9. Variance Reduction

  1. Dirk P. Kroese1,
  2. Thomas Taimre1 and
  3. Zdravko I. Botev2

Published Online: 20 SEP 2011

DOI: 10.1002/9781118014967.ch9

Handbook of Monte Carlo Methods

Handbook of Monte Carlo Methods

How to Cite

Kroese, D. P., Taimre, T. and Botev, Z. I. (2011) Variance Reduction, in Handbook of Monte Carlo Methods, John Wiley & Sons, Inc., Hoboken, NJ, USA. doi: 10.1002/9781118014967.ch9

Author Information

  1. 1

    University of Queensland

  2. 2

    Université de Montréal

Publication History

  1. Published Online: 20 SEP 2011
  2. Published Print: 28 FEB 2011

ISBN Information

Print ISBN: 9780470177938

Online ISBN: 9781118014967



  • antithetic random variables;
  • control variables;
  • latin hypercube sampling;
  • quasi Monte Carlo;
  • stratified sampling;
  • variance reduction


The estimation of performance measures in Monte Carlo simulation can be made more efficient by utilizing known information about the simulation model. The more that is known about the behavior of the system, the greater the amount of variance reduction that can be achieved. The main variance reduction techniques discussed in this chapter are antithetic random variables, control variables, conditional Monte Carlo, stratification, latin hypercube sampling, importance sampling, and quasi Monte Carlo. Each of the variance reduction methods is illustrated using the following estimation problem concerning a bridge network. The problem is sufficiently complicated to warrant Monte Carlo simulation, while easy enough to implement, so that the workings of each technique can be concisely illustrated.

Controlled Vocabulary Terms

Latin hypercube sampling; Monte Carlo methods; random variables; stratified sampling; variance reduction