Monte Carlo perturbation analysis

This paper deals with two methods allowing for the calculation of small parameter variations. One is based on correlation techniques and the other deals with differential operator sampling. In the first part of the paper the author describes the theoretical basis of the two methods. Terminology and definitions are closed in the second part. In Chapters 3 and 4 correlation, multiple correlation and differential operator sampling is applied to the simple Monte Carlo integration algorithm. Chapter 5 deals in its first part with correlation techniques applied to linear matrix equations describing a random walk problem. The second part illustrates how gradients and higher-order derivatives can be determined for the same type of equations. In chapter 6 two examples of the use of derivatives are discussed. One rather unusual algorithm explores a new zero-variance scheme for solving linear systems describing Markov chain processes. The other example deals with the estimation of the variance of the target quantities as a function of the uncertainty of the system parameters (e.g. transition probabilities) and the Monte Carlo estimates. In the last chapter Monte Carlo perturbation analysis in eigenvalue problems are discussed. Among the different approaches interest is focussed on the fission matrix approach which appears to be particularly suited for performing low-variance perturbation estimates of the multiplication factor as well as all other target quantities of interest in a self-multiplying system. A list of examples dealing with 3-D benchmarks concludes this part. All the schemes discussed in Chapters 8 and 9 were realized in the Monte Carlo code KENEUR developed out of KENO-IV. (author)