@book{gumbel,
url = {https://doi.org/10.7312/gumb92958},
title = {Statistics of Extremes},
author = {E. J. Gumbel},
publisher = {Columbia University Press},
address = {New York Chichester, West Sussex},
doi = {doi:10.7312/gumb92958},
isbn = {9780231891318},
year = {1958},
lastchecked = {2023-12-22}
}
@article{beck_mls,
title = {Estimation of small failure probabilities in high dimensions by subset simulation},
journal = {Probabilistic Engineering Mechanics},
volume = {16},
number = {4},
pages = {263-277},
year = {2001},
issn = {0266-8920},
doi = {https://doi.org/10.1016/S0266-8920(01)00019-4},
url = {https://www.sciencedirect.com/science/article/pii/S0266892001000194},
author = {Siu-Kui Au and James L. Beck},
keywords = {Markov chain Monte Carlo method, Monte Carlo simulation, Reliability, First excursion probability, First passage problem, Metropolis algorithm},

}
@article{survey_morio,
  TITLE = {{A survey of rare event simulation methods for static input--output models}},
  AUTHOR = {Morio, J{\'e}r{\^o}me and Balesdent, Mathieu and Jacquemart, Damien and Verg{\'e}, Christelle},
  URL = {https://hal.science/hal-01081888},
  JOURNAL = {{Simulation Modelling Practice and Theory}},
  PUBLISHER = {{Elsevier}},
  VOLUME = {49},
  PAGES = {287-304},
  YEAR = {2014},
  MONTH = Dec,
  DOI = {10.1016/j.simpat.2014.10.007},
  KEYWORDS = {Monte-Carlo methods ; Rare event ; Input--output model ; Simulation},
  PDF = {https://hal.science/hal-01081888/file/reviewrareevent_v2.pdf},
  HAL_ID = {hal-01081888},
  HAL_VERSION = {v1},
}

@article{kde_r,
author = {Murray Rosenblatt},
title = {{Remarks on Some Nonparametric Estimates of a Density Function}},
volume = {27},
journal = {The Annals of Mathematical Statistics},
number = {3},
publisher = {Institute of Mathematical Statistics},
pages = {832 -- 837},
year = {1956},
doi = {10.1214/aoms/1177728190},
URL = {https://doi.org/10.1214/aoms/1177728190}
}
@article{kde_p,
author = {Emanuel Parzen},
title = {{On Estimation of a Probability Density Function and Mode}},
volume = {33},
journal = {The Annals of Mathematical Statistics},
number = {3},
publisher = {Institute of Mathematical Statistics},
pages = {1065 -- 1076},
year = {1962},
doi = {10.1214/aoms/1177704472},
URL = {https://doi.org/10.1214/aoms/1177704472}
}
@INPROCEEDINGS{mls_tuffin,
  author={L'Ecuyer, Pierre and Demers, Valerie and Tuffin, Bruno},
  booktitle={Proceedings of the 2006 Winter Simulation Conference}, 
  title={Splitting for Rare-Event Simulation}, 
  year={2006},
  volume={},
  number={},
  pages={137-148},
  keywords={Monte Carlo methods;State estimation;State-space methods;Discrete event simulation;H infinity control;Costs;Sufficient conditions},
  doi={10.1109/WSC.2006.323046}}

