
QuasiMonte Carlo sampling for machinelearning partial differential equations
Solving partial differential equations in high dimensions by deep neural...
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Using Supervised Learning to Improve Monte Carlo Integral Estimation
Monte Carlo (MC) techniques are often used to estimate integrals of a mu...
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A randomized Halton algorithm in R
Randomized quasiMonte Carlo (RQMC) sampling can bring orders of magnitu...
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Why Simple Quadrature is just as good as Monte Carlo
We motive and calculate NewtonCotes quadrature integration variance and...
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On the Opportunities and Pitfalls of Nesting Monte Carlo Estimators
We present a formalization of nested Monte Carlo (NMC) estimation, where...
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Adaptive Monte Carlo Multiple Testing via MultiArmed Bandits
Monte Carlo (MC) permutation testing is considered the gold standard for...
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Noise contrastive estimation: asymptotics, comparison with MCMLE
A statistical model is said to be unnormalised when its likelihood func...
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On dropping the first Sobol' point
QuasiMonte Carlo (QMC) points are a substitute for plain Monte Carlo (MC) points that greatly improve integration accuracy under mild assumptions on the problem. Because QMC can give errors that are o(1/n) as n→∞, changing even one point can change the estimate by an amount much larger than the error would have been and worsen the convergence rate. As a result, certain practices that fit quite naturally and intuitively with MC points are very detrimental to QMC performance. These include thinning, burnin, and taking sample sizes such as powers of 10, other than the ones for which the QMC points were designed. This article looks at the effects of a common practice in which one skips the first point of a Sobol' sequence. The retained points ordinarily fail to be a digital net and when scrambling is applied, skipping over the first point can increase the numerical error by a factor proportional to √(n) where n is the number of function evaluations used.
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