Antithetic variates in higher dimensions
| Autor: | Rollin, Sebastian del Baño, Lázaro-Camí, Joan-Andreu |
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| Rok vydání: | 2009 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | We introduce the concept of multidimensional antithetic as the absolute minimum of the covariance defined on the orthogonal group by $A\mapsto Cov(f(\xi),f(A\xi))$ where $\xi$ is a standard $N$-dimensional normal random variable and $f:\mathbb{R}^{N}\to\mathbb{R}$ is an almost everywhere differentiable function. The antithetic matrix is designed to optimise the calculation of $E[f(\xi)]$ in a Monte Carlo simulation. We present an iterative annealing algorithm that dynamically incorporates the estimation of the antithetic matrix within the Monte Carlo calculation. Comment: 18 pages. Some errors were corrected |
| Databáze: | arXiv |
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