Monte Carlo Sampling Methods

By Alexander Shapiro. 2003

1,241 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Management Science and Operations Research, Statistics and Probability, Probabilistic & Bayesian Methods

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Citations in the corpus

Predicting Tactical Solutions to Operational Planning Problems under Imperfect Information (2018, methodology): “These methods originate from two broad areas of research and perspectives: Monte Carlo stochastic programming (e.g., de Mello and Bayraksan, 2014, Shapiro, 2003) and simulation optimization (e.g., Fu, 2015).”
Stochastic First- and Zeroth-Order Methods for Nonconvex Stochastic Programming (2013, methodology): “…an optimal O (1 /ǫ 2 ) iteration complexity for solving these problems. in [19 This method has been shown , 23] to be competitive to the widely-accepted sample average approximation approach (see, e.g., [17, 38]) and even signiﬁcantly outperform it for solving a class of convex SP problems.”
Contemporary Bayesian Econometrics and Statistics (2005, background): “4.1 Direct Sampling, 106 4.2 Acceptance and Importance Sampling, 110 4.2.1 Acceptance Sampling, 111 4.2.2 Importance Sampling, 114 4.3 Markov Chain Monte Carlo, 119 4.3.1 The Gibbs Sampler, 120 4.3.2 The Metropolis–Hastings Algorithm, 122 4.4 Variance Reduction, 127 4.4.1 Concentrated Expectations, ”
An optimal method for stochastic composite optimization (2011, methodology): “Recent theoretical studies (cf., [16,45,46]) and numerical experiments (see e.g., [23,27,51]) show that the SAA method coupled with a good (deterministic) algorithm could be reasonably efﬁcient for solving certain classes of two stage stochastic programming problems.”
Mix and Match: Learning-free Controllable Text Generationusing Energy Language Models (2022, methodology): “To sample from the energy parametrizations 257 described in the previous section, we follow the 258 Metroplolis Hastings (Hastings, 1970) MCMC 259 scheme for sampling from the masked language 260 models introduced by Goyal et al.”
Marginal Likelihood From the Metropolis–Hastings Output (2001, methodology): “Under the prior distributions 4‚5 = ”34‚—01 10I45 and 4‘5 / ”214‘ —03i211 02I215IS , where i21 is a vector of ones and S is the subset of R21 that leads to a positive de nite correlation matrix, the posterior distribution is sampled using the algorithm of Chib and Greenberg (1998), which is based on”
Robust Stochastic Approximation Approach to Stochastic Programming (2008, methodology): “Recent theoretical studies (cf. [ 11, 25, 26]) and numerical experiments (see, e.g., [12, 13, 29]) show that the SAA method coupled with a good (deterministic) algorithm could be reasonably eﬃcient for solving certain classes of two-stage stochastic programming problems.”
Statistical Interpretation of Species Composition (2001, methodology): “The conditional distribution for ztj (given current values of Ìt and è) is sampled via Hastings’ algorithm (Hastings 1970).”
The design of robust value-creating supply chain networks (2010, methodology): “To consider the random variables explicitly in the SCN design model, a proactive stochastic programming (Birge and Louveaux, 1997; Ruszczynski and Shapiro, 2003, Shapiro, 2007) approach must be used.”
A Sampling-and-Discarding Approach to Chance-Constrained Optimization: Feasibility and Optimality (2011, neutral): “[24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35], and sample-based optimization has also been used in connection of various application domains, see e.”
Computer Model Calibration Using High-Dimensional Output (2008, background): “The first is the interplay between the discrepancy term δ(x) and the calibration parameters θ ; this is noted in the discussion of Kennedy and O’Hagan (2001), as well as in a number of other articles (Higdon et al. 2004; Loeppky, Bingham, Sacks, and Welch 2005; Bayarri et al. 2007). The basic point ”
On the convergence to equilibrium of Kac’s random walk on matrices (2007, methodology): “The second process is also mathematically natural and has been considered as a Monte Carlo method to sample approximately from Haar measure [5] and do dimensionality reduction [1].”
A Component GARCH Model with Time Varying Weights (2009, methodology): “Since direct sampling from φ(β|θ2, Y T ) is not feasible, we use the Metropolis-Hastings algorithm (Hastings, 1970), choosing a k-dimensional multivariate Gaussian distribution as a proposal.”
A Stochastic forward-backward splitting method for solving monotone inclusions in Hilbert spaces (2014, background): “in [50, 12] (see also references therein), and a mirror proximal stochastic approximation algorithm to solve variational inequalities corresponding to a maximal monotone operator has been proposed in [25].”
A Two-Part Random-Effects Model for Semicontinuous Longitudinal Data (2001, methodology): “In preliminary work, we implemented a Gibbs sampler in Fortran embedded with steps of a Metropolis–Hastings algorithm (Hastings 1970; Tierney 1994) to sample from the conditional distributions of ‚ and bi .”
Sampling strategies and stopping criteria for stochastic dual dynamic programming: a case study in long-term hydrothermal scheduling (2011, methodology): “The SAA approach has solid foundation in terms of convergence properties as a function of the sample size N ,s ee for instance [ 34 ] for a compilation of results.”