
Density estimation by Randomized QuasiMonte Carlo
We consider the problem of estimating the density of a random variable X...
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Sensitivity estimation of conditional value at risk using randomized quasiMonte Carlo
Conditional value at risk (CVaR) is a popular measure for quantifying po...
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Creative Telescoping on Multiple Sums
We discuss the strategies and difficulties of determining a recurrence w...
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New Tricks for Estimating Gradients of Expectations
We derive a family of Monte Carlo estimators for gradients of expectatio...
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Quantifying uncertainties on excursion sets under a Gaussian random field prior
We focus on the problem of estimating and quantifying uncertainties on t...
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Cooperation on the monte carlo rule Prison's dilemma game on the grid
In this paper, we investigate the prison's dilemma game with monte carlo...
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Fully probabilistic quasar continua predictions near Lymanα with conditional neural spline flows
Measurement of the red damping wing of neutral hydrogen in quasar spectr...
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Monte Carlo and QuasiMonte Carlo Density Estimation via Conditioning
Estimating the unknown density from which a given independent sample originates is more difficult than estimating the mean, in the sense that for the best popular density estimators, the mean integrated square error converges slower than at the canonical rate of O(1/n). When the sample is generated from a simulation model and we have control over how this is done, we can do better. We study an approach in which conditional Monte Carlo permits one to obtain a smooth estimator of the cumulative distribution function, whose sample derivative is an unbiased estimator of the density at any point, and therefore converges at a faster rate than the usual density estimators, under mild conditions. By combining this with randomized quasiMonte Carlo to generate the sample, we can achieve an even faster rate.
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