Numerische Mathematik

, Volume 55, Issue 2, pp 137–157

A Monte Carlo method for high dimensional integration

  • Yosihiko Ogata

DOI: 10.1007/BF01406511

Cite this article as:
Ogata, Y. Numer. Math. (1989) 55: 137. doi:10.1007/BF01406511


A new method for the numerical integration of very high dimensional functions is introduced and implemented based on the Metropolis' Monte Carlo algorithm. The logarithm of the high dimensional integral is reduced to a 1-dimensional integration of a certain statistical function with respect to a scale parameter over the range of the unit interval. The improvement in accuracy is found to be substantial comparing to the conventional crude Monte Carlo integration. Several numerical demonstrations are made, and variability of the estimates are shown.

Subject Classifications

AMS(MOS): 65D30CR: G1.4

Copyright information

© Springer-Verlag 1989

Authors and Affiliations

  • Yosihiko Ogata
    • 1
  1. 1.The Institute of Statistical MathematicsTokyo 106Japan