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Data Science and Machine Learning, 2019
Many quantitative problems in science, engineering, and economics are nowadays solved via statistical sampling on a computer. Such Monte Carlo methods can be used in three different ways: (1) to generate random objects and processes in order to observe ...
Dirk P. Kroese +3 more
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Many quantitative problems in science, engineering, and economics are nowadays solved via statistical sampling on a computer. Such Monte Carlo methods can be used in three different ways: (1) to generate random objects and processes in order to observe ...
Dirk P. Kroese +3 more
openaire +2 more sources
Monte Carlo and Quasi-Monte Carlo Methods
2020Monte Carlo is one of the most versatile and widely used numerical methods. Its convergence rate, O(N~1^2), is independent of dimension, which shows Monte Carlo to be very robust but also slow. This article presents an introduction to Monte Carlo methods for integration problems, including convergence theory, sampling methods and variance reduction ...
Tuffin, Bruno, L'Écuyer, Pierre
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2019
The sequential use of random numbers, to sample the values of probability variables, allows obtaining solutions to mathematical problems such as the Monte Carlo method, that allows to model stochastic parameters or deterministic based on random sampling.
Lorenzo Cevallos-Torres +1 more
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The sequential use of random numbers, to sample the values of probability variables, allows obtaining solutions to mathematical problems such as the Monte Carlo method, that allows to model stochastic parameters or deterministic based on random sampling.
Lorenzo Cevallos-Torres +1 more
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Markov Chain Monte Carlo in Practice.
Annual Review of Public Health, 2021Markov chain Monte Carlo (MCMC) is an essential set of tools for estimating features of probability distributions commonly encountered in modern applications.
Galin L. Jones, Qian Qin
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Monte Carlo Techniques in Radiation Therapy
, 2021Monte Carlo Fundamentals History of Monte Carlo Alex F. Bielajew Basics of Monte Carlo Simulations Matthias Fippel Variance Reduction Techniques Matthias Fippel Application of Monte Carlo Techniques in Radiation Therapy Applications of Monte Carlo to ...
J. Seco, F. Verhaegen
semanticscholar +1 more source
1987
The term ‘Monte Carlo methods’ is used to refer to two different, though closely related, techniques. The first meaning, currently the less common one among economists, is the evaluation of definite integrals by use of random variables. The idea is to evaluate \(\int_a^b {F\left( x \right)} {\text{d}}x\) where x may be a vector) by estimating \(\int_a ...
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The term ‘Monte Carlo methods’ is used to refer to two different, though closely related, techniques. The first meaning, currently the less common one among economists, is the evaluation of definite integrals by use of random variables. The idea is to evaluate \(\int_a^b {F\left( x \right)} {\text{d}}x\) where x may be a vector) by estimating \(\int_a ...
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Journal of the Society for Industrial and Applied Mathematics, 1958
A description of the many facets of the Monte Carlo Method is presented. The subject is traversed from the most elementary to the more difficult techniques, and from the least practical to the most fruitful applications. The generation of random numbers in the modern electronic computing machine is dealt with.
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A description of the many facets of the Monte Carlo Method is presented. The subject is traversed from the most elementary to the more difficult techniques, and from the least practical to the most fruitful applications. The generation of random numbers in the modern electronic computing machine is dealt with.
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The No-U-turn sampler: adaptively setting path lengths in Hamiltonian Monte Carlo
Journal of machine learning research, 2011Hamiltonian Monte Carlo (HMC) is a Markov chain Monte Carlo (MCMC) algorithm that avoids the random walk behavior and sensitivity to correlated parameters that plague many MCMC methods by taking a series of steps informed by first-order gradient ...
M. Hoffman, A. Gelman
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Monte Carlo and Quasi-Monte Carlo Methods
2013Chapter 12 discusses Monte Carlo and quasi-Monte Carlo methods and demonstrates how these techniques can be used to compute functionals of multidimensional diffusions. Monte Carlo methods feature prominently in this book, in particular we discuss how to use Lie Symmetry methods to construct unbiased Monte Carlo estimators in Chap. 6, and we discuss how
Jan Baldeaux, Eckhard Platen
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2018
Stochastic-simulation, or Monte-Carlo, methods are used extensively in the area of credit-risk modelling. This technique has, in fact, been employed inveterately in previous chapters. Care and caution are always advisable when employing a complex numerical technique. Prudence is particularly appropriate, in this context, because default is a rare event.
Philip Dutré +2 more
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Stochastic-simulation, or Monte-Carlo, methods are used extensively in the area of credit-risk modelling. This technique has, in fact, been employed inveterately in previous chapters. Care and caution are always advisable when employing a complex numerical technique. Prudence is particularly appropriate, in this context, because default is a rare event.
Philip Dutré +2 more
openaire +2 more sources