Splitting simulation
May 29, 2017 — September 28, 2020
Bayes
density
Monte Carlo
probabilistic algorithms
probability
tail risk
time series
I have just spent so much time writing about this that I had better pause for a while and leave this as a placeholder.
1 References
Aalen, Borgan, and Gjessing. 2008. Survival and Event History Analysis: A Process Point of View. Statistics for Biology and Health.
Alouini, Ben Rached, Kammoun, et al. 2018. “On the Efficient Simulation of the Left-Tail of the Sum of Correlated Log-Normal Variates.” Monte Carlo Methods and Applications.
Andersen, Borgan, Gill, et al. 1997. Statistical models based on counting processes. Springer series in statistics.
Applebaum. 2004. “Lévy Processes — from Probability to Finance and Quantum Groups.” Notices of the AMS.
———. 2009. Lévy Processes and Stochastic Calculus. Cambridge Studies in Advanced Mathematics 116.
Asmussen, Søren, Binswanger, and Højgaard. 2000. “Rare Events Simulation for Heavy-Tailed Distributions.” Bernoulli.
Asmussen, Søren, Blanchet, Juneja, et al. 2011. “Efficient Simulation of Tail Probabilities of Sums of Correlated Lognormals.” Annals OR.
Asmussen, Søren, and Glynn. 2007. Stochastic Simulation: Algorithms and Analysis.
Asmussen, Soren, Jensen, and Rojas-Nandayapa. 2016. “Exponential Family Techniques for the Lognormal Left Tail.” Scandinavian Journal of Statistics.
Asmussen, Søren, and Kroese. 2006. “Improved Algorithms for Rare Event Simulation with Heavy Tails.” Advances in Applied Probability.
Au, and Beck. 2001. “Estimation of Small Failure Probabilities in High Dimensions by Subset Simulation.” Probabilistic Engineering Mechanics.
Avramidis, L’Ecuyer, and Tremblay. 2003. “New Simulation Methodology for Finance: Efficient Simulation of Gamma and Variance-Gamma Processes.” In Proceedings of the 35th Conference on Winter Simulation: Driving Innovation. WSC ’03.
Balesdent, Morio, and Marzat. 2015. “Recommendations for the Tuning of Rare Event Probability Estimators.” Reliability Engineering & System Safety.
Barkhuijsen, de Beer, Bovée, et al. 1985. “Retrieval of Frequencies, Amplitudes, Damping Factors, and Phases from Time-Domain Signals Using a Linear Least-Squares Procedure.” Journal of Magnetic Resonance (1969).
Beaulieu, and Xie. 2004. “An Optimal Lognormal Approximation to Lognormal Sum Distributions.” IEEE Transactions on Vehicular Technology.
Ben Issaid, Ben Rached, Kammoun, et al. 2017. “On the Efficient Simulation of the Distribution of the Sum of Gamma-Gamma Variates With Application to the Outage Probability Evaluation Over Fading Channels.” IEEE Transactions on Communications.
Ben Rached, Nadhir, Botev, Kammoun, et al. 2018a. “Importance Sampling Estimator of Outage Probability Under Generalized Selection Combining Model.” In Proc of the IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP).
———, et al. 2018b. “On the Sum of Order Statistics and Applications to Wireless Communication Systems Performances.” IEEE Transactions on Wireless Communications.
Ben Rached, N., Kammoun, Alouini, et al. 2016. “Unified Importance Sampling Schemes for Efficient Simulation of Outage Capacity over Generalized Fading Channels.” IEEE Journal of Selected Topics in Signal Processing.
Ben Rached, N., Kammoun, Alouini, et al. 2017a. “A Unified Moment-Based Approach for the Evaluation of the Outage Probability With Noise and Interference.” IEEE Transactions on Wireless Communications.
Ben Rached, N., Kammoun, Alouini, et al. 2017b. “On the Efficient Simulation of Outage Probability in a Log-Normal Fading Environment.” IEEE Transactions on Communications.
———, et al. 2018. “Accurate Outage Probability Evaluation of Equal Gain Combining Receivers.” In Proc of the IEEE Global Communications Conference (GLOBECOM).