@article{mls_proof,
author = {Amrein, Michael and K\"{u}nsch, Hans R.},
title = {A variant of importance splitting for rare event estimation: Fixed number of successes},
year = {2011},
issue_date = {February 2011},
publisher = {Association for Computing Machinery},
address = {New York, NY, USA},
volume = {21},
number = {2},
issn = {1049-3301},
url = {https://doi.org/10.1145/1899396.1899401},
doi = {10.1145/1899396.1899401},
abstract = {Importance splitting is a simulation technique to estimate very small entrance probabilities for Markov processes by splitting sample paths at various stages before reaching the set of interest. This can be done in many ways, yielding different variants of the method. In this context, we propose a new one, called fixed number of successes. We prove unbiasedness for the new and some known variants, because in many papers, the proof is based on an incorrect argument. Further, we analyze its behavior in a simplified setting in terms of efficiency and asymptotics in comparison to the standard variant. The main difference is that it controls the imprecision of the estimator rather than the computational effort. Our analysis and simulation examples show that it is rather robust in terms of parameter choice and we present a two-stage procedure which also yields confidence intervals.},
journal = {ACM Trans. Model. Comput. Simul.},
month = {feb},
articleno = {13},
numpages = {20},
keywords = {tandem queue, robust estimation, rare event, importance splitting, Monte Carlo, Markov chain, Entrance probability}
}
@article{elmasri_nograd,
title = {Improvement of the cross-entropy method in high dimension for failure probability estimation through a one-dimensional projection without gradient estimation},
journal = {Reliability Engineering & System Safety},
volume = {216},
pages = {107991},
year = {2021},
issn = {0951-8320},
doi = {https://doi.org/10.1016/j.ress.2021.107991},
url = {https://www.sciencedirect.com/science/article/pii/S0951832021005019},
author = {Maxime {El Masri} and Jérôme Morio and Florian Simatos},
keywords = {Rare event simulation, Failure probability, Importance sampling, Cross-entropy, High dimension, Projection},
abstract = {Rare event probability estimation is an important topic in reliability analysis. Stochastic methods, such as importance sampling, have been developed to estimate such probabilities but they often fail in high dimension. In this paper, we propose a new cross-entropy-based importance sampling algorithm to improve rare event probability estimation in high dimension. We focus on the cross-entropy method with Gaussian auxiliary distributions and we suggest to update the Gaussian covariance matrix only in a one-dimensional subspace. For that purpose, the main idea is to consider the projection in the one-dimensional subspace spanned by the sample mean vector, which gives an influential direction for the variance estimation. This approach does not require any additional simulation budget compared to the basic cross-entropy algorithm and we show on different numerical test cases that it greatly improves its performance in high dimension.}
}
@article{kahn,
  added-at = {2020-01-29T18:29:49.000+0100},
  author = {Kahn, Herman and Harris, Theodore E},
  biburl = {https://www.bibsonomy.org/bibtex/22f9cb11c7aaa4af53ede2235b936238b/salotz},
  interhash = {628f57b0f02692c5c87991899fbcb706},
  intrahash = {2f9cb11c7aaa4af53ede2235b936238b},
  journal = {National Bureau of Standards applied mathematics series},
  keywords = {enhanced-sampling history path-sampling splitting-methods},
  pages = {27--30},
  timestamp = {2020-01-29T18:29:49.000+0100},
  title = {Estimation of particle transmission by random sampling},
  volume = 12,
  year = 1951
}


@techreport{ESSkong,
    author = {A. Kong},
    title = {A note on importance sampling using standardized weights.},
    institution = {University of Chicago, Dept. of Statistics},
    year = {1992}
}

@book{rubinstein_kroese,
author = {Rubinstein, Reuven Y. and Kroese, Dirk P.},
title = {Simulation and the Monte Carlo Method},
year = {2016},
isbn = {1118632168},
publisher = {Wiley Publishing},
edition = {3rd},
}

@article{delta_method,
author = {Gary W. Oehlert},
title = {A Note on the Delta Method},
journal = {The American Statistician},
volume = {46},
number = {1},
pages = {27-29},
year = {1992},
publisher = {Taylor & Francis},
doi = {10.1080/00031305.1992.10475842},


