Bücher der Reihe Monographs on Statistics and Applied Probability

The theory of risk already has its traditions. Further, non-life insurance, to which risk theory has, in fact, its most rewarding applications, was mainly outside the field of interest of the risk theorists.

Time-series analysis is an area of statistics which is of particular interest at the present time. Throughout the book, references are usually given to recent readily accessible books and journals rather than to the original attributive references.

The problem of outliers is one of the oldest in statistics, and during the last century and a half interest in it has waxed and waned several times. Currently it is once again an active research area after some years of relative neglect, and recent work has solved a number of old problems in outlier theory, and identified new ones.

Prior to the computer it was essential that any design had a straightforward method of analysis, which meant that the mathematical and combinatorial properties of the designs were of primary importance.

Latent variable models are used in many areas of the social and behavioural sciences, and the increasing availability of computer packages for fitting such models is likely to increase their popularity.

The type of system we are interested in is a discrete-time or sampled-data system where the relation between input and output is (at least approximately) linear and where additive random dis turbances are also present, so that the behaviour of the system must be investigated by statistical methods.

Population genetics is the mathematical investigation of the changes in the genetic structure of populations brought about by selection, mutation, inbreeding, migration, and other phenomena, together with those random changes deriving from chance events.

Finite mixture distributions arise in a variety of applications ranging from the length distribution of fish to the content of DNA in the nuclei of liver cells. 1 Introduction This monograph is concerned with statistical distributions which can be expressed as superpositions of (usually simpler) component distributions.

This monograph surveys the present state of Monte Carlo methods. For the sake of completeness, we cast a very brief glance in Chapter 4 at the direct simulation used in industrial and operational research, where the very simplest Monte Carlo techniques are usually sufficient.

Each element is a member of one and only one class, and we shall mainly be concerned with populations with a large number of classes.

Our purpose in writing this monograph is to give a comprehensive treatment of the subject. We define bandit problems and give the necessary foundations in Chapter 2. We give proofs unless they are very easy or the result is not used in the sequel. All results given have been incorporated into our style and notation.