Ben Rached, Nadhir, MacKinlay, Botev, et al. 2020. “A Universal Splitting Estimator for the Performance Evaluation of Wireless Communications Systems.” IEEE Transactions on Wireless Communications.
Beskos, Papaspiliopoulos, and Roberts. 2006. “Retrospective Exact Simulation of Diffusion Sample Paths with Applications.” Bernoulli.
Bithas, and Rontogiannis. 2015. “Mobile Communication Systems in the Presence of Fading/Shadowing, Noise and Interference.” IEEE Transactions on Communications.
Blanchet, and Lam. 2012. “State-Dependent Importance Sampling for Rare-Event Simulation: An Overview and Recent Advances.” Surveys in Operations Research and Management Science.
Bock, Diaconis, Huffer, et al. 1987. “Inequalities for Linear Combinations of Gamma Random Variables.” The Canadian Journal of Statistics / La Revue Canadienne de Statistique.
Booth, and Hendricks. 1984. “Importance Estimation in Forward Monte Carlo Calculations.” Nuclear Technology - Fusion.
Botev, Z. n.d. “Sampling via Regenerative Chain Monte Carlo.”
Botev, Zdravko I., and Kroese. 2008. “An Efficient Algorithm for Rare-Event Probability Estimation, Combinatorial Optimization, and Counting.” Methodology and Computing in Applied Probability.
———. 2012. “Efficient Monte Carlo Simulation via the Generalized Splitting Method.” Statistics and Computing.
Botev, Zdravko, and L’Ecuyer. 2017. “Simulation from the Normal Distribution Truncated to an Interval in the Tail.” In Proceedings of the 10th EAI International Conference on Performance Evaluation Methodologies and Tools. VALUETOOLS’16.
———. 2019. “Simulation from the Tail of the Univariate and Multivariate Normal Distribution.” In Systems Modeling: Methodologies and Tools. EAI/Springer Innovations in Communication and Computing.
Botev, Zdravko I., and L’Ecuyer. 2020. “Sampling Conditionally on a Rare Event via Generalized Splitting.” INFORMS Journal on Computing.
Botev, Zdravko I., L’Ecuyer, Rubino, et al. 2012. “Static Network Reliability Estimation via Generalized Splitting.” INFORMS Journal on Computing.
Botev, Zdravko I., L’Ecuyer, and Tuffin. 2012. “Dependent Failures in Highly Reliable Static Networks.” In Proceedings of the 2012 Winter Simulation Conference (WSC).
———. 2013. “Markov Chain Importance Sampling with Applications to Rare Event Probability Estimation.” Statistics and Computing.
Botev, Zdravko I, L’Ecuyer, and Tuffin. 2018. “Reliability Estimation for Networks with Minimal Flow Demand and Random Link Capacities.”
Bréhier, Goudenège, and Tudela. 2016. “Central Limit Theorem for Adaptive Multilevel Splitting Estimators in an Idealized Setting.” In Monte Carlo and Quasi-Monte Carlo Methods. Springer Proceedings in Mathematics & Statistics.
Bréhier, Lelièvre, and Rousset. 2015. “Analysis of Adaptive Multilevel Splitting Algorithms in an Idealized Case.” ESAIM: Probability and Statistics.
Brereton, Kroese, and Chan. 2013. “Monte Carlo Methods for Portfolio Credit Risk.” In Credit Securitizations and Derivatives.
Casella, and Roberts. 2011. “Exact Simulation of Jump-Diffusion Processes with Monte Carlo Applications.” Methodology and Computing in Applied Probability.
Cemgil. 2009. “Bayesian Inference for Nonnegative Matrix Factorisation Models.” Computational Intelligence and Neuroscience.
Cérou, Del Moral, Le Gland, et al. 2006. “Genetic Genealogical Models in Rare Event Analysis.” ALEA, Latin American Journal of Probability and Mathematical Statistics.
Cérou, and Guyader. 2007. “Adaptive Multilevel Splitting for Rare Event Analysis.” Stochastic Analysis and Applications.
———. 2016. “Fluctuation Analysis of Adaptive Multilevel Splitting.” The Annals of Applied Probability.
