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This book is intended to provoke, entertain, and inform by challenging the reader's ideas about randomness, providing first one and then another interpretation of what this elusive concept means. As the book progresses, the author teases out the various threads and shows how mathematics, communication engineering, computer science, philosophy, physics, and psychology all contribute to the discourse by illuminating different facets of the same idea. The material in this book should be readily accessible to anyone with experience in undergraduate mathematics, no calculus needed. Three appendices provide some of the background information regarding binary representations and logarithms that are needed. Although an effort is made to justify most statements of a mathematical nature, a few are presented without corroboration, since they entail close-knit arguments that would detract from the main ideas. Readers can safely bypass the details without any loss, and in any case, the fine points are available in the technical notes assembled at the end. .
Chance --- Probabilities --- Probability --- Statistical inference --- Combinations --- Mathematics --- Least squares --- Mathematical statistics --- Risk --- Fortune --- Necessity (Philosophy) --- Probabilities. --- Probability Theory and Stochastic Processes. --- Chance. --- Probabilités
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Decoupling theory provides a general framework for analyzing problems involving dependent random variables as if they were independent. It was born in the early eighties as a natural continuation of martingale theory and has acquired a life of its own due to vigorous development and wide applicability. The authors provide a friendly and systematic introduction to the theory and applications of decoupling. The book begins with a chapter on sums of independent random variables and vectors, with maximal inequalities and sharp estimates on moments which are later used to develop and interpret decoupling inequalities. Decoupling is first introduced as it applies in two specific areas, randomly stopped processes (boundary crossing problems) and unbiased estimation (U-- statistics and U--processes), where it has become a basic tool in obtaining several definitive results. In particular, decoupling is an essential component in the development of the asymptotic theory of U-- statistics and U--processes. The authors then proceed with the theory of decoupling in full generality. Special attention is given to comparison and interplay between martingale and decoupling theory, and to applications. Among other results, the applications include limit theorems, momemt and exponential inequalities for martingales and more general dependence structures, results with biostatistical implications, and moment convergence in Anscombe's theorem and Wald's equation for U--statistics. This book is addressed to researchers in probability and statistics and to graduate students. The expositon is at the level of a second graduate probability course, with a good portion of the material fit for use in a first year course. Victor de la Pe$a is Associate Professor of Statistics at Columbia University and is one of the more active developers of decoupling.
Stochastic processes --- Decoupling (Mathematics) --- Decoupling (Mathematics). --- Probabilities. --- Statistics . --- Probability Theory and Stochastic Processes. --- Statistics, general. --- Statistical analysis --- Statistical data --- Statistical methods --- Statistical science --- Mathematics --- Econometrics --- Probability --- Statistical inference --- Combinations --- Chance --- Least squares --- Mathematical statistics --- Risk --- Inequalities (Mathematics)
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Part I, Bertoin, J.: Subordinators: Examples and Applications: Foreword.- Elements on subordinators.- Regenerative property.- Asymptotic behaviour of last passage times.- Rates of growth of local time.- Geometric properties of regenerative sets.- Burgers equation with Brownian initial velocity.- Random covering.- Lévy processes.- Occupation times of a linear Brownian motion.- Part II, Martinelli, F.: Lectures on Glauber Dynamics for Discrete Spin Models: Introduction.- Gibbs Measures of Lattice Spin Models.- The Glauber Dynamics.- One Phase Region.- Boundary Phase Transitions.- Phase Coexistence.- Glauber Dynamics for the Dilute Ising Model.- Part III, Peres, Yu.: Probability on Trees: An Introductory Climb: Preface.- Basic Definitions and a Few Highlights.- Galton-Watson Trees.- General percolation on a connected graph.- The first-Moment method.- Quasi-independent Percolation.- The second Moment Method.- Electrical Networks.- Infinite Networks.- The Method of Random Paths.- Transience of Percolation Clusters.- Subperiodic Trees.- The Random Walks RW (lambda) .- Capacity.-.Intersection-Equivalence.- Reconstruction for the Ising Model on a Tree,- Unpredictable Paths in Z and EIT in Z3.- Tree-Indexed Processes.- Recurrence for Tree-Indexed Markov Chains.- Dynamical Pecsolation.- Stochastic Domination Between Trees.
