This book explains how computer software is designed to perform the tasks required for sophisticated statistical analysis. For statisticians, it examines the nitty-gritty computational problems behind statistical methods. For mathematicians and computer scientists, it looks at the application of mathematical tools to statistical problems. The first half of the book offers a basic background in numerical analysis that emphasizes issues important to statisticians. The next several chapters cover a broad array of statistical tools, such as maximum likelihood and nonlinear regression. The author...

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 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...

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 self-contained book is a graduate-level introduction for mathematicians and for physicists interested in the mathematical foundations of the field, and can be used as a textbook for a two-semester course on mathematical statistical mechanics. It assumes only basic knowledge of classical physics and, on the mathematics side, a good working knowledge of graduate-level probability theory. The book starts with a concise introduction to statistical mechanics, proceeds to disordered lattice spin systems, and concludes with a presentation of the latest developments in the mathematical...

Aimed primarily at those outside of the field of statistics, this book not only provides an accessible introduction to measure theory, stochastic calculus, and stochastic processes, with particular emphasis on martingales and Brownian motion, but develops into an excellent user's guide to filtering. Including exercises for students, it will be a complete resource for engineers, signal processing researchers, or anyone with an interest in practical implementation of filtering techniques, in particular, the Kalman filter. Three separate chapters concentrate on applications arising in finance,...

Point-to-point vs hub-and-spoke. Questions of network design are real and involve many billions of dollars. Yet little is known about optimising design - nearly all work concerns optimising flow assuming a given design. This foundational book tackles optimisation of network structure itself, deriving comprehensible and realistic design principles. With fixed material cost rates, a natural class of models implies the optimality of direct source-destination connections, but considerations of variable load and environmental intrusion then enforce trunking in the optimal design, producing an...

Big data poses challenges that require both classical multivariate methods and contemporary techniques from machine learning and engineering. This modern text equips you for the new world integrating the old and the new, fusing theory and practice and bridging the gap to statistical learning. The theoretical framework includes formal statements that set out clearly the guaranteed safe operating zone for the methods and allow you to assess whether data is in the zone, or near enough. Extensive examples showcase the strengths and limitations of different methods with small classical data, data...

Many electronic and acoustic signals can be modeled as sums of sinusoids and noise. However, the amplitudes, phases and frequencies of the sinusoids are often unknown and must be estimated in order to characterize the periodicity or near-periodicity of a signal and consequently to identify its source. Quinn and Hannan present and analyze several practical techniques used for such estimation. The problem of tracking slow frequency changes of a very noisy sinusoid over time is also considered. Rigorous analyses are presented via asymptotic or large sample theory, together with physical insight....

The classical probability theory initiated by Kolmogorov and its quantum counterpart, pioneered by von Neumann, were created at about the same time in the 1930s, but development of the quantum theory has trailed far behind. Although highly appealing, the quantum theory has a steep learning curve, requiring tools from both probability and analysis and a facility for combining the two viewpoints. This book is a systematic, self-contained account of the core of quantum probability and quantum stochastic processes for graduate students and researchers. The only assumed background is knowledge of...