Approximating Integrals Via Monte Carlo and Deterministic Methods

By M. Evans, Tim B. Swartz. 2000

451 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/d52eef68442eff8dd029d228c8f2cf01d60e3ab8

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Citations in the corpus

Variance Reduction Techniques for Gradient Estimates in Reinforcement Learning (2001, methodology): “One generic approach to reducing the variance of Monte Carlo estimates of integrals is to use an additive control variate (see, for example, [6]).”
Generalized Gaussian Process Regression Model for Non-Gaussian Functional Data (2014, methodology): “…(τm), then by Laplace approximation we have∫ exp{ (τm)}dτm = exp { (τ̂m) + Nm 2 log(2π ) − 1 2 log |C−1m + Km| } , (14) where Km is the second-order derivative of ∑Nm i=1 log {p(zmi |τmi, B)} with respect to τm and evaluated at τ̂m (see, e.g., Barndorff-Nielsen and Cox 1989; Evans and Swartz 2000).”
Numerical Techniques for Maximum Likelihood Estimation of Continuous-Time Diffusion Processes (2002, methodology): “Finally, it should be noted that the 4M ƒ 15-fold integrations that were computed by the authors using sampling-based methods (based on pseudorandom sequences; see, for example, Evans and Swartz 2000) could alternatively be evaluated via quasirandom sequences.”
A theory of statistical models for Monte Carlo integration (2003, methodology): “For good summaries, see Hammersley and Hanscomb (1964), Ripley (1987), Evans and Swartz (2000) or Liu (2001).”
yambo: An ab initio tool for excited state calculations (2008, methodology): “The Iq integrals are calculated via a three dimensional Monte Carlo technique [24].”
Semiparametric Transformation Models With Random Effects for Recurrent Events (2007, unknown): “(B.1) The integrations in this formula are evaluated by numerical approximations (e.g., Evans and Swartz 2000, chap.”
Design of computer experiments: A review (2017, background): “This has resulted in an abundant literature [44, 66, 67, 94, 108, 136, 137, 154].”
Quasi Importance Sampling (2005, methodology): “Key words: quasi-Monte Carlo method, nonuniform random variate generation, inversion method, importance sampling, Markov chain Monte Carlo PACS: 02.70.”
Survey of sampling-based methods for uncertainty and sensitivity analysis (2006, background): “If large sample sizes are required to provide appropriate coverage of low probability/high consequence subsets of values for x, then importance sampling may be a more effective sampling procedure than either random or Latin hypercube sampling [126–134].”
Integral approximation by kernel smoothing (2014, result): “For a comprehensive comparison between both approach, we refer to [8].”