Stochastic processes --- Mathematics. --- Probabilities. --- Statistics. --- Probability Theory and Stochastic Processes. --- Statistical Theory and Methods. --- Mathematical statistics --- Statistique mathématique --- Wiskundige statistiek --- Statistics . --- Statistical analysis --- Statistical data --- Statistical methods --- Statistical science --- Mathematics --- Econometrics --- Probability --- Statistical inference --- Combinations --- Chance --- Least squares --- Risk
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Whyanothertextbook? The statistical community generally agrees that at the upper undergraduate level, or the beginning master’s level, students of statistics should begin to study the mathematical methods of the ?eld. We assume that by thentheywillhavestudiedtheusualtwo yearcollegesequence,includingcalculus through multiple integrals and the basics of matrix algebra. Therefore, they are ready to learn the foundations of their subject, in much more depth than is usual in an applied, “cookbook,” introduction to statistical methodology. There are a number of well written, widely used textbooks for such a course. These seem to re?ect a consensus for what needs to be taught and how it should be taught. So, why do we need yet another book for this spot in the curriculum? I learned mathematical statistics with the help of the standard texts. Since then, Ihavetaughtthiscourseandsimilaronesmanytimes,atseveraldifferentuniversi ties,usingwell thought oftextbooks.Butfromthebeginning,Ifeltthatsomething was wrong. It took me several years to articulate the problem, and many more to assemble my solution into the book you have in your hand. You see, I spend the rest of my day in statistical consulting and statistical re search. I should have been preparing my mathematical statistics students to join me in this exciting work. But from seeing what the better graduating seniors and beginning graduate students usually knew, I concluded that the standard curricu lumwasnotteachingthemtobesophisticatedcitizensofthestatisticalcommunity.
Mathematical statistics --- Mathematical statistics. --- Statistics. --- Probabilities. --- Statistical Theory and Methods. --- Probability Theory and Stochastic Processes. --- Distribution (Probability theory. --- Statistics . --- Probability --- Statistical inference --- Combinations --- Mathematics --- Chance --- Least squares --- Risk --- Statistical analysis --- Statistical data --- Statistical methods --- Statistical science --- Econometrics --- Acqui 2006
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This book has been designed for a final year undergraduate course in stochastic processes. It will also be suitable for mathematics undergraduates and others with interest in probability and stochastic processes, who wish to study on their own. The main prerequisite is probability theory: probability measures, random variables, expectation, independence, conditional probability, and the laws of large numbers. The only other prerequisite is calculus. This covers limits, series, the notion of continuity, differentiation and the Riemann integral. Familiarity with the Lebesgue integral would be a bonus. A certain level of fundamental mathematical experience, such as elementary set theory, is assumed implicitly. Throughout the book the exposition is interlaced with numerous exercises, which form an integral part of the course. Complete solutions are provided at the end of each chapter. Also, each exercise is accompanied by a hint to guide the reader in an informal manner. This feature will be particularly useful for self-study and may be of help in tutorials. It also presents a challenge for the lecturer to involve the students as active participants in the course.
Stochastic processes. --- Processus stochastiques --- Stochastic processes --- Probabilities. --- Observations, Astronomical. --- Astronomy—Observations. --- Probability Theory and Stochastic Processes. --- Astronomy, Observations and Techniques. --- Astronomical observations --- Observations, Astronomical --- Probability --- Statistical inference --- Combinations --- Mathematics --- Chance --- Least squares --- Mathematical statistics --- Risk
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Mathematical statistics --- 519.2 --- Orthogonal arrays --- Arrays, Orthogonal --- Combinatorial designs and configurations --- Probability. Mathematical statistics --- 519.2 Probability. Mathematical statistics --- Probabilities. --- Statistics . --- Probability Theory and Stochastic Processes. --- Statistical Theory and Methods. --- Statistical analysis --- Statistical data --- Statistical methods --- Statistical science --- Mathematics --- Econometrics --- Probability --- Statistical inference --- Combinations --- Chance --- Least squares --- Risk
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Interactive Particle Systems is a branch of Probability Theory with close connections to Mathematical Physics and Mathematical Biology. In 1985, the author wrote a book (T. Liggett, Interacting Particle System, ISBN 3-540-96069) that treated the subject as it was at that time. The present book takes three of the most important models in the area, and traces advances in our understanding of them since 1985. In so doing, many of the most useful techniques in the field are explained and developed, so that they can be applied to other models and in other contexts. Extensive Notes and References sections discuss other work on these and related models. Readers are expected to be familiar with analysis and probability at the graduate level, but it is not assumed that they have mastered the material in the 1985 book. This book is intended for graduate students and researchers in Probability Theory, and in related areas of Mathematics, Biology and Physics.
