Chapter 5

Monte Carlo Integration and Variance Reduction

5.1 Introduction

Monte Carlo integration is a statistical method based on random sampling. Monte Carlo methods were developed in the late 1940’s after World War II, but the idea of random sampling was not new. As early as 1777, Comte de Buffon used a random experiment to empirically check his probability calculation for the famous Buffon’s needle experiment. Another well known example is that W. S. Gossett used random sampling to study the distribution of what are now called “Student t” statistics, publishing uder the alias Student in 1908 [256]. The development of ENIAC, the first electronic computer, completed in 1946 at the University of Pennsylvania, and the seminal article by Metropolis ...

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