On the Error Rate of Conditional Quasi--Monte Carlo for Discontinuous Functions

Error in Monte Carlo, quasi-error in Quasi-Monte Carlo

While the Quasi-Monte Carlo method of numerical integration achieves smaller integration error than standard Monte Carlo, its use in particle physics phenomenology has been hindered by the abscence of a reliable way to estimate that error. The standard Monte Carlo error estimator relies on the assumption that the points are generated independently of each other and, therefore, fails to account ...

Evaluating the Quasi-monte Carlo Method for Discontinuous Integrands

The Monte Carlo method is an important numerical simulation tool in many applied fields such as economics, finance, statistical physics, and optimization. One of the most useful aspects of this method is in numerical integration of higher dimensions. For integrals of higher dimensions, the common numerical methods such as Simpson’s method, fail because the total number of grid points needed to ...

Error trends in Quasi-Monte Carlo integration

Several test functions, whose variation could be calculated, were integrated with up tp 10 trials using different low-discrepancy sequences in dimensions 3, 6, 12, and 24. The integration errors divided by the variation of the functions were compared with exact and asymptotic discrepancies. These errors follow an approximate power law, whose constant is essentially given by the variance of the ...

On Monte Carlo and Quasi-Monte Carlo for Matrix Computations

Monte 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...