Statistical physics --- Processus stochastiques --- Stochastic processes --- Stochastische processen --- Probabilities. --- Mathematical physics. --- Applied mathematics. --- Engineering mathematics. --- Probability Theory and Stochastic Processes. --- Theoretical, Mathematical and Computational Physics. --- Mathematical and Computational Engineering. --- Engineering --- Engineering analysis --- Mathematical analysis --- Physical mathematics --- Physics --- Probability --- Statistical inference --- Combinations --- Mathematics --- Chance --- Least squares --- Mathematical statistics --- Risk
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In this book, the author begins with the elementary theory of Markov chains and very progressively brings the reader to the more advanced topics. He gives a useful review of probability that makes the book self-contained, and provides an appendix with detailed proofs of all the prerequisites from calculus, algebra, and number theory. A number of carefully chosen problems of varying difficulty are proposed at the close of each chapter, and the mathematics are slowly and carefully developed, in order to make self-study easier. The author treats the classic topics of Markov chain theory, both in discrete time and continuous time, as well as the connected topics such as finite Gibbs fields, nonhomogeneous Markov chains, discrete- time regenerative processes, Monte Carlo simulation, simulated annealing, and queuing theory. The result is an up-to-date textbook on stochastic processes. Students and researchers in operations research and electrical engineering, as well as in physics and biology, will find it very accessible and relevant.
Markov processes. --- Probabilities. --- Operations research. --- Decision making. --- Electrical engineering. --- Probability Theory and Stochastic Processes. --- Operations Research/Decision Theory. --- Electrical Engineering. --- Electric engineering --- Engineering --- Deciding --- Decision (Psychology) --- Decision analysis --- Decision processes --- Making decisions --- Management --- Management decisions --- Choice (Psychology) --- Problem solving --- Operational analysis --- Operational research --- Industrial engineering --- Management science --- Research --- System theory --- Probability --- Statistical inference --- Combinations --- Mathematics --- Chance --- Least squares --- Mathematical statistics --- Risk --- Decision making --- Probabilité
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Our object in writing this book is to present the main results of the modern theory of multivariate statistics to an audience of advanced students who would appreciate a concise and mathematically rigorous treatment of that material. It is intended for use as a textbook by students taking a first graduate course in the subject, as well as for the general reference of interested research workers who will find, in a readable form, developments from recently published work on certain broad topics not otherwise easily accessible, as for instance robust inference (using adjusted likelihood ratio tests) and the use of the bootstrap in a multivariate setting. A minimum background expected of the reader would include at least two courses in mathematical statistics, and certainly some exposure to the calculus of several variables together with the descriptive geometry of linear algebra.
Multivariate analysis. --- Mathematical statistics --- 519.2 --- Multivariate analysis --- Multivariate distributions --- Multivariate statistical analysis --- Statistical analysis, Multivariate --- Analysis of variance --- Matrices --- 519.2 Probability. Mathematical statistics --- Probability. Mathematical statistics --- Analyse multivariée --- EPUB-LIV-FT SPRINGER-B --- Mathematics. --- Probabilities. --- Statistics. --- Probability Theory and Stochastic Processes. --- Statistical Theory and Methods. --- Distribution (Probability theory. --- Mathematical statistics. --- Statistics . --- Statistical analysis --- Statistical data --- Statistical methods --- Statistical science --- Mathematics --- Econometrics --- Probability --- Statistical inference --- Combinations --- Chance --- Least squares --- Risk
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Prediction of a random field based on observations of the random field at some set of locations arises in mining, hydrology, atmospheric sciences, and geography. Kriging, a prediction scheme defined as any prediction scheme that minimizes mean squared prediction error among some class of predictors under a particular model for the field, is commonly used in all these areas of prediction. This book summarizes past work and describes new approaches to thinking about kriging.
Stochastic processes --- Kriging. --- Geografie --- Topografie --- Geometric Modelling. --- Probabilities. --- Statistics . --- Geology. --- Geography. --- Earth sciences. --- Probability Theory and Stochastic Processes. --- Statistical Theory and Methods. --- Statistics for Engineering, Physics, Computer Science, Chemistry and Earth Sciences. --- Geography, general. --- Earth Sciences, general. --- Geosciences --- Environmental sciences --- Physical sciences --- Cosmography --- Earth sciences --- World history --- Geognosy --- Geoscience --- Natural history --- Statistical analysis --- Statistical data --- Statistical methods --- Statistical science --- Mathematics --- Econometrics --- Probability --- Statistical inference --- Combinations --- Chance --- Least squares --- Mathematical statistics --- Risk
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