A Practical Approach to the Error Estimation of Quasi-Monte Carlo Integrations
نویسندگان
چکیده
There have been few studies on practical error estimation methods of quasi-Monte Carlo integrations. Recently, some theoretical works were developed by Owen to analyze the quasi-Monte Carlo integration error. However his method given by those works is complicated to be implemented and needs huge computational e orts, so it would be of some interest to investigate into a simple error estimation method. In this paper, we will use a simple method, and give some theoretical considerations on the errors given by these two methods. Numerical experiments are also reported.
منابع مشابه
Estimation of penetration rate of tunnel boring machines using Monte-Carlo simulation method
One of the most important parameters used for determining the performance of tunnel boring machines (TBMs) is their penetration rate. The parameters affecting the penetration rate can be divided in two categories. The first category is the controllable parameters such as the TBM technical characteristics, and type and geometry of the tunnel, and the second one is the uncontrollable parameters s...
متن کاملQuasi- versus Pseudo-random Generators: Discrepancy, Complexity and Integration-error Based Comparison
Presented here are several quasiand pseudo-random number generators along with their numerical discrepancy, i.e., nonuniformity measure and computational/ time complexity. These generators have been compared and ranked based on discrepancy, complexity, and error in multiple Monte Carlo integrations. We believe that such a statistical comparison/ranking will be useful for solving real world prob...
متن کاملEvaluating Quasi-Monte Carlo (QMC) algorithms in blocks decomposition of de-trended
The length of equal minimal and maximal blocks has eected on logarithm-scale logarithm against sequential function on variance and bias of de-trended uctuation analysis, by using Quasi Monte Carlo(QMC) simulation and Cholesky decompositions, minimal block couple and maximal are founded which are minimum the summation of mean error square in Horest power.
متن کاملRandomization of Quasi-Monte Carlo Methods for Error Estimation: Survey and Normal Approximation
Monte Carlo and quasi Monte Carlo methods are simulation techniques that have been de signed to e ciently estimate integrals for instance Quasi Monte Carlo asymptotically outperforms Monte Carlo but the error can hardly be estimated We propose here to recall how hybrid Monte Carlo Quasi Monte Carlo have been developed to easily get error estimations with a special em phasis on the so called ran...
متن کاملMonte Carlo Extension of Quasi-monte Carlo
This paper surveys recent research on using Monte Carlo techniques to improve quasi-Monte Carlo techniques. Randomized quasi-Monte Carlo methods provide a basis for error estimation. They have, in the special case of scrambled nets, also been observed to improve accuracy. Finally through Latin supercube sampling it is possible to use Monte Carlo methods to extend quasi-Monte Carlo methods to hi...
متن کامل