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*  Ancestral reconstruction
... and Bollback first proposed a hierarchical Bayes method to ancestral reconstruction by using Markov chain Monte Carlo (MCMC) ... ML-based methods of ancestral reconstruction tend to provide greater accuracy than MP methods in the presence of variation in ... The upshot of the "minimum evolution" heuristic underlying such methods is that such methods assume that changes are rare, and ... Bayesian inference is the method that many have argued is the most accurate. In general, Bayesian statistical methods allow ...
*  Monte Carlo method
... for Monte Carlo molecular modeling Mean field particle methods Monte Carlo method for photon transport Monte Carlo methods for ... Monte Carlo method Comparison of risk analysis Microsoft Excel add-ins Direct simulation Monte Carlo Dynamic Monte Carlo method ... a Monte Carlo method, and a Monte Carlo simulation: a simulation is a fictitious representation of reality, a Monte Carlo ... Monte Carlo methods are also used in the ensemble models that form the basis of modern weather forecasting. Monte Carlo methods ...
*  Quasi-Monte Carlo method
Monte Carlo method Monte Carlo methods in finance Quasi-Monte Carlo methods in finance Biology Monte Carlo method Computational ... on Monte Carlo and quasi-Monte Carlo methods A very intuitive and comprehensive introduction to Quasi-Monte Carlo methods. ... Hence, the Monte Carlo method and the quasi-Monte Carlo method are beneficial in these situations. The approximation error of ... Hence, in general, the accuracy of the quasi-Monte Carlo method increases faster than that of the Monte Carlo method. However, ...
*  Biology Monte Carlo method
Monte Carlo method Biology Computational biology T.A. van der Straaten, G. Kathawala, A. Trellakis, R.S. Eisenberg, and U. ... Biology Monte Carlo methods (BioMOCA) have been developed at the University of Illinois at Urbana-Champaign to simulate ion ... namely the Boltzmann transport Monte Carlo (BTMC) and particle-particle-particle-mesh (P3M). The first one uses Monte Carlo ... The Monte Carlo Method for Semiconductor Device Simulation, Springer Verlag, New York (1989) R. Hockney, J. Eastwood, Computer ...
*  Multilevel Monte Carlo method
... and the combination of MLMC with the Quasi-Monte Carlo method. Monte Carlo method Monte Carlo methods in finance Quasi-Monte ... is then approximated by a Monte Carlo method, resulting in the multilevel Monte Carlo method. Note that taking a sample of the ... "Multilevel Monte Carlo Methods". Acta Numerica. 24: 259-328. Giles, M. B. (2008). "Multilevel Monte Carlo Path Simulation". ... Recent extensions of the multilevel Monte Carlo method include multi-index Monte Carlo, where more than one direction of ...
*  Dynamic Monte Carlo method
The DMC method is very similar to the kinetic Monte Carlo method. There are several well-known methods for performing DMC ... In chemistry, dynamic Monte Carlo (DMC) is a Monte Carlo method for modeling the dynamic behaviors of molecules by comparing ... It is essentially the same as Kinetic Monte Carlo. Unlike the Metropolis Monte Carlo method, which has been employed to study ... Large-scale systems are able to be calculated by this method. Hybrid Monte Carlo (Meng and Weinberg 1994): B. Meng and W. H. ...
*  Monte Carlo method for photon transport
This flexibility makes Monte Carlo modeling a powerful tool. Thus, while computationally inefficient, Monte Carlo methods are ... in biological tissue Monte Carlo method Convolution for optical broad-beam responses in scattering media Monte Carlo methods ... Due to the nature of PDT, it is useful to use Monte Carlo methods for modeling scattering and absorption in the tissue in order ... Monte Carlo methods provide a flexible framework that has been used by different techniques to reconstruct optical properties ...
*  Monte Carlo method in statistical physics
Monte Carlo integration Metropolis algorithm Importance sampling Quantum Monte Carlo Monte Carlo molecular modeling Allen, M.P ... Monte Carlo in statistical physics refers to the application of the Monte Carlo method to problems in statistical physics, or ... For those systems, the Monte Carlo integration (and not to be confused with Monte Carlo method, which is used to simulate ... The general motivation to use the Monte Carlo method in statistical physics is to evaluate a multivariable integral. The ...
*  Monte Carlo methods in finance
Monte Carlo methods are ideally suited to evaluating difficult integrals (see also Monte Carlo method). Thus if we suppose that ... Quasi-Monte Carlo methods in finance Monte Carlo method Historical simulation (finance) Stock market simulator Real options ... Monte Carlo methods in financial engineering. New York: Springer. p. 205. Boyle, P., Broadie, M. and Glasserman, P. Monte Carlo ... global-derivatives.com Monte Carlo Method, riskglossary.com The Monte Carlo Framework, Examples from Finance, Martin Haugh, ...
