Among the various tools that have been developed for use in statistics and probability over the years, perhaps the least understood and most remarkable tool is the saddlepoint approximation. It is remarkable because it usually provides probability approximations whose accuracy is much greater than the current supporting theory would suggest. It is least understood because of the difficulty of the subject itself and the difficulty of the research papers and books that have been written about it. Indeed this lack of accessibility has placed its understanding out of the reach of many researchers in both statistics and its related subjects.

The primary aim of this book is to provide an accessible account of the theory and application of saddlepoint methods that can be understood by the widest possible audience. To do this, the book has been written at graduated levels of difficulty with the first six chapters forming the easiest part and the core of the subject. These chapters use little mathematics beyond the difficulty of advanced calculus (no complex variables) and should provide relatively easy reading to first year graduate students in statistics, engineering, and other quantitative fields. These chapters would also be accessible to senior-level undergraduate mathematics and advanced engineering majors. With the accessibility issue in mind, the first six chapters have been purposefully written to address the issue and should assure that the widest audience is able to read and learn the subject.

The presentation throughout the book takes the point of view of users of saddlepoint approximations; theoretical aspects of the methods are also covered but are given less emphasis than they are in journal articles.