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Still, in the examples studied by Morokoff and Caflisch, the quasi-Monte Carlo method did yield a more accurate result than the Monte Carlo method with the same number of points. Morokoff and Caflisch remark that the advantage of the quasi-Monte Carlo method is greater if the integrand is smooth, and the number of dimensions s of the integral ...
An example of distribution with 500 LDS points is given in Figure 2. Figure 2. 500 low discrepancy points. Numerous LDS have been created named after their inventors, for example: Halton, Hammersley, Sobol, Faure, Niederreiter. Generally, the quasi-Monte Carlo (QMC) method is defined by
Markov chain quasi-Monte Carlo methods [18] [19] such as the Array–RQMC method combine randomized quasi–Monte Carlo and Markov chain simulation by simulating chains simultaneously in a way that better approximates the true distribution of the chain than with ordinary MCMC. [20]
A Monte Carlo simulation shows a large number and variety of possible outcomes, including the least likely as well … Continue reading → The post Understanding How the Monte Carlo Method Works ...
Monte Carlo methods are often used in physical and mathematical problems and are most useful when it is difficult or impossible to use other approaches. Monte Carlo methods are mainly used in three problem classes: [2] optimization, numerical integration, and generating draws from a probability distribution.
The Monte Carlo approach involves generating a sequence of randomly distributed points inside the unit hypercube (strictly speaking these will be pseudorandom). In practice, it is common to substitute random sequences with low-discrepancy sequences to improve the efficiency of the estimators. This is then known as the quasi-Monte Carlo method.