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This book expands on the classical statistical multivariate analysis theory by focusing on bilinear regression models, a class of models comprising the classical growth curve model and its extensions. In order to analyze the bilinear regression models in an interpretable way, concepts from linear models are extended and applied to tensor spaces. Further, the book considers decompositions of tensor products into natural subspaces, and addresses maximum likelihood estimation, residual analysis, influential observation analysis and testing hypotheses, where properties of estimators such as moments, asymptotic distributions or approximations of distributions are also studied. Throughout the text, examples and several analyzed data sets illustrate the different approaches, and fresh insights into classical multivariate analysis are provided. This monograph is of interest to researchers and Ph.D. students in mathematical statistics, signal processing and other fields where statistical multivariate analysis is utilized. It can also be used as a text for second graduate-level courses on multivariate analysis.
Aimed primarily at graduate students and researchers, this text is a comprehensive course in modern probability theory and its measure-theoretical foundations. It covers a wide variety of topics, many of which are not usually found in introductory textbooks. The theory is developed rigorously and in a self-contained way, with the chapters on measure theory interlaced with the probabilistic chapters in order to display the power of the abstract concepts in the world of probability theory. In addition, plenty of figures, computer simulations, biographic details of key mathematicians, and a wealth of examples support and enliven the presentation.
The two volume International Handbook of Earthquake and Engineering Seismology represents the International Association of Seismology and Physics of the Earth's Interior's (IASPEI) ambition to provide a comprehensive overview of our present knowledge of earthquakes and seismology. This state-of-the-art work is the only reference to cover all aspects of seismology--a "resource library" for civil and structural engineers, geologists, geophysicists, and seismologists in academia and industry around the globe. Part B, by more than 100 leading researchers from major institutions of science around the globe, features 34 chapters detailing strong-motion seismology, earthquake engineering, quake prediction and hazards mitigation, as well as detailed reports from more than 40 nations. Also available is The International Handbook of Earthquake and Engineering Seismology, Part A. Authoritative articles by more than 100 leading scientists Extensive glossary of terminology plus 2000+ biographical sketches of notable seismologists
This book is aimed at a wide range of readers who lack confidence in the mathematical and statistical sciences, particularly in the fields of Agriculture, Veterinary, Fishery, Dairy and other related areas. Its goal is to present the subject of statistics and its useful tools in various disciplines in such a manner that, after reading the book, readers will be equipped to apply the statistical tools to extract otherwise hidden information from their data sets with confidence. Starting with the meaning of statistics, the book introduces measures of central tendency, dispersion, association, sampling methods, probability, inference, designs of experiments and many other subjects of interest in a step-by-step and lucid manner. The relevant theories are described in detail, followed by a broad range of real-world worked-out examples, solved either manually or with the help of statistical packages. In closing, the book also includes a chapter on which statistical packages to use, depending on the user’s respective requirements.
In various scientific and industrial fields, stochastic simulations are taking on a new importance. This is due to the increasing power of computers and practitioners’ aim to simulate more and more complex systems, and thus use random parameters as well as random noises to model the parametric uncertainties and the lack of knowledge on the physics of these systems. The error analysis of these computations is a highly complex mathematical undertaking. Approaching these issues, the authors present stochastic numerical methods and prove accurate convergence rate estimates in terms of their numerical parameters (number of simulations, time discretization steps). As a result, the book is a self-contained and rigorous study of the numerical methods within a theoretical framework. After briefly reviewing the basics, the authors first introduce fundamental notions in stochastic calculus and continuous-time martingale theory, then develop the analysis of pure-jump Markov processes, Poisson processes, and stochastic differential equations. In particular, they review the essential properties of Itô integrals and prove fundamental results on the probabilistic analysis of parabolic partial differential equations. These results in turn provide the basis for developing stochastic numerical methods, both from an algorithmic and theoretical point of view. The book combines advanced mathematical tools, theoretical analysis of stochastic numerical methods, and practical issues at a high level, so as to provide optimal results on the accuracy of Monte Carlo simulations of stochastic processes. It is intended for master and Ph.D. students in the field of stochastic processes and their numerical applications, as well as for physicists, biologists, economists and other professionals working with stochastic simulations, who will benefit from the ability to reliably estimate and control the accuracy of their simulations.
The second edition enhanced with new chapters, figures, andappendices to cover the new developments in applied mathematicalfunctions This book examines the topics of applied mathematical functionsto problems that engineers and researchers solve daily in thecourse of their work. The text covers set theory, combinatorics,random variables, discrete and continuous probability, distributionfunctions, convergence of random variables, computer generation ofrandom variates, random processes and stationarity concepts withassociated autocovariance and cross covariance functions,estimation theory and Wiener and Kalman filtering ending with twoapplications of probabilistic methods. Probability tables with ninedecimal place accuracy and graphical Fourier transform tables areincluded for quick reference. The author facilitates understandingof probability concepts for both students and practitioners bypresenting over 450 carefully detailed figures and illustrations,and over 350 examples with every step explained clearly and somewith multiple solutions. Additional features of the second edition of Probability andRandom Processes are: Updated chapters with new sections on Newton-Pepys’problem; Pearson, Spearman, and Kendal correlation coefficients;adaptive estimation techniques; birth and death processes; andrenewal processes with generalizations A new chapter on Probability Modeling in TeletrafficEngineering written by Kavitha Chandra An eighth appendix examining the computation of the roots ofdiscrete probability-generating functions With new material on theory and applications of probability,Probability and Random Processes, Second Edition is athorough and comprehensive reference for commonly occurringproblems in probabilistic methods and their applications.
Most questions in social and biomedical sciences are causal in nature: what would happen to individuals, or to groups, if part of their environment were changed? In this groundbreaking text, two world-renowned experts present statistical methods for studying such questions. This book starts with the notion of potential outcomes, each corresponding to the outcome that would be realized if a subject were exposed to a particular treatment or regime. In this approach, causal effects are comparisons of such potential outcomes. The fundamental problem of causal inference is that we can only observe one of the potential outcomes for a particular subject. The authors discuss how randomized experiments allow us to assess causal effects and then turn to observational studies. They lay out the assumptions needed for causal inference and describe the leading analysis methods, including matching, propensity-score methods, and instrumental variables. Many detailed applications are included, with special focus on practical aspects for the empirical researcher.