Cérou, Le Gland, François, Del Moral, et al. 2005. “Limit Theorems for the Multilevel Splitting Algorithm in the Simulation of Rare Events.” In Proceedings of the Winter Simulation Conference, 2005.
Chan, and Lai. 2013. “A General Theory of Particle Filters in Hidden Markov Models and Some Applications.” The Annals of Statistics.
Charles-Edouard, Maxime, Ludovic, et al. 2015. “Unbiasedness of Some Generalized Adaptive Multilevel Splitting Algorithms.” arXiv:1505.02674 [Math, Stat].
Chatzidiamantis, and Karagiannidis. 2011. “On the Distribution of the Sum of Gamma-Gamma Variates and Applications in RF and Optical Wireless Communications.” IEEE Transactions on Communications.
Cox, and Oakes. 2018. Analysis of Survival Data.
Cutler, and Ederer. 1958. “Maximum utilization of the life table method in analyzing survival.” Journal of Chronic Diseases.
Damien, Wakefield, and Walker. 1999. “Gibbs Sampling for Bayesian Non-Conjugate and Hierarchical Models by Using Auxiliary Variables.” Journal of the Royal Statistical Society. Series B (Statistical Methodology).
Dean, and Dupuis. 2009. “Splitting for Rare Event Simulation: A Large Deviation Approach to Design and Analysis.” Stochastic Processes and Their Applications.
Del Moral. 2004. Feynman-Kac Formulae: Genealogical and Interacting Particle Systems with Applications.
Del Moral, and Lezaud. 2006. “Branching and Interacting Particle Interpretations of Rare Event Probabilities.” In Stochastic Hybrid Systems. Lecture Notes in Control and Information Science, Volume 337.
Doucet, Freitas, and Gordon. 2001. Sequential Monte Carlo Methods in Practice.
Duan, and Kroese. 2016. “Splitting for Optimization.” Computers & Operations Research.
Embrechts, Lindskog, and McNeil. 2003. “Modelling Dependence with Copulas and Applications to Risk Management.” Handbook of Heavy Tailed Distributions in Finance.
Ermolova, and Tirkkonen. 2014. “Outage Probability Analysis in Generalized Fading Channels with Co-Channel Interference and Background Noise: Η-μ/η-μ, η-μ/κ-μ, and κ-μ Scenarios.” IEEE Transactions on Wireless Communications.
Frühwirth-Schnatter, and Frühwirth. 2010. “Data Augmentation and MCMC for Binary and Multinomial Logit Models.” In Statistical Modelling and Regression Structures.
Garvels, M. J. J. 2000. “The Splitting Method in Rare Event Simulation.”
Garvels, M. J. J., and Kroese. 1998. “A Comparison of RESTART Implementations.” In Proceedings of the 1998 Winter Simulation Conference.
Garvels, Marnix J. J., Ommeren, and Kroese. 2002. “On the Importance Function in Splitting Simulation.” European Transactions on Telecommunications.
Gilks, and Berzuini. 2001. “Following a Moving Target—Monte Carlo Inference for Dynamic Bayesian Models.” Journal of the Royal Statistical Society: Series B (Statistical Methodology).
Glasserman, P., Heidelberger, Shahabuddin, et al. 1998. “A Large Deviations Perspective on the Efficiency of Multilevel Splitting.” IEEE Transactions on Automatic Control.
Glasserman, Paul, Heidelberger, Shahabuddin, et al. 1998. “A Look At Multilevel Splitting.” In Monte Carlo and Quasi-Monte Carlo Methods 1996. Lecture Notes in Statistics.
———, et al. 1999. “Multilevel Splitting for Estimating Rare Event Probabilities.” Operations Research.
Glasserman, Paul, and Kim. 2008. “Beta Approximations for Bridge Sampling.” In.
Glynn, and Whitt. 1992. “The Asymptotic Efficiency of Simulation Estimators.” Operations Research.
Gulisashvili, and Tankov. 2016. “Tail Behavior of Sums and Differences of Log-Normal Random Variables.” Bernoulli.
Guyader, Hengartner, and Matzner-Løber. 2011. “Simulation and Estimation of Extreme Quantiles and Extreme Probabilities.” Applied Mathematics & Optimization.
