Handbook of Monte Carlo Methods

By Dirk P. Kroese, Thomas Taimre, Zdravko I. Botev. 2011

1,010 citations recorded by the source corpus.

Subfields: Numerical Analysis, Statistical and Nonlinear Physics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/858650f45819136baed33ac6526cc64635b805ee

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Citations in the corpus

Interacting Particle Solutions of Fokker–Planck Equations Through Gradient–Log–Density Estimation (2020, background): “On the other hand, in the sample-based category, Monte Carlo methods resort to stochastic integration of a large number of independent stochastic trajectories that as an ensemble represent the probability density [39,40].”
Why the Monte Carlo method is so important today (2014, background): “For example, the complexity of a simulation program for a machine repair facility would typically not depend on the number of machines or repairers involved.”
Reconciling Output Gaps: Unobserved Components Model and Hodrick-Prescott Filter (2017, methodology): “For example, using US real GDP from 1947Q1 to 1998Q2, Perron and Wada (2009) find a break in trend growth at 1973Q1.”
Hydrological uncertainty processor based on a copula function (2018, background): “…steps: a. Generate M random numbers u2 from uniform distribution U(0, 1); b. Compute the value of cðu1; u2; u3Þ; c. Calculate the mean of the M calculated cðu1; u2; u3Þ values, which is approximately equal to the definite integral ð1 0 cðu1; u2; u3Þdu2 (Kroese et al. 2013, Robert and Casella 2013).”
Resampled Priors for Variational Autoencoders (2018, methodology): “A mixture of Gaussian prior [5, 22] provides a simpler alternative to the VampPrior, but is harder to optimize and does not perform as well [30].”
Hawkes Processes (2015, background): “7b. Quantitative extensions exist; for example see Section 3.3.3 of [51], or serial correlation tests in [52].”
The normal law under linear restrictions: simulation and estimation via minimax tilting (2016, methodology): “In an appropriate asymptotic tail regime, the minimax tilting yields an estimator with vanishing relative error (VRE) property (Kroese et al., 2011).”
A Comparative Study of Multiple-Criteria Decision-Making Methods under Stochastic Inputs (2016, background): “…ﬁnite states, the probability distribution of ﬁnite states, the output space and a mapping function between the ﬁnite states and the output space [71]. method is an approach function for the finite states, the probability The approach proposed in this paper for the stochastic expansion of…”
The Stochastic Volatility in Mean Model With Time-Varying Parameters: An Application to Inflation Modeling (2017, methodology): “We first discuss how one can quickly locate the maximum of p(h | y, x, γ , μ, φ, σ 2), or equivalently that of log p(h | y, x, γ , μ, φ, σ 2), using the Newton–Raphson method (see, e.g., Kroese, Taimre, and Botev 2011, pp. 688–689).”
Bayesian Model Comparison for Time-Varying Parameter VARs with Stochastic Volatility (2018, methodology): “This can be done using the Newton–Raphson method (see, e.g., Kroese et al., 2011).”
The cross-entropy method for estimation (2013, background): “…the n-dimensional sphere can be obtained by normalizing an n-dimensional standard normal random vector: Y = Z/‖Z‖, with Z ∼ N(0,In); see, for example, Kroese et al. (2011); Blanchet and Rojas-Nandayapa (in press) consider efficient simulation procedures for estimating probabilities of the form =…”