The third edition of Testing Statistical Hypotheses updates and expands upon the classic graduate text, emphasizing optimality theory for hypothesis testing and confidence sets. The principal additions include a rigorous treatment of large sample optimality, together with the requisite tools. In addition, an introduction to the theory of resampling methods such as the bootstrap is developed. The sections on multiple testing and goodness of fit testing are expanded. The text is suitable for Ph.D. students in statistics and includes over 300 new problems out of a total of more than 760.

This state-of-the-art account unifies material developed in journal articles over the last 35 years, with two central thrusts: It describes a broad class of system models that the authors call 'stochastic processing networks' (SPNs), which include queueing networks and bandwidth sharing networks as prominent special cases; and in that context it explains and illustrates a method for stability analysis based on fluid models. The central mathematical result is a theorem that can be paraphrased as follows: If the fluid model derived from an SPN is stable, then the SPN itself is stable. Two topics discussed in detail are (a) the derivation of fluid models by means of fluid limit analysis, and (b) stability analysis for fluid models using Lyapunov functions. With regard to applications, there are chapters devoted to max-weight and back-pressure control, proportionally fair resource allocation, data center operations, and flow management in packet networks. Geared toward researchers and graduate students in engineering and applied mathematics, especially in electrical engineering and computer science, this compact text gives readers full command of the methods.

Stochastic Modeling for Medical Image Analysis provides a brief introduction to medical imaging, stochastic modeling, and model-guided image analysis. Today, image-guided computer-assisted diagnostics (CAD) faces two basic challenging problems. The first is the computationally feasible and accurate modeling of images from different modalities to obtain clinically useful information. The second is the accurate and fast inferring of meaningful and clinically valid CAD decisions and/or predictions on the basis of model-guided image analysis. To help address this, this book details original stochastic appearance and shape models with computationally feasible and efficient learning techniques for improving the performance of object detection, segmentation, alignment, and analysis in a number of important CAD applications. The book demonstrates accurate descriptions of visual appearances and shapes of the goal objects and their background to help solve a number of important and challenging CAD problems. The models focus on the first-order marginals of pixel/voxel-wise signals and second- or higher-order Markov-Gibbs random fields of these signals and/or labels of regions supporting the goal objects in the lattice. This valuable resource presents the latest state of the art in stochastic modeling for medical image analysis while incorporating fully tested experimental results throughout.

Providing a novel approach to sparse stochastic processes, this comprehensive book presents the theory of stochastic processes that are ruled by stochastic differential equations, and that admit a parsimonious representation in a matched wavelet-like basis. Two key themes are the statistical property of infinite divisibility, which leads to two distinct types of behaviour - Gaussian and sparse - and the structural link between linear stochastic processes and spline functions, which is exploited to simplify the mathematical analysis. The core of the book is devoted to investigating sparse processes, including a complete description of their transform-domain statistics. The final part develops practical signal-processing algorithms that are based on these models, with special emphasis on biomedical image reconstruction. This is an ideal reference for graduate students and researchers with an interest in signal/image processing, compressed sensing, approximation theory, machine learning, or statistics.

An introduction to general theories of stochastic processes and modern martingale theory. The volume focuses on consistency, stability and contractivity under geometric invariance in numerical analysis, and discusses problems related to implementation, simulation, variable step size algorithms, and random number generation.

Method of Variation of Parameters for Dynamic Systems presents a systematic and unified theory of the development of the theory of the method of variation of parameters, its unification with Lyapunov's method and typical applications of these methods. No other attempt has been made to bring all the available literature into one volume. This book is a clear exposition of this important topic in control theory, which is not covered by any other text. Such an exposition finally enables the comparison and contrast of the theory and the applications, thus facilitating further development in this fascinating field.

Explore a Kinetic Approach to the Description of Nucleation - An Alternative to the Classical Nucleation Theory Kinetic Theory of Nucleation presents an alternative to the classical theory of nucleation in gases and liquids-the kinetic nucleation theory of Ruckenstein-Narsimhan-Nowakowski (RNNT). RNNT uses the kinetic theory of fluids to calculate the rate of evaporation of molecules from clusters, and unlike the classical nucleation theory (CNT), does not require macroscopic thermodynamics or the detailed balance principle. The book compares the rates of evaporation of molecules from-and condensation on-the surface of a nucleus of a new phase, and explains how this alternate approach can provide much higher nucleation rates than the CNT. It applies RNNT to various case studies that include the liquid-to-solid and vapor-to-liquid phase transitions, binary nucleation, heterogeneous nucleation, nucleation on soluble particles and protein folding. It also describes the system, introduces the basic equations of the kinetic theory, and defines a new model for the nucleation mechanism of protein folding. Adaptable to coursework as well as self-study, this insightful book: Uses a kinetic approach to calculate the rate of growth and decay of a cluster Includes description of vapor-to-liquid and liquid-to-solid nucleation Outlines the application of density-functional theory (DFT) methods to nucleation Proposes the combination of the new kinetic theory of nucleation with the DFT methods Illustrates the new theory with numerical calculations Describes the model for the nucleation mechanism of protein folding, and more A comprehensive guide dedicated to the kinetic theory of nucleation and cluster growth, Kinetic Theory of Nucleation emphasizes the basic concepts of the kinetic nucleation theory, incorporates findings developed from years of research and experience, and is written by highly-regarded experts.

This volume represents the proceedings of the Ninth Annual MaxEnt Workshop, held at Dartmouth College in Hanover, New Hampshire, on August 14-18, 1989. These annual meetings are devoted to the theory and practice of Bayesian Probability and the Maximum Entropy Formalism. The fields of application exemplified at MaxEnt '89 are as diverse as the foundations of probability theory and atmospheric carbon variations, the 1987 Supernova and fundamental quantum mechanics. Subjects include sea floor drug absorption in man, pressures, neutron scattering, plasma equilibrium, nuclear magnetic resonance, radar and astrophysical image reconstruction, mass spectrometry, generalized parameter estimation, delay estimation, pattern recognition, heave responses in underwater sound and many others. The first ten papers are on probability theory, and are grouped together beginning with the most abstract followed by those on applications. The tenth paper involves both Bayesian and MaxEnt methods and serves as a bridge to the remaining papers which are devoted to Maximum Entropy theory and practice. Once again, an attempt has been made to start with the more theoretical papers and to follow them with more and more practical applications. Papers number 29, 30 and 31, by Kesaven, Seth and Kapur, represent a somewhat different, perhaps even "unorthodox" viewpoint, and are included here even though the editor and, indeed many in the audience at Dartmouth, disagreed with their content. I feel that scientific disagreements are essential in any developing field, and often lead to a deeper understanding.

This book describes how model selection and statistical inference can be founded on the shortest code length for the observed data, called the stochastic complexity. This generalization of the algorithmic complexity not only offers an objective view of statistics, where no prejudiced assumptions of 'true' data generating distributions are needed, but it also in one stroke leads to calculable expressions in a range of situations of practical interest and links very closely with mainstream statistical theory. The search for the smallest stochastic complexity extends the classical maximum likelihood technique to a new global one, in which models can be compared regardless of their numbers of parameters. The result is a natural and far reaching extension of the traditional theory of estimation, where the Fisher information is replaced by the stochastic complexity and the Cramer-Rao inequality by an extension of the Shannon-Kullback inequality. Ideas are illustrated with applications from parametric and non-parametric regression, density and spectrum estimation, time series, hypothesis testing, contingency tables, and data compression.