ABSTRACT
This chapter begins with the integration rules which are most familiar, namely, weighted sums of function values evaluated on an equally-spaced grid of points. These methods have the generic name of Newton-Cotes rules. The chapter shows how to adapt these and other methods to cope with infinite or semi-infinite ranges of integration. It discusses some approaches both to multiple integration in general and to Bayesian analysis in particular. The chapter also discusses methods for function evaluation and approximation, with particular emphasis on computing cumulative distribution functions, their complements, and their inverses. The inverse transformation must be easily computed for the computation to be possible, and the resulting integrand must be amenable to numerical integration using simple rules. Extended rules are usually formed by using exactly the same basic rule on each subinterval. In dealing with distribution functions, their complements, and percent points, polynomial approximation is generally not helpful except for the very limited purpose of interpolating tabulated values.