Hofert. 2008. “Sampling Archimedean Copulas.” Computational Statistics & Data Analysis.
Holmes, and Held. 2006. “Bayesian Auxiliary Variable Models for Binary and Multinomial Regression.” Bayesian Analysis.
Hosmer, and Lemeshow. 1999. Applied Survival Analysis: Regression Modeling of Time to Event Data. Wiley Series in Probability and Statistics.
Hu, and Beaulieu. 2005. “Accurate Closed-Form Approximations to Ricean Sum Distributions and Densities.” IEEE Communications Letters.
Hug, Baker, Anantharaman, et al. 2016. “A new view of the tree of life.” Nature Microbiology.
Jacquemart, and Morio. 2016. “Tuning of Adaptive Interacting Particle System for Rare Event Probability Estimation.” Simulation Modelling Practice and Theory.
Kahn, and Harris. 1951. “Estimation of Particle Transmission by Random Sampling.” National Bureau of Standards Applied Mathematics Series.
Kleinbaum. 2010. Survival Analysis: A Self-Learning Text. Statistics for Biology and Health 1.0.
Kooperberg, and Stone. 1991. “A Study of Logspline Density Estimation.” Computational Statistics & Data Analysis.
———. 1992. “Logspline Density Estimation for Censored Data.” Journal of Computational and Graphical Statistics.
Kroese, Taimre, and Botev. 2011. Handbook of Monte Carlo Methods. Wiley Series in Probability and Statistics 706.
Kundu, and Gupta. 2007. “A Convenient Way of Generating Gamma Random Variables Using Generalized Exponential Distribution.” Computational Statistics & Data Analysis.
Kyprianou. 2014. Fluctuations of Lévy Processes with Applications: Introductory Lectures. Universitext.
L’Ecuyer, Blanchet, Tuffin, et al. 2010. “Asymptotic Robustness of Estimators in Rare-Event Simulation.” ACM Transactions on Modeling and Computer Simulation.
L’Ecuyer, Botev, and Kroese. 2018. “On a Generalized Splitting Method for Sampling from a Conditional Distribution.” In 2018 Winter Simulation Conference (WSC).
L’Ecuyer, Demers, and Tuffin. 2006. “Splitting for Rare-Event Simulation.” In 38th Conference on Winter Simulation. WSC ’06.
———. 2007. “Rare Events, Splitting, and Quasi-Monte Carlo.” ACM Transactions on Modeling and Computer Simulation (TOMACS).
L’Ecuyer, Le Gland, Lezaud, et al. 2009. “Splitting Techniques.” In Rare Event Simulation Using Monte Carlo Methods.
Lagnoux. 2006. “Rare Event Simulation.” Probability in the Engineering and Informational Sciences.
Lam, and Botev. 2015. “The Dynamic Splitting Method with an Application to Portfolio Credit Risk.” arXiv:1511.00326 [Stat].
Le Gland, and Oudjane. 2006. “A Sequential Particle Algorithm That Keeps the Particle System Alive.” In Stochastic Hybrid Systems.
Liu, Martin, and Syring. 2013. “Simulating from a Gamma Distribution with Small Shape Parameter.” arXiv:1302.1884 [Math, Stat].
Mai, and Scherer. 2011. “Reparameterizing Marshall–Olkin Copulas with Applications to Sampling.” Journal of Statistical Computation and Simulation.
Marsaglia, and Tsang. 2000. “A Simple Method for Generating Gamma Variables.” ACM Trans. Math. Softw.
Masood, and Doshi-Velez. 2016. “Rapid Posterior Exploration in Bayesian Non-Negative Matrix Factorization.” arXiv:1610.08928 [Stat].
Meerschaert, and Scheffler. 2008. “Triangular Array Limits for Continuous Time Random Walks.” Stochastic Processes and Their Applications.
Mehta, Wu, Molisch, et al. 2007. “Approximating a Sum of Random Variables with a Lognormal.” IEEE Transactions on Wireless Communications.
Morio, Pastel, and Le Gland. 2010. “An Overview of Importance Splitting for Rare Event Simulation.” European Journal of Physics.
