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Monte Carlo method

About: Monte Carlo method is a(n) research topic. Over the lifetime, 95966 publication(s) have been published within this topic receiving 2181896 citation(s). The topic is also known as: MC method & Monte Carlo experiments.

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Open accessJournal ArticleDOI: 10.1063/1.1699114
Abstract: A general method, suitable for fast computing machines, for investigating such properties as equations of state for substances consisting of interacting individual molecules is described. The method consists of a modified Monte Carlo integration over configuration space. Results for the two‐dimensional rigid‐sphere system have been obtained on the Los Alamos MANIAC and are presented here. These results are compared to the free volume equation of state and to a four‐term virial coefficient expansion.

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32,876 Citations


Journal ArticleDOI: 10.1093/BIOMET/57.1.97
W. K. Hastings1Institutions (1)
01 Apr 1970-Biometrika
Abstract: SUMMARY A generalization of the sampling method introduced by Metropolis et al. (1953) is presented along with an exposition of the relevant theory, techniques of application and methods and difficulties of assessing the error in Monte Carlo estimates. Examples of the methods, including the generation of random orthogonal matrices and potential applications of the methods to numerical problems arising in statistics, are discussed. For numerical problems in a large number of dimensions, Monte Carlo methods are often more efficient than conventional numerical methods. However, implementation of the Monte Carlo methods requires sampling from high dimensional probability distributions and this may be very difficult and expensive in analysis and computer time. General methods for sampling from, or estimating expectations with respect to, such distributions are as follows. (i) If possible, factorize the distribution into the product of one-dimensional conditional distributions from which samples may be obtained. (ii) Use importance sampling, which may also be used for variance reduction. That is, in order to evaluate the integral J = X) p(x)dx = Ev(f), where p(x) is a probability density function, instead of obtaining independent samples XI, ..., Xv from p(x) and using the estimate J, = Zf(xi)/N, we instead obtain the sample from a distribution with density q(x) and use the estimate J2 = Y{f(xj)p(x1)}/{q(xj)N}. This may be advantageous if it is easier to sample from q(x) thanp(x), but it is a difficult method to use in a large number of dimensions, since the values of the weights w(xi) = p(x1)/q(xj) for reasonable values of N may all be extremely small, or a few may be extremely large. In estimating the probability of an event A, however, these difficulties may not be as serious since the only values of w(x) which are important are those for which x -A. Since the methods proposed by Trotter & Tukey (1956) for the estimation of conditional expectations require the use of importance sampling, the same difficulties may be encountered in their use. (iii) Use a simulation technique; that is, if it is difficult to sample directly from p(x) or if p(x) is unknown, sample from some distribution q(y) and obtain the sample x values as some function of the corresponding y values. If we want samples from the conditional dis

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13,481 Citations


Open accessBook
01 Jun 1969-
Abstract: Uncertainties in measurements probability distributions error analysis estimates of means and errors Monte Carlo techniques dependent and independent variables least-squares fit to a polynomial least-squares fit to an arbitrary function fitting composite peaks direct application of the maximum likelihood. Appendices: numerical methods matrices graphs and tables histograms and graphs computer routines in Pascal.

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12,721 Citations


Open accessJournal ArticleDOI: 10.1109/78.978374
Abstract: Increasingly, for many application areas, it is becoming important to include elements of nonlinearity and non-Gaussianity in order to model accurately the underlying dynamics of a physical system. Moreover, it is typically crucial to process data on-line as it arrives, both from the point of view of storage costs as well as for rapid adaptation to changing signal characteristics. In this paper, we review both optimal and suboptimal Bayesian algorithms for nonlinear/non-Gaussian tracking problems, with a focus on particle filters. Particle filters are sequential Monte Carlo methods based on point mass (or "particle") representations of probability densities, which can be applied to any state-space model and which generalize the traditional Kalman filtering methods. Several variants of the particle filter such as SIR, ASIR, and RPF are introduced within a generic framework of the sequential importance sampling (SIS) algorithm. These are discussed and compared with the standard EKF through an illustrative example.

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  • Fig. 4. Evolution of the upper and lower2 positions of the state as estimated by the EKF (dotted) with the true state also shown (solid).
    Fig. 4. Evolution of the upper and lower2 positions of the state as estimated by the EKF (dotted) with the true state also shown (solid).
  • Fig. 5. Image representing evolution of probability density for approximate grid-based filter.
    Fig. 5. Image representing evolution of probability density for approximate grid-based filter.
  • Fig. 3. Evolution of the EKFs mean estimate of the state.
    Fig. 3. Evolution of the EKFs mean estimate of the state.
  • Fig. 9. Image representing evolution of probability density for “likelihood” particle filter.
    Fig. 9. Image representing evolution of probability density for “likelihood” particle filter.
Topics: Particle filter (67%), Auxiliary particle filter (63%), Monte Carlo localization (59%) ...read more

10,977 Citations


Open accessBook
Christian P. Robert1, George Casella1Institutions (1)
01 Jan 1999-
Abstract: We have sold 4300 copies worldwide of the first edition (1999). This new edition contains five completely new chapters covering new developments.

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6,854 Citations


Performance
Metrics
No. of papers in the topic in previous years
YearPapers
202269
20212,921
20203,204
20193,418
20183,290
20173,567

Top Attributes

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Topic's top 5 most impactful authors

Kurt Binder

330 papers, 24.2K citations

David P. Landau

128 papers, 7.5K citations

Wolfhard Janke

123 papers, 1.8K citations

Enrico Zio

91 papers, 2K citations

Ivan Dimov

78 papers, 716 citations

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