theoretical 54, no. 34 (August 4, 2021): 345202. http://dx.doi.org/10.1088/1751-8121/ac16c6.

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35

Meyers, Timothy, Amine Stambouli, Karen McClure, and Daniel Brod. "Risk Assessment of Positive Train Control by Using Simulation of Rare Events." Transportation Research Record: Journal of the Transportation Research Board 2289, no. 1 (January 2012): 34–41. http://dx.doi.org/10.3141/2289-05.

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36

Hua, Bowen, Zhaohong Bie, Siu-Kui Au, Wenyuan Li, and Xifan Wang. "Extracting Rare Failure Events in Composite System Reliability Evaluation Via Subset Simulation." IEEE Transactions on Power Systems 30, no. 2 (March 2015): 753–62. http://dx.doi.org/10.1109/tpwrs.2014.2327753.

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37

King, Leanna M., and Slobodan P. Simonovic. "A Deterministic Monte Carlo Simulation Framework for Dam Safety Flow Control Assessment." Water 12, no. 2 (February 12, 2020): 505. http://dx.doi.org/10.3390/w12020505.

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Simulation has become more widely applied for analysis of dam safety flow control in recent years. Stochastic simulation has proven to be a useful tool that allows for easy estimation of the overall probability of dam overtopping failure. However, it is difficult to analyze “uncommon combinations of events” with a stochastic approach given current computing abilities, because (a) the likelihood of these combinations of events is small, and (b) there may not be enough simulated instances of these rare scenarios to determine their criticality. In this research, a Deterministic Monte Carlo approach is presented, which uses an exhaustive list of possible combinations of events (scenarios) as a deterministic input. System dynamics simulation is used to model the dam system interactions so that low-level events within the system can be propagated through the model to determine high-level system outcomes. Monte Carlo iterations are performed for each input scenario. A case study is presented with results from a single example scenario to demonstrate how the simulation framework can be used to estimate the criticality parameters for each combination of events simulated. The approach can analyze these rare events in a thorough and systematic way, providing a better coverage of the possibility space as well as valuable insights into system vulnerabilities.

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38

Li, Xiaoou, and Gongjun Xu. "Uniformly efficient simulation for extremes of Gaussian random fields." Journal of Applied Probability 55, no. 1 (March 2018): 157–78. http://dx.doi.org/10.1017/jpr.2018.11.

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AbstractIn this paper we consider the problem of simultaneously estimating rare-event probabilities for a class of Gaussian random fields. A conventional rare-event simulation method is usually tailored to a specific rare event and consequently would lose estimation efficiency for different events of interest, which often results in additional computational cost in such simultaneous estimation problems. To overcome this issue, we propose a uniformly efficient estimator for a general family of Hölder continuous Gaussian random fields. We establish the asymptotic and uniform efficiency of the proposed method and also conduct simulation studies to illustrate its effectiveness.

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39

Chen, Bohan, Jose Blanchet, Chang-Han Rhee, and Bert Zwart. "Efficient Rare-Event Simulation for Multiple Jump Events in Regularly Varying Random Walks and Compound Poisson Processes." Mathematics of Operations Research 44, no. 3 (August 2019): 919–42. http://dx.doi.org/10.1287/moor.2018.0950.

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40

Shayesteh Zadeh, Armin, and Baron Peters. "Multiscale Models for Fibril Formation: Rare Events Methods, Microkinetic Models, and Population Balances." Life 11, no. 6 (June 17, 2021): 570. http://dx.doi.org/10.3390/life11060570.

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Amyloid fibrils are thought to grow by a two-step dock-lock mechanism. However, previous simulations of fibril formation (i) overlook the bi-molecular nature of the docking step and obtain rates with first-order units, or (ii) superimpose the docked and locked states when computing the potential of mean force for association and thereby muddle the docking and locking steps. Here, we developed a simple microkinetic model with separate locking and docking steps and with the appropriate concentration dependences for each step. We constructed a simple model comprised of chiral dumbbells that retains qualitative aspects of fibril formation. We used rare events methods to predict separate docking and locking rate constants for the model. The rate constants were embedded in the microkinetic model, with the microkinetic model embedded in a population balance model for “bottom-up” multiscale fibril growth rate predictions. These were compared to “top-down” results using simulation data with the same model and multiscale framework to obtain maximum likelihood estimates of the separate lock and dock rate constants. We used the same procedures to extract separate docking and locking rate constants from experimental fibril growth data. Our multiscale strategy, embedding rate theories, and kinetic models in conservation laws should help to extract docking and locking rate constants from experimental data or long molecular simulations with correct units and without compromising the molecular description.

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41

Elabd, Ali A., El-Sayed M. El-Rabaie, and Abdelaziz T. Shalaby. "Analysis of rare events effect on single-electronics simulation based on orthodox theory." Journal of Computational Electronics 14, no. 2 (April 16, 2015): 604–10. http://dx.doi.org/10.1007/s10825-015-0694-0.

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42

Paul, Sanjib, Nisanth N. Nair, and Harish Vashisth. "Phase space and collective variable based simulation methods for studies of rare events." Molecular Simulation 45, no. 14-15 (June 28, 2019): 1273–84. http://dx.doi.org/10.1080/08927022.2019.1634268.

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43

Budde, Carlos E., Pedro R. D’Argenio, Arnd Hartmanns, and Sean Sedwards. "An efficient statistical model checker for nondeterminism and rare events." International Journal on Software Tools for Technology Transfer 22, no. 6 (May 28, 2020): 759–80. http://dx.doi.org/10.1007/s10009-020-00563-2.