*  Monte Carlo methods for electron transport
Monte Carlo method Semiconductor device Monte Carlo method for photon transport Band structure Method of quantum ... characteristics Quantum Monte Carlo Quasi-Monte Carlo method K. Hess, Monte Carlo Device Simulation: Full Band and Beyond, ... The Monte Carlo method for electron transport is a semiclassical Monte Carlo(MC) approach of modeling semiconductor transport. ... whereas the Monte Carlo is the stochastic approach used to solve the BTE. The semiclassical Monte Carlo method is a statistical ...
*  Quasi-Monte Carlo methods in finance
The quasi-Monte Carlo (QMC) method is defined by φ Q M C ( f ) = 1 n ∑ i = 1 n f ( x i ) , {\displaystyle \varphi ^{\mathop {\ ... To break this curse of dimensionality one can use the Monte Carlo (MC) method defined by φ M C ( f ) = 1 n ∑ i = 1 n f ( x i ... The standard terminology quasi-Monte Carlo is somewhat unfortunate since MC is a randomized method whereas QMC is purely ... It is well known that the expected error of Monte Carlo is of order n − 1 / 2 {\displaystyle n^{-1/2}} . Thus the cost of the ...
*  Kinetic Monte Carlo surface growth method
Monte Carlo (MC) Kinetic Monte Carlo (KMC) Diffusion-limited growth. ... and other computer simulation methods such as Molecular Dynamics (MD), and Monte Carlo (MC) simulation are widely used. First, ... Kinetic Monte Carlo (KMC) is a form of computer simulation in which atoms and molecules are allowed to interact at given rate ... This simulation method is typically used in the micro-electrical industry to study crystal surface growth, and it can provide ...
*  Timeline of numerical analysis after 1945
The Monte Carlo Method: Classic Papers Monte Carlo Landmark Papers "Must read" papers in numerical analysis. Discussion at Math ... Metropolis, N. (1987). "The Beginning of the Monte Carlo method" (PDF). Los Alamos Science. No. 15, Page 125. . Accessed 5 may ... N. Metropolis and S. Ulam (1949). The Monte Carlo method. Journal of the American Statistical Association 44:335-341. Crank, J ... Monte Carlo simulation (voted one of the top 10 algorithms of the 20th century) invented at Los Alamos by von Neumann, Ulam and ...
*  N-body units
Hénon, Michel (1971). "The Monte Carlo Method". Astrophysics and Space Science. 14 (1): 151-167. Bibcode:1971Ap&SS..14..151H. ...
*  Low-discrepancy sequence
Discrepancy theory Quasi-Monte Carlo method Markov chain Monte Carlo Sparse grid Kuipers and Niederreiter, 2005, p. 123 http:// ... this is the Monte Carlo method. If the points are chosen as elements of a low-discrepancy sequence, this is the quasi-Monte ... Elements need not be recomputed in the random Monte Carlo method if N is increased, but the point sets do not have minimal ... 3 Hammersley, J. M.; Handscomb, D. C. (1964). Monte Carlo Methods. doi:10.1007/978-94-009-5819-7. Herman Tulleken. "Poisson ...
*  Variance reduction
Monte Carlo Methods. London: Methuen. ISBN 0-416-52340-4. Kahn, H.; Marshall, A. W. (1953). "Methods of Reducing Sample Size in ... In mathematics, more specifically in the theory of Monte Carlo methods, variance reduction is a procedure used to increase the ... MCNP - A General Monte Carlo N-Particle Transport Code, Version 5 Los Alamos Report LA-UR-03-1987. ... "The Method of Common Random Numbers: An Example". Wolfram Demonstrations Project. Retrieved 29 March 2016. Hammersley, J. M.; ...
*  Stanislaw Ulam
"The Monte Carlo method". Metropolis and Ulam published the first unclassified paper on the Monte Carlo method in 1949. Fermi, ... The Monte Carlo method has become a ubiquitous and standard approach to computation, and the method has been applied to a vast ... The Day After Trinity on IMDb Eckhardt, Roger (1987). "Stan Ulam, John von Neumann, and the Monte Carlo Method" (PDF). Los ... Eckhardt, Roger (1987). "Stan Ulam, John von Neumann, and the Monte Carlo method" (PDF). Los Alamos Science, No 15. Retrieved ...
*  Morris method
Monte Carlo method Andrea Saltelli; Stefano Tarantola; Francesca Campolongo; Marco Ratto (2004). Sensitivity analysis in ... In applied statistics, the Morris method for global sensitivity analysis is a so-called one-step-at-a-time method (OAT), ... Such number is very efficient compared to more demanding methods for sensitivity analysis. A sensitivity analysis method widely ... In Revised Morris method µ* is used to detect input factors with an important overall influence on the output. σ is used to ...
