Statistical methods for sequential hypothesis testing and changepoint detection have applications across many fields, including quality control, biomedical engineering, communication networks, econometrics, image processing, security, etc. This book presents an overview of methodology in these related areas, providing a synthesis of research from the last few decades. The methods are illustrated through real data examples, and software is referenced where possible. The emphasis is on providing all the theoretical details in a unified framework, with pointers to new research directions.
Sequential Analysis: Hypothesis Testing and Changepoint Detection systematically develops the theory of sequential hypothesis testing and quickest changepoint detection. It also describes important applications in which theoretical results can be used efficiently. The book reviews recent accomplishments in hypothesis testing and changepoint detecti
Sequential Analysis: Hypothesis Testing and Changepoint Detection systematically develops the theory of sequential hypothesis testing and quickest changepoint detection. It also describes important applications in which theoretical results can be used efficiently. The book reviews recent accomplishments in hypothesis testing and changepoint detection both in decision-theoretic (Bayesian) and non-decision-theoretic (non-Bayesian) contexts. The authors not only emphasize traditional binary hypotheses but also substantially more difficult multiple decision problems. They address scenarios with simple hypotheses and more realistic cases of two and finitely many composite hypotheses. The book primarily focuses on practical discrete-time models, with certain continuous-time models also examined when general results can be obtained very similarly in both cases. It treats both conventional i.i.d. and general non-i.i.d. stochastic models in detail, including Markov, hidden Markov, state-space, regression, and autoregression models. Rigorous proofs are given for the most important results. Written by leading authorities in the field, this book covers the theoretical developments and applications of sequential hypothesis testing and sequential quickest changepoint detection in a wide range of engineering and environmental domains. It explains how the theoretical aspects influence the hypothesis testing and changepoint detection problems as well as the design of algorithms.
Statistical methods for sequential hypothesis testing and changepoint detection have applications across many fields, including quality control, biomedical engineering, communication networks, econometrics, image processing, security, etc. This book presents an overview of methodology in these related areas, providing a synthesis of research from the last few decades. The methods are illustrated through real data examples, and software is referenced where possible. The emphasis is on providing all the theoretical details in a unified framework, with pointers to new research directions.
Set during the Pugachov rebellion against Catherine the Great, The Captain's Daughter was Pushkin's only completed novel and remains one of his most popular works. The inexperienced and impetuous young nobleman Pyotr Grinyev is sent on military service to a remote fortress, where he falls in love with Masha, Captain Mironov's daughter - but then the ruthless Cossack Pugachov lays siege to the stronghold, setting in motion a tragic train of events.This volume also contains another work by Pushkin on the same theme, A History of Pugachov, which presents an impartial, meticulously researched history of the revolt, but was regarded in aristocratic circles as subversive on its publication. Together, these two works provide a fascinating insight into the character of the peasant who tried to overthrow an empress, written with the clarity and insight of Russia's greatest poet.
Personalized Computational Hemodynamics: Models, Methods, and Applications for Vascular Surgery and Antitumor Therapy offers practices and advances surrounding the multiscale modeling of hemodynamics and their personalization with conventional clinical data. Focusing on three physiological disciplines, readers will learn how to derive a suitable mathematical model and personalize its parameters to account for pathologies and diseases. Written by leading experts, this book mirrors the top trends in mathematical modeling with clinical applications. In addition, the book features the major results of the "Research group in simulation of blood flow and vascular pathologies" at the Institute of Numerical Mathematics of the Russian Academy of Sciences. Two important features distinguish this book from other monographs on numerical methods for biomedical applications. First, the variety of medical disciplines targeted by the mathematical modeling and computer simulations, including cardiology, vascular neurology and oncology. Second, for all mathematical models, the authors consider extensions and parameter tuning that account for vascular pathologies. Examines a variety of medical disciplines targeted by mathematical modeling and computer simulation Discusses how the results of numerical simulations are used to support clinical decision-making Covers hemodynamics relating to various subject areas, including vascular surgery and oncological tumor treatments
If the sheer diversity of recent hits from Twelve Years a Slave and Moonlight to Get Out, Black Panther, and BlackkKlansman tells us anything, it might be that there's no such thing as "black film" per se. This book is especially timely, then, in expanding our idea of what black films are and, going back to the 1960s, showing us new and interesting ways to understand them. When critics and scholars write about films from the Blaxploitation movement—such as Cotton Comes to Harlem, Shaft, Superfly, and Cleopatra Jones—they emphasize their importance as films made for black audiences. Consequently, Lisa Doris Alexander points out, a film like the highly popular, Oscar-nominated Blazing Saddles—costarring and co-written by Richard Pryor—is generally left out of the discussion because it doesn't fit the profile of what a black film of the period should be. This is the kind of categorical thinking that Alexander seeks to broaden, looking at films from the 60s to the present day in the context of their time. Applying insights from black feminist thought and critical race theory to one film per decade, she analyzes what each can tell us about the status of black people and race relations in the United States at the time of its release. By teasing out the importance of certain films excluded from the black film canon, Alexander hopes to expand that canon to include films typically relegated to the category of popular entertainment—and to show how these offer more nuanced representations of black characters even as they confront, negate, or parody the controlling images that have defined black filmic characters for decades.
