Synopses & Reviews
How approximate probability calculations make complex models tractable; clear, simple explanations; real data examples.
Synopsis
Explains in simple language how saddlepoint approximations make computations of probabilities tractible for complex models. No previous background in the area is required as the book introduces the subject from the very beginning. Many real data examples show the methods at work. For statisticians, biostatisticians, electrical engineers, econometricians, and applied mathematicians.
Synopsis
Modern statistical methods use sophisticated and complex models that can lead to intractable computations. Saddlepoint approximations can be the answer. Written from the user's point of view, this book explains in clear, simple language how such approximate probability computations are made. No previous background in the area is required as the book introduces the subject from the very beginning. Many data examples from real applications show the methods at work and demonstrate their practical value. For statisticians, biostatisticians, electrical engineers, econometricians, and applied mathematicians.
Table of Contents
Preface; 1. Fundamental approximations; 2. Properties and derivatives; 3. Multivariate densities; 4. Conditional densities and distribution functions; 5. Exponential families and tilted distributions; 6. Further exponential family examples and theory; 7. Probability computation with p*; 8. Probabilities with r*-type approximations; 9. Nuisance parameters; 10. Sequential saddlepoint applications; 11. Applications to multivariate testing; 12. Ratios and roots of estimating equations; 13. First passage and time to event distributions; 14. Bootstrapping in the transform domain; 15. Bayesian applications; 16. Non-normal bases; References; Index.