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Guaranteed Conservative Fixed Width Confidence Intervals via Monte Carlo Sampling
| Content Provider | Semantic Scholar |
|---|---|
| Author | Hickernell, Fred J. Jiang, Lan Liu, Yuewei Owen, Art B. |
| Copyright Year | 2013 |
| Abstract | Monte Carlo methods are used to approximate the means, μ, of random variables Y, whose distributions are not known explicitly. The key idea is that the average of a random sample, Y 1, …, Y n , tends to μ as n tends to infinity. This article explores how one can reliably construct a confidence interval for μ with a prescribed half-width (or error tolerance) \(\varepsilon\). Our proposed two-stage algorithm assumes that the kurtosis of Y does not exceed some user-specified bound. An initial independent and identically distributed (IID) sample is used to confidently estimate the variance of Y. A Berry-Esseen inequality then makes it possible to determine the size of the IID sample required to construct the desired confidence interval for μ. We discuss the important case where \(Y = f(\boldsymbol{X})\) and \(\boldsymbol{X}\) is a random d-vector with probability density function ρ. In this case μ can be interpreted as the integral \(\int _{{\mathbb{R}}^{d}}f(\boldsymbol{x})\rho (\boldsymbol{x})\,\,\mathrm{d}\boldsymbol{x}\), and the Monte Carlo method becomes a method for multidimensional cubature. |
| Starting Page | 105 |
| Ending Page | 128 |
| Page Count | 24 |
| File Format | PDF HTM / HTML |
| DOI | 10.1007/978-3-642-41095-6_5 |
| Volume Number | 65 |
| Alternate Webpage(s) | http://statweb.stanford.edu/~owen/reports/AdaptiveMCProbErrAnalj.pdf |
| Alternate Webpage(s) | http://www-stat.stanford.edu/~owen//reports/AdaptiveMCProbErrAnalj.pdf |
| Alternate Webpage(s) | https://page-one.springer.com/pdf/preview/10.1007/978-3-642-41095-6_5 |
| Alternate Webpage(s) | http://www-stat.stanford.edu/~owen/reports/AdaptiveMCProbErrAnalj.pdf |
| Alternate Webpage(s) | https://arxiv.org/pdf/1208.4318v3.pdf |
| Alternate Webpage(s) | http://www-stat.stanford.edu/reports/pub-pre-move/owen/reports/AdaptiveMCProbErrAnalj.pdf |
| Alternate Webpage(s) | http://arxiv.org/pdf/1208.4318.pdf |
| Alternate Webpage(s) | http://www.math.iit.edu/~Meshfree-methods-seminar/presentations/paper_guaranteedMC.pdf |
| Alternate Webpage(s) | https://doi.org/10.1007/978-3-642-41095-6_5 |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