Volume I, entitled Russian Mathematics Education: History and World Significance, consists of several chapters written by distinguished authorities from Russia, the United States and other nations. It Examines the hostory of mathematics education in Russia and its relevance to mathematics education throughout the world. The second volume, entitled Russian Mathematics education is highly respected for its achievements and was once very influential internationally, it has never been explored in depth. This publication does just that. --Book Jacket.
This three-part book provides a comprehensive and systematic introduction to these challenging topics such as model calibration, parameter estimation, reliability assessment, and data collection design. Part 1 covers the classical inverse problem for parameter estimation in both deterministic and statistical frameworks, Part 2 is dedicated to system identification, hyperparameter estimation, and model dimension reduction, and Part 3 considers how to collect data and construct reliable models for prediction and decision-making. For the first time, topics such as multiscale inversion, stochastic field parameterization, level set method, machine learning, global sensitivity analysis, data assimilation, model uncertainty quantification, robust design, and goal-oriented modeling, are systematically described and summarized in a single book from the perspective of model inversion, and elucidated with numerical examples from environmental and water resources modeling. Readers of this book will not only learn basic concepts and methods for simple parameter estimation, but also get familiar with advanced methods for modeling complex systems. Algorithms for mathematical tools used in this book, such as numerical optimization, automatic differentiation, adaptive parameterization, hierarchical Bayesian, metamodeling, Markov chain Monte Carlo, are covered in details. This book can be used as a reference for graduate and upper level undergraduate students majoring in environmental engineering, hydrology, and geosciences. It also serves as an essential reference book for professionals such as petroleum engineers, mining engineers, chemists, mechanical engineers, biologists, biology and medical engineering, applied mathematicians, and others who perform mathematical modeling.
Semi-empirical Neural Network Modeling presents a new approach on how to quickly construct an accurate, multilayered neural network solution of differential equations. Current neural network methods have significant disadvantages, including a lengthy learning process and single-layered neural networks built on the finite element method (FEM). The strength of the new method presented in this book is the automatic inclusion of task parameters in the final solution formula, which eliminates the need for repeated problem-solving. This is especially important for constructing individual models with unique features. The book illustrates key concepts through a large number of specific problems, both hypothetical models and practical interest. Offers a new approach to neural networks using a unified simulation model at all stages of design and operation Illustrates this new approach with numerous concrete examples throughout the book Presents the methodology in separate and clearly-defined stages
This book is devoted primarily to the various kinds of resonant nonlinear in teractions of light with two-level (or, in many cases, multilevel) systems. The interactions can involve one-photon as well as multiphoton processes in which some combinations of frequencies of participating photons are close to tran sitions of atoms or molecules (e.g., we consider stimulated Raman scattering (SRS) as a resonant interaction). This approach involves a broad spectrum of problems. Discussion of some of the basic phenomena as well as the pertinent theory could be found, for instance, in such well-known books as the ones due to N. Bloembergen; S.A. Akhmanov and R.V. Khokhlov; L. Allen and J.H. Eberly, and to V.M. Fain and Ya.1. Khanin. The book "Quantum Electronics" by A. Yariv could serve as an introductory guide to the subject. Thus, some of the basic material in the present book will already be well known to the reader who is an expert in the field. There are, for instance, general density matrix equations; two-level model and basic effects associated with this model, such as saturation of one-photon absorption and Raby oscillations; some basic multiphoton processes such as two-photon absorption, SRS, etc.
In many parts of the world, groundwater resources are under increasing threat from growing demands, wasteful use, and contamination. To face the challenge, good planning and management practices are needed. A key to the management of groundwater is the ability to model the movement of fluids and contaminants in the subsurface. The purpose of this book is to construct conceptual and mathematical models that can provide the information required for making decisions associated with the management of groundwater resources, and the remediation of contaminated aquifers. The basic approach of this book is to accurately describe the underlying physics of groundwater flow and solute transport in heterogeneous porous media, starting at the microscopic level, and to rigorously derive their mathematical representation at the macroscopic levels. The well-posed, macroscopic mathematical models are formulated for saturated, single phase flow, as well as for unsaturated and multiphase flow, and for the transport of single and multiple chemical species. Numerical models are presented and computer codes are reviewed, as tools for solving the models. The problem of seawater intrusion into coastal aquifers is examined and modeled. The issues of uncertainty in model input data and output are addressed. The book concludes with a chapter on the management of groundwater resources. Although one of the main objectives of this book is to construct mathematical models, the amount of mathematics required is kept minimal.
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