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Abstract Statistical model checking avoids the state space explosion problem in verification and naturally supports complex non-Markovian formalisms. Yet as a simulation-based approach, its runtime becomes excessive in the presence of rare events, and it cannot soundly analyse nondeterministic models. In this article, we present : a statistical model checker that combines fully automated importance splitting to estimate the probabilities of rare events with smart lightweight scheduler sampling to approximate optimal schedulers in nondeterministic models. As part of the Modest Toolset, it supports a variety of input formalisms natively and via the Jani exchange format. A modular software architecture allows its various features to be flexibly combined. We highlight its capabilities using experiments across multi-core and distributed setups on three case studies and report on an extensive performance comparison with three current statistical model checkers.

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44

Xiao, Chao, Yu Lou, Jie Liu, Yuan Zhao, and Yikang Tian. "Economic events and the volatility of government bill rates." PLOS ONE 17, no. 10 (October 19, 2022): e0276345. http://dx.doi.org/10.1371/journal.pone.0276345.

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Many studies show that in many countries (especially the G7), volatility in government bill rates far exceeds that in consumption growth rates. This volatility puzzle cannot be predicted by traditional disaster models, in which rare economic disasters are defined as a peak-to-trough percent fall in consumption (or real per capita GDP) by a high threshold (≥10%). For this purpose, we extend the traditional definition of rare economic disasters and propose a novel asset pricing model that models both good and bad events. We define a bad (or good) event as a peak-to-trough absolute decline (or a trough-to-peak absolute rise) in consumption growth rates by a low threshold (<10%). Compared to traditional disaster models, our model contains three improvements. First, model good and bad events, not just bad ones (e.g., rare economic disasters). Second, the event’s impact lasts for multiple periods rather than one period. Third, model non-rare economic events. We calibrate the parameters in our model to match the moments from U.S. asset return data. Simulation results indicate that the model can successfully predict the volatility of U.S. government bill rates higher than that of U.S. consumption growth rates.

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Emad, Ahmed, Seemi Ayub, Oumar Samassékou, Marie-Chantal Grégoire, Macoura Gadji, Aimé Ntwari, Josée Lamoureux, et al. "Efficiency of Manual Scanning in Recovering Rare Cellular Events Identified by FluorescenceIn SituHybridization: Simulation of the Detection of Fetal Cells in Maternal Blood." Journal of Biomedicine and Biotechnology 2012 (2012): 1–8. http://dx.doi.org/10.1155/2012/610856.

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Fluorescencein situhybridization (FISH) and manual scanning is a widely used strategy for retrieving rare cellular events such as fetal cells in maternal blood. In order to determine the efficiency of these techniques in detection of rare cells, slides of XX cells with predefined numbers (1–10) of XY cells were prepared. Following FISH hybridization, the slides were scanned blindly for the presence of XY cells by different observers. The average detection efficiency was 84% (125/148). Evaluation of probe hybridization in the missed events showed that 9% (2/23) were not hybridized, 17% (4/23) were poorly hybridized, while the hybridization was adequate for the remaining 74% (17/23). In conclusion, manual scanning is a relatively efficient method to recover rare cellular events, but about 16% of the events are missed; therefore, the number of fetal cells per unit volume of maternal blood has probably been underestimated when using manual scanning.

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Kuwahara, Hiroyuki, and Ivan Mura. "An efficient and exact stochastic simulation method to analyze rare events in biochemical systems." Journal of Chemical Physics 129, no. 16 (October 28, 2008): 165101. http://dx.doi.org/10.1063/1.2987701.

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Rjasanow, S., and W. Wagner. "Simulation of rare events by the stochastic weighted particle method for the Boltzmann equation." Mathematical and Computer Modelling 33, no. 8-9 (April 2001): 907–26. http://dx.doi.org/10.1016/s0895-7177(00)00289-2.

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Fuchigami, Sotaro. "Rare Events in Protein Simulation Revealed by using Time-Structure Based Independent Component Analysis." Biophysical Journal 104, no. 2 (January 2013): 170a. http://dx.doi.org/10.1016/j.bpj.2012.11.960.

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Zhang, Yuming, and Juan Ma. "A method of combined metamodel and subset simulation for reliability analysis of rare events." Advances in Engineering Software 195 (September 2024): 103693. http://dx.doi.org/10.1016/j.advengsoft.2024.103693.

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Abdel Menaem, Amir, Rustam Valiev, Vladislav Oboskalov, Taher S. Hassan, Hegazy Rezk, and Mohamed N. Ibrahim. "An Efficient Framework for Adequacy Evaluation through Extraction of Rare Load Curtailment Events in Composite Power Systems." Mathematics 8, no. 11 (November 13, 2020): 2021. http://dx.doi.org/10.3390/math8112021.

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With the growing robustness of modern power systems, the occurrence of load curtailment events is becoming lower. Hence, the simulation of these events constitutes a challenge in adequacy indices assessment. Due to the rarity of the load curtailment events, the standard Monte Carlo simulation (MCS) estimator of adequacy indices is not practical. Therefore, a framework based on the enhanced cross-entropy-based importance sampling (ECE-IS) method is introduced in this paper for computing the adequacy indices. The framework comprises two stages. Using the proposed ECE-IS method, the first stage’s purpose is to identify the samples or states of the nodal generation and load that are greatly significant to the adequacy indices estimators. In the second stage, the density of the input variables’ conditional on the load curtailment domain obtained by the first stage are used to compute the nodal and system adequacy indices. The performance of the ECE-IS method is verified through a comparison with the standard MCS method and the recent techniques of rare events simulation in literature. The results confirm that the proposed method develops an accurate estimation for the nodal and system adequacy indices (loss of load probability (LOLP), expected power not supplied (EPNS)) with appropriate convergence value and low computation time.

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