This book grew from a one-semester course offered for many years to a mixed audience of graduate and undergraduate students who have not had the luxury of taking a course in measure theory. The core of the book covers the basic topics of independence, conditioning, martingales, convergence in distribution, and Fourier transforms. In addition there are numerous sections treating topics traditionally thought of as more advanced, such as coupling and the KMT strong approximation, option pricing via the equivalent martingale measure, and the isoperimetric inequality for Gaussian processes. The...

This exposition of the Bayesian approach to statistics at a level suitable for final year undergraduate and Masters students is unique in presenting its subject with a practical flavor and an emphasis on mainstream statistics. It shows how to infer scientific, medical, and social conclusions from numerical data. The authors draw on many years of experience with practical and research programs and describe many new statistical methods, not available elsewhere. It will be essential reading for all statisticians, statistics students, and related interdisciplinary researchers.

The analysis of time series data is essential to many areas of science, engineering, finance and economics. This introduction to wavelet analysis "from the ground level and up," and to wavelet-based statistical analysis of time series focuses on practical discrete time techniques, with detailed descriptions of the theory and algorithms needed to understand and implement the discrete wavelet transforms. Numerous examples illustrate the techniques on actual time series. The many embedded exercises--with complete solutions provided in the Appendix--allow readers to use the book for self-guided...

Science abounds with problems where the data are noisy and the answer is not a straight line. Semiparametric regression analysis helps make sense of such data in application areas that include engineering, finance, medicine and public health. The book is geared towards researchers and professionals with little background in regression as well as statistically oriented scientists (biostatisticians, econometricians, quantitative social scientists, and epidemiologists) with knowledge of regression and the desire to begin using more flexible semiparametric models. Author resource page: http:...

This introduction to ways of modelling a wide variety of phenomena that occur over time is accessible to anyone with a basic knowledge of statistical ideas. J.K. Lindsey concentrates on tractable models involving simple processes for which explicit probability models, hence likelihood functions, can be specified. (These models are the most useful in statistical applications modelling empirical data.) Examples are drawn from physical, biological and social sciences, to show how the book's underlying ideas can be applied, and data sets and R code are supplied for them. Author resource page:...

This detailed introduction to distribution theory is designed as a text for the probability portion of the first year statistical theory sequence for Master's and PhD students in statistics, biostatistics, and econometrics. The text uses no measure theory, requiring only a background in calculus and linear algebra. Topics range from the basic distribution and density functions, expectation, conditioning, characteristic functions, cumulants, convergence in distribution and the central limit theorem to more advanced concepts such as exchangeability, models with a group structure, asymptotic...

Modern statistical methods use complex, sophisticated 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 language how such approximate probability computations are made, taking readers from the very beginnings to current applications. The core material is presented in chapters 1-6 at an elementary mathematical level. Chapters 7-9 then give a highly readable account of higher-order asymptotic inference. Later chapters address areas where saddlepoint methods have had substantial...