Monte Carlo Sampling Techniques

To understand the mathematical basis of Monte Carlo calculations, to develop means of increasing the efficiency of such calculations, and to estimate the statistical uncertainty in the results obtained, it is necessary to have some understanding of statistics and probability theory. A brief description of the terminology that will be used in the remainder of this book is also necessary. The intent of this chapter is to introduce the mathematical concepts that underlie the Monte Carlo method and provide a basis for further development of selected topics. To obtain a broader and more rigorous development of the underlying mathematical concepts than is presented here the interested reader may consult any of a number of standard textbooks and references on statistics and probability.