Murphy. 2012. Machine learning: a probabilistic perspective. Adaptive computation and machine learning series.
Nagaraja. 2006. “Order Statistics from Independent Exponential Random Variables and the Sum of the Top Order Statistics.” In Advances in Distribution Theory, Order Statistics, and Inference.
Nam, Alouini, and Yang. 2010. “An MGF-Based Unified Framework to Determine the Joint Statistics of Partial Sums of Ordered Random Variables.” IEEE Transactions on Information Theory.
Nam, Ko, and Alouini. 2017. “New Closed-Form Results on Ordered Statistics of Partial Sums of Gamma Random Variables and Its Application to Performance Evaluation in the Presence of Nakagami Fading.” IEEE Access.
Peppas, Alexandropoulos, Datsikas, et al. 2011. “Multivariate Gamma-Gamma Distribution with Exponential Correlation and Its Applications in Radio Frequency and Optical Wireless Communications.” Antennas Propagation IET Microwaves.
Renzo, Graziosi, and Santucci. 2009. “Further Results on the Approximation of Log-Normal Power Sum via Pearson Type IV Distribution: A General Formula for Log-Moments Computation.” IEEE Transactions on Communications.
Royen. 2015. “Some Probability Inequalities for Multivariate Gamma and Normal Distributions.” arXiv:1507.00528 [Math].
Rubino, and Tuffin, eds. 2009. Rare Event Simulation Using Monte Carlo Methods.
Rubinstein, and Kroese. 2016. Simulation and the Monte Carlo Method. Wiley series in probability and statistics.
Salakhutdinov, and Mnih. 2008. “Bayesian Probabilistic Matrix Factorization Using Markov Chain Monte Carlo.” In Proceedings of the 25th International Conference on Machine Learning. ICML ’08.
Schmidt. 2006. “CS535D Project: Bayesian Logistic Regression Through Auxiliary Variables.”
Shahabuddin. 1994. “Importance Sampling for the Simulation of Highly Reliable Markovian Systems.” Management Science.
Simon, and Alouini. 2005. Digital Communication over Fading Channels. Wiley Series in Telecommunications and Signal Processing.
Tan, Lu, and Xia. 2018. “Relative Error of Scaled Poisson Approximation via Stein’s Method.” arXiv:1810.04300 [Math].
Vehtari, Simpson, Gelman, et al. 2019. “Pareto Smoothed Importance Sampling.” arXiv:1507.02646 [Stat].
Veillette, and Taqqu. 2010a. “Using Differential Equations to Obtain Joint Moments of First-Passage Times of Increasing Lévy Processes.” Statistics & Probability Letters.
———. 2010b. “Numerical Computation of First-Passage Times of Increasing Lévy Processes.” Methodology and Computing in Applied Probability.
Villén-Altamirano, M., Martínez-Marrón, Gamo, et al. 1994. “Enhancement of the Accelerated Simulation Method RESTART by Considering Multiple Thresholds.” In Teletraffic Science and Engineering. The Fundamental Role of Teletraffic in the Evolution of Telecommunications Networks.
Villén-Altamirano, Manuel, and Villén-Altamirano. 2006. “On the Efficiency of RESTART for Multidimensional State Systems.” ACM Trans. Model. Comput. Simul.
———. 2011. “The Rare Event Simulation Method RESTART: Efficiency Analysis and Guidelines for Its Application.” In Network Performance Engineering: A Handbook on Convergent Multi-Service Networks and Next Generation Internet. Lecture Notes in Computer Science.
von Sachs. 2020. “Nonparametric Spectral Analysis of Multivariate Time Series.” Annual Review of Statistics and Its Application.
Walter. 2017. “Point Process-Based Monte Carlo Estimation.” Statistics and Computing.
Zhang, Matthaiou, Karagiannidis, et al. 2016. “On the Multivariate Gamma–Gamma Distribution With Arbitrary Correlation and Applications in Wireless Communications.” IEEE Transactions on Vehicular Technology.
Zhaxybayeva, and Gogarten. 2004. “Cladogenesis, coalescence and the evolution of the three domains of life.” Trends in genetics: TIG.