Probability Approximation Via The Poisson Clumping Heuristic
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Probability Approximations Via The Poisson Clumping Heuristic
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Author : David Aldous
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
Probability Approximations Via The Poisson Clumping Heuristic written by David Aldous and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-09 with Mathematics categories.
If you place a large number of points randomly in the unit square, what is the distribution of the radius of the largest circle containing no points? Of the smallest circle containing 4 points? Why do Brownian sample paths have local maxima but not points of increase, and how nearly do they have points of increase? Given two long strings of letters drawn i. i. d. from a finite alphabet, how long is the longest consecutive (resp. non-consecutive) substring appearing in both strings? If an imaginary particle performs a simple random walk on the vertices of a high-dimensional cube, how long does it take to visit every vertex? If a particle moves under the influence of a potential field and random perturbations of velocity, how long does it take to escape from a deep potential well? If cars on a freeway move with constant speed (random from car to car), what is the longest stretch of empty road you will see during a long journey? If you take a large i. i. d. sample from a 2-dimensional rotationally-invariant distribution, what is the maximum over all half-spaces of the deviation between the empirical and true distributions? These questions cover a wide cross-section of theoretical and applied probability. The common theme is that they all deal with maxima or min ima, in some sense.
Probability Approximation Via The Poisson Clumping Heuristic
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Author :
language : en
Publisher:
Release Date : 1989
Probability Approximation Via The Poisson Clumping Heuristic written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989 with categories.
Normal Approximation By Stein S Method
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Author : Louis H.Y. Chen
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-10-13
Normal Approximation By Stein S Method written by Louis H.Y. Chen and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-10-13 with Mathematics categories.
Since its introduction in 1972, Stein’s method has offered a completely novel way of evaluating the quality of normal approximations. Through its characterizing equation approach, it is able to provide approximation error bounds in a wide variety of situations, even in the presence of complicated dependence. Use of the method thus opens the door to the analysis of random phenomena arising in areas including statistics, physics, and molecular biology. Though Stein's method for normal approximation is now mature, the literature has so far lacked a complete self contained treatment. This volume contains thorough coverage of the method’s fundamentals, includes a large number of recent developments in both theory and applications, and will help accelerate the appreciation, understanding, and use of Stein's method by providing the reader with the tools needed to apply it in new situations. It addresses researchers as well as graduate students in Probability, Statistics and Combinatorics.
Approximate Iterative Algorithms
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Author : Anthony Louis Almudevar
language : en
Publisher: CRC Press
Release Date : 2014-02-18
Approximate Iterative Algorithms written by Anthony Louis Almudevar and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-02-18 with Computers categories.
Iterative algorithms often rely on approximate evaluation techniques, which may include statistical estimation, computer simulation or functional approximation. This volume presents methods for the study of approximate iterative algorithms, providing tools for the derivation of error bounds and convergence rates, and for the optimal design of such
An Introduction To Stein S Method
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Author : A. D. Barbour
language : en
Publisher: World Scientific
Release Date : 2005
An Introduction To Stein S Method written by A. D. Barbour and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with Mathematics categories.
A common theme in probability theory is the approximation of complicated probability distributions by simpler ones, the central limit theorem being a classical example. Stein's method is a tool which makes this possible in a wide variety of situations. Traditional approaches, for example using Fourier analysis, become awkward to carry through in situations in which dependence plays an important part, whereas Stein's method can often still be applied to great effect. In addition, the method delivers estimates for the error in the approximation, and not just a proof of convergence. Nor is there in principle any restriction on the distribution to be approximated; it can equally well be normal, or Poisson, or that of the whole path of a random process, though the techniques have so far been worked out in much more detail for the classical approximation theorems.This volume of lecture notes provides a detailed introduction to the theory and application of Stein's method, in a form suitable for graduate students who want to acquaint themselves with the method. It includes chapters treating normal, Poisson and compound Poisson approximation, approximation by Poisson processes, and approximation by an arbitrary distribution, written by experts in the different fields. The lectures take the reader from the very basics of Stein's method to the limits of current knowledge.
Probability Approximations Via The Poisson Clumping Heuristic
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Author : David Aldous
language : en
Publisher: Springer
Release Date : 1988-11-14
Probability Approximations Via The Poisson Clumping Heuristic written by David Aldous and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 1988-11-14 with Mathematics categories.