URL = { 
    
    
        https://www.tandfonline.com/doi/abs/10.1080/00031305.1992.10475842
    

},
eprint = { 
    
    
        https://www.tandfonline.com/doi/pdf/10.1080/00031305.1992.10475842
    

}

}
@article{ice,
title = {Improved cross entropy-based importance sampling with a flexible mixture model},
journal = {Reliability Engineering & System Safety},
volume = {191},
pages = {106564},
year = {2019},
issn = {0951-8320},
doi = {https://doi.org/10.1016/j.ress.2019.106564},
url = {https://www.sciencedirect.com/science/article/pii/S0951832019301528},
author = {Iason Papaioannou and Sebastian Geyer and Daniel Straub},
keywords = {Reliability analysis, Simulation method, Importance sampling, Cross entropy method, High dimensions, Mixture model},
abstract = {The probability of a rare event or failure event is defined through a potentially high-dimensional integral, whose integration domain is often only known point-wise in terms of the outcome of a numerical model. The probability of failure can be estimated efficiently through importance sampling (IS), provided that an effective IS density is chosen. The cross entropy (CE) method is an adaptive sampling approach that determines the IS density through minimizing the Kullback–Leibler divergence between the theoretically optimal IS density and a chosen parametric family of distributions. We propose an improved version of the classical CE method that introduces a smooth transition to make better use of the samples from intermediate sampling levels for fitting the sought IS density. The improved CE method is combined with a novel flexible parametric distribution model that is able to handle low- and high-dimensional problems as well as problems with multimodal failure domains. A set of numerical examples demonstrate that the proposed approach performs consistently better than the classical CE method in various problem settings.}
}

@phdthesis{elmasri,
  TITLE = {{High dimensional importance sampling through projections on a low dimensional subspace}},
  AUTHOR = {El Masri, Maxime},
  URL = {https://hal.science/tel-03927607},
  SCHOOL = {{ISAE - Institut Sup{\'e}rieur de l'A{\'e}ronautique et de l'Espace}},
  YEAR = {2022},
  MONTH = Mar,
  KEYWORDS = {ESTIMATION ; IMPORTANCE SAMPLING ; HIGH DIMENSION ; PROJECTION ; ESTIMATION ; ECHANTILLONNAGE PREFERENTIEL ; GRANDE DIMENSION ; PROJECTION},
  TYPE = {Theses},
  PDF = {https://hal.science/tel-03927607/file/DTIS22111.1648111910.pdf},
  HAL_ID = {tel-03927607},
  HAL_VERSION = {v1},

}
@Article{rethink_ESS,
  author={Víctor Elvira and Luca Martino and Christian P. Robert},
  title={{Rethinking the Effective Sample Size}},
  journal={International Statistical Review},
  year=2022,
  volume={90},
  number={3},
  pages={525-550},
  month={December},
  keywords={},
  doi={10.1111/insr.12500},
  abstract={The effective sample size (ESS) is widely used in sample‐based simulation methods for assessing the quality of a Monte Carlo approximation of a given distribution and of related integrals. In this paper, we revisit the approximation of the ESS in the specific context of importance sampling. The derivation of this approximation, that we will denote as ESS^, is partially available in a 1992 foundational technical report of Augustine Kong. This approximation has been widely used in the last 25 years due to its simplicity as a practical rule of thumb in a wide variety of importance sampling methods. However, we show that the multiple assumptions and approximations in the derivation of ESS^ make it difficult to be considered even as a reasonable approximation of the ESS. We extend the discussion of the ESS^ in the multiple importance sampling setting, we display numerical examples and we discuss several avenues for developing alternative metrics. This paper does not cover the use of ESS for Markov chain Monte Carlo algorithms.},
  url={https://ideas.repec.org/a/bla/istatr/v90y2022i3p525-550.html}
}

@misc{qiming_variance,
      title={Variance Estimation in Adaptive Sequential Monte Carlo}, 
      author={Qiming Du and Arnaud Guyader},
      year={2020},
      eprint={1909.13602},
      archivePrefix={arXiv},
      primaryClass={math.ST}
}
@article{choice_divergence,
 ISSN = {03067734, 17515823},
 URL = {http://www.jstor.org/stable/1403865},
 number = {3},
 pages = {419--435},
 publisher = {[Wiley, International Statistical Institute (ISI)]},
 title = {On Choosing and Bounding Probability Metrics},
 urldate = {2024-02-03},
 volume = {70},
 year = {2002}
}

