Variance reduction for Monte Carlo methods by means of deterministic numerical computation
By Stefan Heinrich. 1995
A new variance reduction technique for the Monte Carlo solution of integral equations is introduced. It is based on separation of the main part. A neighboring equation with exactly known solution is constructed by the help of a deterministic Galerkin scheme. The variance of the method is analyzed, and an application to the radiosity equation of computer graphics, together with numerical test results is given.
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
- Chris J. Oates
- Mark A. Girolami
- Jon Cockayne
- François‐Xavier Briol
- Qiang Liu
- Nicolas Chopin
- Jackson Gorham
- Paul Fearnhead
Citations in the corpus
- Control functionals for Monte Carlo integration (2014, methodology): “t-hoc scheme. 2.2 From control variates to control functionals 2.2.1 A class of control variates Our starting point is to trade o integration error and functional approximation error, as suggested by Heinrich (1995) and more recently by Bach (2015). Consider surrogate functions f~ of the form f~(x) ”
- Convergence rates for a class of estimators based on Stein’s method (2016, background): “on-independent sampling. Recall that a well-known trade-o between random sampling and deterministic approximation has been studied on several separate occasions by authors including Bakhvalov (1959); Heinrich (1995); Giles (2013); Oates and Girolami (2016). Our starting point is, instead, to establi”