*  Rejection sampling
It is also commonly called the acceptance-rejection method or "accept-reject algorithm" and is a type of Monte Carlo method. ... In high dimensions, it is necessary to use a different approach, typically a Markov chain Monte Carlo method such as Metropolis ... Robert, C.P. and Casella, G. "Monte Carlo Statistical Methods" (second edition). New York: Springer-Verlag, 2004. J. von ... Monte Carlo methods", Nat. Bureau Standards, 12 (1951), pp. 36-38.. ...
*  Path integral molecular dynamics
doi:10.1016/0370-1573(75)90030-7. Barker, J. A. (1979). "A quantum-statistical Monte Carlo method; path integrals with boundary ... method. The same techniques are also used in path integral Monte Carlo (PIMC). The technique has been used to calculate time ... John Shumway; Matthew Gilbert (2008). "Path Integral Monte Carlo Simulation". ... Jang, S.; Voth, G. A. (1999). "A derivation of centroid molecular dynamics and other approximate time evolution methods for ...
*  Path integral Monte Carlo
... (PIMC) is a quantum Monte Carlo method in the path integral formulation of quantum statistical ... As with all Monte Carlo method based approaches, a large number of points must be calculated. As more "replicas" are used to ... Path integral molecular dynamics Barker, J. A. (1979). "A quantum-statistical Monte Carlo method; path integrals with boundary ... Wang, Q.; Johnson, J. K.; Broughton, J. Q. (1997). "Path integral grand canonical Monte Carlo". The Journal of Chemical Physics ...
*  Markov chain
The use of Markov chains in Markov chain Monte Carlo methods covers cases where the process follows a continuous state space. ... Such can occur in Markov chain Monte Carlo (MCMC) methods in situations where a number of different transition matrices are ... Reuven Y. Rubinstein; Dirk P. Kroese (20 September 2011). Simulation and the Monte Carlo Method. John Wiley & Sons. p. 225. ... Markov processes are the basis for general stochastic simulation methods known as Gibbs sampling and Markov Chain Monte Carlo, ...
*  Stochastic process
For example, they are the basis for a general stochastic simulation method known as Markov chain Monte Carlo, which is used for ... ISBN 978-0-08-057041-9. Reuven Y. Rubinstein; Dirk P. Kroese (20 September 2011). Simulation and the Monte Carlo Method. John ... ISBN 978-0-19-852525-7. Carlo Laing; Gabriel J Lord (2010). Stochastic Methods in Neuroscience. OUP Oxford. ISBN 978-0-19- ... ISBN 978-1-118-21052-9. Dani Gamerman; Hedibert F. Lopes (10 May 2006). Markov Chain Monte Carlo: Stochastic Simulation for ...
*  ChIA-PET
Monte Carlo method Barski et al., (2007). High-resolution profiling of histone methylations in the human genome. Cell. (129); ... Monte Carlo simulation Used to estimate the false discovery rates. PET-Tool A software suite for processing and managing of ... The ChIA-PET method combines ChIP-based methods (Kuo & Allis, 1999), and Chromosome conformation capture (3C), to extend the ... Methods. (19); 425-33. Li, G., Fullwood, M.J., Xu, H., Mulawadi, F.H., Velkov, S., Vega, V., Ariyaratne, P.N., Mohamed, Y.B., ...
*  Random number generation
Random number generators are very useful in developing Monte Carlo-method simulations, as debugging is facilitated by the ... Handbook of Monte Carlo Methods. New York: John Wiley & Sons. p. 772. ISBN 0-470-17793-4. Press, WH; Teukolsky, SA; Vetterling ... such as the computation of integrals by the Monte Carlo method. For such problems, it may be possible to find a more accurate ... One method, called the inversion method, involves integrating up to an area greater than or equal to the random number (which ...
*  Uncertainty quantification
Techniques such as the Monte Carlo method are frequently used. A probability distribution can be represented by its moments (in ... Local expansion-based methods: Taylor series, perturbation method, etc. These methods have advantages when dealing with ... Most probable point (MPP)-based methods: first-order reliability method (FORM) and second-order reliability method (SORM). ... Markov chain Monte Carlo (MCMC) is often used for integration; however it is computationally expensive. The fully Bayesian ...
*  Cauchy process
Kroese, D.P.; Taimre, T.; Botev, Z.I. (2011). Handbook of Monte Carlo Methods. John Wiley & Sons. p. 214. ISBN 9781118014950. ... Bertoin, J. (2001). "Some elements on Lévy processes". In Shanbhag, D.N. Stochastic Processes: Theory and Methods. Gulf ...