@article{subsetsim,
author = {S. K. Au  and J. L. Beck },
title = {Subset Simulation and its Application to Seismic Risk Based on Dynamic Analysis},
journal = {Journal of Engineering Mechanics},
volume = {129},
number = {8},
pages = {901-917},
year = {2003},
doi = {10.1061/(ASCE)0733-9399(2003)129:8(901)},

URL = {https://ascelibrary.org/doi/abs/10.1061/%28ASCE%290733-9399%282003%29129%3A8%28901%29},
eprint = {https://ascelibrary.org/doi/pdf/10.1061/%28ASCE%290733-9399%282003%29129%3A8%28901%29}
,

}
@article{robbins,
author = {Herbert Robbins and Sutton Monro},
title = {{A Stochastic Approximation Method}},
volume = {22},
journal = {The Annals of Mathematical Statistics},
number = {3},
publisher = {Institute of Mathematical Statistics},
pages = {400 -- 407},
year = {1951},
doi = {10.1214/aoms/1177729586},
URL = {https://doi.org/10.1214/aoms/1177729586}
}

@article{fluctuation_ams,
 ISSN = {10505164},
 URL = {http://www.jstor.org/stable/44249966},
 abstract = {Multilevel Splitting, also called Subset Simulation, is a Sequential Monte Carlo method to simulate realisations of a rare event as well as to estimate its probability. This article is concerned with the convergence and the fluctuation analysis of Adaptive Multilevel Splitting techniques. In contrast to their fixed level version, adaptive techniques estimate the sequence of levels on the fly and in an optimal way, with only a low additional computational cost. However, very few convergence results are available for this class of adaptive branching models, mainly because the sequence of levels depends on the occupation measures of the particle systems. This article proves the consistency of these methods as well as a central limit theorem. In particular, we show that the precision of the adaptive version is the same as the one of the fixed-level version where the levels would have been placed in an optimal manner.},
 author = {Frédéric Cérou and Arnaud Guyader},
 journal = {The Annals of Applied Probability},
 number = {6},
 pages = {3319--3380},
 publisher = {Institute of Mathematical Statistics},
 title = {FLUCTUATION ANALYSIS OF ADAPTIVE MULTILEVEL SPLITTING},
 urldate = {2024-02-04},
 volume = {26},
 year = {2016}
}
@article{nonparam_high_dim,
author = {Wang, Zhipeng and Scott, David W.},
title = {Nonparametric density estimation for high-dimensional data—Algorithms and applications},
journal = {WIREs Computational Statistics},
volume = {11},
number = {4},
pages = {e1461},
keywords = {density estimation, high-dimensional data, clustering, neural networks, data partitioning},
doi = {https://doi.org/10.1002/wics.1461},
url = {https://wires.onlinelibrary.wiley.com/doi/abs/10.1002/wics.1461},
eprint = {https://wires.onlinelibrary.wiley.com/doi/pdf/10.1002/wics.1461},
abstract = {Density estimation is one of the central areas of statistics whose purpose is to estimate the probability density function underlying the observed data. It serves as a building block for many tasks in statistical inference, visualization, and machine learning. Density estimation is widely adopted in the domain of unsupervised learning especially for the application of clustering. As big data become pervasive in almost every area of data sciences, analyzing high-dimensional data that have many features and variables appears to be a major focus in both academia and industry. High-dimensional data pose challenges not only from the theoretical aspects of statistical inference, but also from the algorithmic/computational considerations of machine learning and data analytics. This paper reviews a collection of selected nonparametric density estimation algorithms for high-dimensional data, some of them are recently published and provide interesting mathematical insights. The important application domain of nonparametric density estimation, such as modal clustering, is also included in this paper. Several research directions related to density estimation and high-dimensional data analysis are suggested by the authors. This article is categorized under: Statistical and Graphical Methods of Data Analysis > Multivariate Analysis Statistical and Graphical Methods of Data Analysis > Density Estimation Statistical Learning and Exploratory Methods of the Data Sciences > Clustering and Classification},
year = {2019}
}