If you place a large number of points randomly in the unit square, what is the distribution of the radius of the largest circle containing no points? Of the smallest circle containing 4 points? Why do Brownian sample paths have local maxima but not points of increase, and how nearly do they have points of increase? Given two long strings of letters drawn i. i. d. from a finite alphabet, how long is the longest consecutive (resp. non-consecutive) substring appearing in both strings? If an imaginary particle performs a simple random walk on the vertices of a high-dimensional cube, how long does it take to visit every vertex? If a particle moves under the influence of a potential field and random perturbations of velocity, how long does it take to escape from a deep potential well? If cars on a freeway move with constant speed (random from car to car), what is the longest stretch of empty road you will see during a long journey? If you take a large i. i. d. sample from a 2-dimensional rotationally-invariant distribution, what is the maximum over all half-spaces of the deviation between the empirical and true distributions? These questions cover a wide cross-section of theoretical and applied probability. The common theme is that they all deal with maxima or min ima, in some sense.
Stein S Method And Applications
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Author : Louis Hsiao Yun Chen
language : en
Publisher: World Scientific
Release Date : 2005-05-03
Stein S Method And Applications written by Louis Hsiao Yun Chen and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-05-03 with Mathematics categories.
Stein's startling technique for deriving probability approximations first appeared about 30 years ago. Since then, much has been done to refine and develop the method, but it is still a highly active field of research, with many outstanding problems, both theoretical and in applications. This volume, the proceedings of a workshop held in honour of Charles Stein in Singapore, August 2003, contains contributions from many of the mathematicians at the forefront of this effort. It provides a cross-section of the work currently being undertaken, with many pointers to future directions. The papers in the collection include applications to the study of random binary search trees, Brownian motion on manifolds, Monte-Carlo integration, Edgeworth expansions, regenerative phenomena, the geometry of random point sets, and random matrices.
Applied Probability
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Author : Kenneth Lange
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-08-13
Applied Probability written by Kenneth Lange and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-08-13 with Mathematics categories.
Applied Probability presents a unique blend of theory and applications, with special emphasis on mathematical modeling, computational techniques, and examples from the biological sciences. It can serve as a textbook for graduate students in applied mathematics, biostatistics, computational biology, computer science, physics, and statistics. Readers should have a working knowledge of multivariate calculus, linear algebra, ordinary differential equations, and elementary probability theory. Chapter 1 reviews elementary probability and provides a brief survey of relevant results from measure theory. Chapter 2 is an extended essay on calculating expectations. Chapter 3 deals with probabilistic applications of convexity, inequalities, and optimization theory. Chapters 4 and 5 touch on combinatorics and combinatorial optimization. Chapters 6 through 11 present core material on stochastic processes. If supplemented with appropriate sections from Chapters 1 and 2, there is sufficient material for a traditional semester-long course in stochastic processes covering the basics of Poisson processes, Markov chains, branching processes, martingales, and diffusion processes. The second edition adds two new chapters on asymptotic and numerical methods and an appendix that separates some of the more delicate mathematical theory from the steady flow of examples in the main text. Besides the two new chapters, the second edition includes a more extensive list of exercises, many additions to the exposition of combinatorics, new material on rates of convergence to equilibrium in reversible Markov chains, a discussion of basic reproduction numbers in population modeling, and better coverage of Brownian motion. Because many chapters are nearly self-contained, mathematical scientists from a variety of backgrounds will find Applied Probability useful as a reference
Probability Dynamics And Causality
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Author : D. Costantini
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Probability Dynamics And Causality written by D. Costantini and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
The book is a collection of essays on various issues in philosophy of science, with special emphasis on the foundations of probability and statistics, and quantum mechanics. The main topics, addressed by some of the most outstanding researchers in the field, are subjective probability, Bayesian statistics, probability kinematics, causal decision making, probability and realism in quantum mechanics.
Passage Times For Markov Chains
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Author : R. Syski
language : en
Publisher: Sage Publications Limited
Release Date : 1992
Passage Times For Markov Chains written by R. Syski and has been published by Sage Publications Limited this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992 with Mathematics categories.
This book is a survey of work on passage times in stable Markov chains with a discrete state space and a continuous time. Passage times have been investigated since early days of probability theory and its applications. The best known example is the first entrance time to a set, which embraces waiting times, busy periods, absorption problems, extinction phenomena, etc. Another example of great interest is the last exit time from a set. The book presents a unifying treatment of passage times, written in a systematic manner and based on modern developments. The appropriate unifying framework is provided by probabilistic potential theory, and the results presented in the text are interpreted from this point of view. In particular, the crucial role of the Dirichlet problem and the Poisson equation is stressed. The work is addressed to applied probalilists, and to those who are interested in applications of probabilistic methods in their own areas of interest. The level of presentation is that of a graduate text in applied stochastic processes. Hence, clarity of presentation takes precedence over secondary mathematical details whenever no serious harm may be expected. Advanced concepts described in the text gain nowadays growing acceptance in applied fields, and it is hoped that this work will serve as an useful introduction.