Randomization and Monte Carlo Method

This book aims to illustrate the value of modern computer intensive methods for a wide range of statistical problems. There is coverage of randomization methods of inference that were first proposed by R.A. Fisher in 1935, but are only now becoming practical because of the ready availability of computer power. Applications to analysis of variance and regression multivariate analysis are covered. Monte Carlo methods, jacknifing and bootstrapping are also discussed as being alternatives to randomization in some circumstances. The examples used have been chosen to attract interest and include the controversial topics of whether there is periodicity in fossil extinction records and whether there is evidence for a relationship between species co-occurences on islands. The first chapter introduces the ideas of randomization methods through some examples and the second introduces Monte Carlo tests and also the computer intensive techniques of jacknifing and bootstrapping since these are sometimes used as alternatives to randomization. The following chapters discuss some general theoretical matters concerning randomization and Monte Carlo methods and the analysis of various standard types of data. The final chapter gives some examples of non-standard situations where computer intensive methods seem to provide the best method for statistical analysis. In all chapters the emphasis is on applications in biology.