@article{vmce,
author = {Chan, Joshua and Glynn, Peter and Kroese, Dirk},
year = {2011},
month = {08},
pages = {183-194},
title = {A comparison of cross-entropy and variance minimization strategies},
volume = {48},
journal = {Journal of Applied Probability},
doi = {10.1017/S0021900200099216}
}
@article{ams_first,
author = {Frédéric Cérou and Arnaud Guyader},
title = {Adaptive Multilevel Splitting for Rare Event Analysis},
journal = {Stochastic Analysis and Applications},
volume = {25},
number = {2},
pages = {417-443},
year = {2007},
publisher = {Taylor & Francis},
doi = {10.1080/07362990601139628},


URL = { 
    
        https://doi.org/10.1080/07362990601139628
    
    

},
eprint = { 
    
        https://doi.org/10.1080/07362990601139628
    
    

}

}
@article{amshistory,
    author = {Cérou, Frédéric and Guyader, Arnaud and Rousset, Mathias},
    title = "{Adaptive multilevel splitting: Historical perspective and recent results}",
    journal = {Chaos: An Interdisciplinary Journal of Nonlinear Science},
    volume = {29},
    number = {4},
    pages = {043108},
    year = {2019},
    month = {04},

    issn = {1054-1500},
    doi = {10.1063/1.5082247},
    url = {https://doi.org/10.1063/1.5082247},
    eprint = {https://pubs.aip.org/aip/cha/article-pdf/doi/10.1063/1.5082247/14620716/043108\_1\_online.pdf},
}

@book{tuffin,
author = {Rubino, Gerardo and Tuffin, Bruno},
publisher = {John Wiley & Sons, Ltd},
isbn = {9780470745403},
title = {Introduction to Rare Event Simulation},
booktitle = {Rare Event Simulation using Monte Carlo Methods},

doi = {https://doi.org/10.1002/9780470745403.ch1},
url = {https://onlinelibrary.wiley.com/doi/abs/10.1002/9780470745403.ch1},
eprint = {https://onlinelibrary.wiley.com/doi/pdf/10.1002/9780470745403.ch1},
year = {2009},
keywords = {rare event simulation, transportation systems - catastrophic failures being rare, transportation systems - critical in dependability area, basics in Monte Carlo, importance sampling (IS), splitting techniques, splitting technique (fixed-splitting version), techniques for rare event simulation},
}
@book{RNG,
author = {Niederreiter, Harald},
title = {Random Number Generation and Quasi-Monte Carlo Methods},
publisher = {Society for Industrial and Applied Mathematics},
year = {1992},
doi = {10.1137/1.9781611970081},
address = {},
edition   = {},
URL = {https://epubs.siam.org/doi/abs/10.1137/1.9781611970081},
eprint = {https://epubs.siam.org/doi/pdf/10.1137/1.9781611970081}
}
@book{mcbook,
   author = {Art B. Owen},
   year = 2013,
   title = {Monte Carlo theory, methods and examples},
   publisher = {\url{https://artowen.su.domains/mc/}}
}
@article{mcmc_ml,
  added-at = {2016-11-26T13:19:29.000+0100},
  author = {Andrieu, Christophe and de Freitas, Nando and Doucet, Arnaud and Jordan, Michael I.},
  biburl = {https://www.bibsonomy.org/bibtex/26156c1d21e3a2e0898501a01ee8880f5/machinelearning},
  date-added = {2006-12-05 09:44:22 -0800},
  date-modified = {2006-12-05 09:52:31 -0800},
  interhash = {9472a63cb58f414b99668bf8b5ee8acd},
  intrahash = {6156c1d21e3a2e0898501a01ee8880f5},
  journal = {Machine Learning},
  keywords = {filtering ml particle simulation, stochastic},
  number = {1--2},
  pages = {5--43},
  timestamp = {2016-11-26T13:20:49.000+0100},
  title = {An Introduction to {MCMC} for Machine Learning},
  volume = 50,
  year = 2003
}

