Monte Carlo Strategies in Scientific Computing

By Tim Hesterberg. 2002

2,328 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Management Information Systems, Management Science and Operations Research, Probabilistic & Bayesian Methods

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Artificial Intelligence

In Management Information Systems

In Management Science and Operations Research

In Probabilistic & Bayesian Methods

Citations in the corpus

A Theory of Generative ConvNet (2016, methodology): “(3) For generative models, we usually need to use Markov chain Monte Carlo (MCMC) [20, 19] to generate images from the models, but the convergence properties of the MCMC algorithms are unknown.”
Batch Stationary Distribution Estimation (2020, background): “…demonstrate its applicability and efﬁcacy in a range of important scenarios beyond queueing, including: • Stochastic differential equations (SDEs) SDEs are an essential modeling tool in many ﬁelds like statistical physics (Kadanoff, 2000), ﬁnance (Oksendal, 2013) and molecular dynamcis (Liu, 2001).”
Doubly Robust Bias Reduction in Infinite Horizon Off-Policy Estimation (2019, methodology): “The second approach is to use importance sampling to correct the sampling bias in off-policy data, so that an (almost) unbiased estimator can be obtained (Liu, 2001; Strehl et al., 2010; Bottou et al., 2013).”
Breaking the Curse of Horizon: Infinite-Horizon Off-Policy Estimation (2018, methodology): “We do not report the results of unnormalized IS because they are generally significantly worse than WIS methods [22, 30].”
Handbook of Markov Chain Monte Carlo (2011, positive): “…their procedure performs better than the original on high-dimensional multivariate Gaussian distributions, but their experiments are flawed.4 Qin and Liu (2001)also introduce the more useful idea of weighting the states in the accept and reject windows non-uniformly, which can be incorporated…”
On the stability of sequential Monte Carlo methods in high dimensions (2011, background): “The variability of the weights is often measured by the effective sample size [37], and one often resamples when this drops below a threshold (dynamic-resampling).”
Weighted importance sampling for off-policy learning with linear function approximation (2014, neutral): “…is biased, but consistent (asymptotically correct) and typically of much lower variance than the ordinary importance-sampling (OIS) estimate, as acknowledged by many authors (Hesterberg 1988, Casella & Robert 1998, Precup, Sutton & Singh 2000, Shelton 2001, Liu 2001, Koller & Friedman 2009).”
PhyloGibbs: A Gibbs Sampling Motif Finder That Incorporates Phylogeny (2005, methodology): “using a Monte Carlo Markov-chain sampling strategy [”
Diffusion limits of the random walk metropolis algorithm in high dimensions (2010, methodology): “Metropolis–Hastings methods [18, 21] form a widely used class of MCMC methods [19, 22] for sampling from complex probability distributions.”
Batch means and spectral variance estimators in Markov chain Monte Carlo (2008, neutral): “As is now widely recognized (Liu [30], Robert and Casella [41]), we can often simulate a Harris ergodic (i.”
Analysis of Multifactor Affine Yield Curve Models (2008, neutral): “For instance, they did not provide inefficiency factors and other related measures that can be useful in evaluating the efficiency of MCMC sampling (Chib 2001; Liu 2001; Robert and Casella 2004).”
Multi-step Off-policy Learning Without Importance Sampling Ratios (2017, background): “Although importance sampling plays a key role in correcting the discrepancy between the policies, the highly varying nature of importance sampling ratios often results in large estimation variance (Liu 2001, Koller & Friedman 2009, Dann et al. 2014, Mahmood & Sutton 2015, White & White 2016a).”
Data Assimilation: A Mathematical Introduction (2015, background): “The subject is overviewed from an algorithmic point of view in [74].”
Importance sampling: a review (2010, neutral): “d(α, λ) = ∫ (log g(x) − α − log qλ(x))(2)p(x)dx (8)”
Adaptive methods for sequential importance sampling with application to state space models (2008, methodology): “A first criterion, advocated in Kong et al. (1994) and Liu (2004) is the chi-square distance (CSD) between the proposal and the target distributions, which coincides with the coefficient of variation (CV2) of the importance weights.”