Mean-value identities as an opportunity for Monte Carlo error reduction

Mean-value identities as an opportunity for Monte Carlo error reduction.

In the Monte Carlo simulation of both lattice field theories and of models of statistical mechanics, identities verified by exact mean values, such as Schwinger-Dyson equations, Guerra relations, Callen identities, etc., provide well-known and sensitive tests of thermalization bias as well as checks of pseudo-random-number generators. We point out that they can be further exploited as control v...

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 ...

On variance reduction of mean-CVaR Monte Carlo estimators

An Error Metric for Monte Carlo Ray Tracing

A method has been developed for controlling the error in Monte Carlo calculations for realistic image synthesis. An error metric has been created that can be used to control the variance in the nal picture by choosing both the number of rays to be cast into the image plane and the number of rays to be spawned at each bounce in the environment. The method provides speci c guidance in how to appl...

An error formula for Monte Carlo based portfolio optimization

One–period utility based portfolio optimization is a classic method in financial economics [13]. The theory is extremely well developed, and extends in many directions, for example to dynamic portfolio optimization in continuous time [12]. Nonetheless, the solutions to these problems, characterized theoretically, often remain dismayingly difficult to compute in practise. Very often, finance pra...