@article{multimod,
 ISSN = {01621459},
 URL = {http://www.jstor.org/stable/2290324},
 author = {Man-Suk Oh and James O. Berger},
 journal = {Journal of the American Statistical Association},
 number = {422},
 pages = {450--456},
 publisher = {[American Statistical Association, Taylor & Francis, Ltd.]},
 title = {Integration of Multimodal Functions by Monte Carlo Importance Sampling},
 urldate = {2024-01-24},
 volume = {88},
 year = {1993}
}

@article{safe_is,
 ISSN = {01621459},
 URL = {http://www.jstor.org/stable/2669533},
 author = {Art Owen and Yi Zhou},
 journal = {Journal of the American Statistical Association},
 number = {449},
 pages = {135--143},
 publisher = {[American Statistical Association, Taylor & Francis, Ltd.]},
 title = {Safe and Effective Importance Sampling},
 urldate = {2024-01-24},
 volume = {95},
 year = {2000}
}

@article{defensive_is,
 ISSN = {00401706},
 URL = {http://www.jstor.org/stable/1269620},

 author = {Tim Hesterberg},
 journal = {Technometrics},
 number = {2},
 pages = {185--194},
 publisher = {[Taylor & Francis, Ltd., American Statistical Association, American Society for Quality]},
 title = {Weighted Average Importance Sampling and Defensive Mixture Distributions},
 urldate = {2024-01-24},
 volume = {37},
 year = {1995}
}

@book{robert_monte_2004,
  added-at = {2020-07-15T00:37:54.000+0200},
  author = {Robert, C.P. and Casella, G.},
  biburl = {https://www.bibsonomy.org/bibtex/2c45ba78e01455a35b301daddc182caed/twagener},
  interhash = {faaab58e84fb4966b7d2118bc839c076},
  intrahash = {c45ba78e01455a35b301daddc182caed},
  keywords = {},
  publisher = {Springer Verlag},
  timestamp = {2020-07-15T00:37:54.000+0200},
  title = {Monte {Carlo} statistical methods},
  year = 2004
}







@article{dim_red_is,
author = {Uribe, Felipe and Papaioannou, Iason and Marzouk, Youssef M. and Straub, Daniel},
title = {Cross-Entropy-Based Importance Sampling with Failure-Informed Dimension Reduction for Rare Event Simulation},
journal = {SIAM/ASA Journal on Uncertainty Quantification},
volume = {9},
number = {2},
pages = {818-847},
year = {2021},
doi = {10.1137/20M1344585},

URL = { 
    
        https://doi.org/10.1137/20M1344585
    
    

},
eprint = { 
    
        https://doi.org/10.1137/20M1344585
    
    

}
,

}


@article{dist_test,
	url = {http://dx.doi.org/10.1561/0100000114},
	year = {2022},
	volume = {19},
	journal = {Foundations and Trends® in Communications and Information Theory},
	title = {Topics and Techniques in Distribution Testing: A Biased but Representative Sample},
	doi = {10.1561/0100000114},
	issn = {1567-2190},
	number = {6},
	pages = {1032-1198},
	author = {Clément L. Canonne}
}
@INPROCEEDINGS{nonparam_is,
  author={Yun Bae Kim and Deok Seon Roh and Myeong Yong Lee},
  booktitle={2000 Winter Simulation Conference Proceedings (Cat. No.00CH37165)}, 
  title={Nonparametric adaptive importance sampling for rare event simulation}, 
  year={2000},
  volume={1},
  number={},
  pages={767-772 vol.1},
  keywords={Monte Carlo methods;Discrete event simulation;Sampling methods;Asynchronous transfer mode;Computational modeling;Random number generation;Telecommunication network management;Engineering management;Systems engineering and theory;Buffer overflow},
  doi={10.1109/WSC.2000.899849}}

