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Arts --- Chance --- Chance in literature
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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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Probabilities. --- Random variables. --- Chance variables --- Stochastic variables --- Probabilities --- Variables (Mathematics) --- Probability --- Statistical inference --- Combinations --- Mathematics --- Chance --- Least squares --- Mathematical statistics --- Risk --- Random variables
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Environmental risk assessment --- Probabilities --- Mathematical models --- Probability --- Statistical inference --- Combinations --- Mathematics --- Chance --- Least squares --- Mathematical statistics --- Risk --- Risk assessment --- Precautionary principle --- Environmental risk assessment - Mathematical models
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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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Philosophy and science. --- Biology --- Philosophical anthropology. --- Bioethics. --- Rabbinical literature. --- Philosophie et sciences --- Biologie --- Anthropologie philosophique --- Bioéthique --- Littérature rabbinique --- Philosophy. --- Philosophie --- Bible --- Allegorical interpretations. --- Necessite (Philosophie) --- Hasard. --- Mythe dans la Bible. --- Philosophie. --- Chance. --- Bioéthique --- Littérature rabbinique --- Biologie - Philosophie.
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Foundational issues in statistical mechanics and the more general question of how probability is to be understood in the context of physical theories are both areas that have been neglected by philosophers of physics. This book fills an important gap in the literature by providing a most systematic study of how to interpret probabilistic assertions in the context of statistical mechanics. The book explores both subjectivist and objectivist accounts of probability, and takes full measure of work in the foundations of probability theory, in statistical mechanics, and in mathematical theory. It will be of particular interest to philosophers of science, physicists and mathematicians interested in foundational issues, and also to historians of science.
Probabilities --- Statistical physics --- Probabilités --- Physique statistique --- Physics --- Mathematical statistics --- Probability --- Statistical inference --- Combinations --- Mathematics --- Chance --- Least squares --- Risk --- Statistical methods --- Probabilities. --- Statistical physics. --- Probabilités --- Arts and Humanities --- Philosophy
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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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