@article{cod_is,
author = {Li, Bo and Bengtsson, Thomas and Bickel, Peter},
year = {2005},
month = {01},
pages = {},
title = {Curse-of-dimensionality revisited: Collapse of importance sampling in very large scale systems}
}
@article{is_mpfp,
title = {Importance sampling in structural systems},
journal = {Structural Safety},
volume = {6},
number = {1},
pages = {3-10},
year = {1989},
issn = {0167-4730},
doi = {https://doi.org/10.1016/0167-4730(89)90003-9},
url = {https://www.sciencedirect.com/science/article/pii/0167473089900039},
author = {R.E. Melchers},
keywords = {failure probability, reliability, Monte Carlo, simulation techniques, importance sampling, systems reliability, integration, parallel systems, series systems},
abstract = {Importance sampling as a technique to improve the Monte Carlo method for probability integration can be shown to be extremely efficient and versatile. This paper addresses the accuracy and efficiency of the method, and its application to series and parallel systems in structures.}
}
@article{multi_model_high_dim,
author = {Yixuan Qiu and Xiao Wang},
title = {Efficient Multimodal Sampling via Tempered Distribution Flow},
journal = {Journal of the American Statistical Association},
volume = {0},
number = {0},
pages = {1-15},
year = {2023},
publisher = {Taylor & Francis},
doi = {10.1080/01621459.2023.2198059},


URL = { 
    
        https://doi.org/10.1080/01621459.2023.2198059
    
    

},
eprint = { 
    
        https://doi.org/10.1080/01621459.2023.2198059
    
    

}

}
@misc{mlmc,
      title={Multilevel Monte Carlo methods}, 
      author={Michael B. Giles},
      year={2013},
      eprint={1304.5472},
      archivePrefix={arXiv},
      primaryClass={math.NA}
}
@article{chi_squared,
   title={On Relations Between the Relative Entropy and χ2-Divergence, Generalizations and Applications},
   volume={22},
   ISSN={1099-4300},
   url={http://dx.doi.org/10.3390/e22050563},
   DOI={10.3390/e22050563},
   number={5},
   journal={Entropy},
   publisher={MDPI AG},
   author={Nishiyama, Tomohiro and Sason, Igal},
   year={2020},
   month=may, pages={563} }

@INPROCEEDINGS{trng,
  author={Marghescu, Andrei and Svasta, Paul},
  booktitle={2015 IEEE 21st International Symposium for Design and Technology in Electronic Packaging (SIITME)}, 
  title={Into generating True Random Numbers - a practical approach using FPGA}, 
  year={2015},
  volume={},
  number={},
  pages={319-322},
  doi={10.1109/SIITME.2015.7342346}}

@article{sample_size_is,
author = {Sourav Chatterjee and Persi Diaconis},
title = {{The sample size required in importance sampling}},
volume = {28},
journal = {The Annals of Applied Probability},
number = {2},
publisher = {Institute of Mathematical Statistics},
pages = {1099 -- 1135},
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  interhash = {bc01e7bb34d4e076a9fff38e9a59c87b},
  intrahash = {0a9c00e0909f45c5d6567b6c49bed7c3},
  journal = {Los Alamos Science},
  keywords = {imported},
  pages = {131--136},
  timestamp = {2019-02-26T21:36:34.000+0100},
  title = {Stan ulam, john von neumann, and the monte carlo method},
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  year = 1987
}

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number = {2},
pages = {218-230},
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issn = {0021-9991},
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url = {https://www.sciencedirect.com/science/article/pii/S0021999185712090},
author = {William J. Morokoff and Russel E. Caflisch},

}

@article{mersenne_twister,
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title = {Mersenne twister: a 623-dimensionally equidistributed uniform pseudo-random number generator},
year = {1998},
issue_date = {Jan. 1998},
publisher = {Association for Computing Machinery},
address = {New York, NY, USA},
volume = {8},
number = {1},
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journal = {ACM Trans. Model. Comput. Simul.},
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numpages = {28},
keywords = {k-distribution, m-sequences, GFSR, MT19937, Mersenne primes, Mersenne twister, TGFSR, finite fields, incomplete array, inversive-decimation method, multiple-recursive matrix method, primitive polynomials, random number generation, tempering}
}