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Probability Approximations and Beyond by Andrew Barbour,Hock Peng Chan,David Siegmund Pdf
In June 2010, a conference, Probability Approximations and Beyond, was held at the National University of Singapore (NUS), in honor of pioneering mathematician Louis Chen. Chen made the first of several seminal contributions to the theory and application of Stein’s method. One of his most important contributions has been to turn Stein’s concentration inequality idea into an effective tool for providing error bounds for the normal approximation in many settings, and in particular for sums of random variables exhibiting only local dependence. This conference attracted a large audience that came to pay homage to Chen and to hear presentations by colleagues who have worked with him in special ways over the past 40+ years. The papers in this volume attest to how Louis Chen’s cutting-edge ideas influenced and continue to influence such areas as molecular biology and computer science. He has developed applications of his work on Poisson approximation to problems of signal detection in computational biology. The original papers contained in this book provide historical context for Chen’s work alongside commentary on some of his major contributions by noteworthy statisticians and mathematicians working today.
Probability Approximations and Beyond by Andrew Barbour,Hock Peng Chan,David Siegmund Pdf
In June 2010, a conference, Probability Approximations and Beyond, was held at the National University of Singapore (NUS), in honor of pioneering mathematician Louis Chen. Chen made the first of several seminal contributions to the theory and application of Stein’s method. One of his most important contributions has been to turn Stein’s concentration inequality idea into an effective tool for providing error bounds for the normal approximation in many settings, and in particular for sums of random variables exhibiting only local dependence. This conference attracted a large audience that came to pay homage to Chen and to hear presentations by colleagues who have worked with him in special ways over the past 40+ years. The papers in this volume attest to how Louis Chen’s cutting-edge ideas influenced and continue to influence such areas as molecular biology and computer science. He has developed applications of his work on Poisson approximation to problems of signal detection in computational biology. The original papers contained in this book provide historical context for Chen’s work alongside commentary on some of his major contributions by noteworthy statisticians and mathematicians working today.
Beyond Chance and Credence by Wayne C. Myrvold Pdf
Concepts related to probability permeate physics. This is most obvious in statistical mechanics, in which probabilities appear explicitly, but even in cases when predictions are made with near-certainty, there are implicit probabilistic assumptions in play. How are we to understand these probabilistic concepts? How do they apply to the physical world? Beyond Chance and Credence offers a fresh look at these familiar topics, urging readers to see them in a new light. The book provides an overview of the history of philosophical debates about the nature of probability over the last three centuries, and clear and accessible introductions to conceptual issues in probability theory, thermodynamics, and statistical mechanics. Myrvold argues that the traditional choice between probabilities as objective chances or else as degrees of belief is too limiting, and introduces a new concept, epistemic chances, that combines physical and epistemic considerations. He goes on to show that conceiving of probabilities in this way solves some of the puzzles associated with the use of probability and statistical mechanics. The result is an innovative perspective on one of the most central topics in the philosophy of science.
Information-Theoretic Methods for Estimating of Complicated Probability Distributions by Zhi Zong Pdf
Mixing up various disciplines frequently produces something that are profound and far-reaching. Cybernetics is such an often-quoted example. Mix of information theory, statistics and computing technology proves to be very useful, which leads to the recent development of information-theory based methods for estimating complicated probability distributions. Estimating probability distribution of a random variable is the fundamental task for quite some fields besides statistics, such as reliability, probabilistic risk analysis (PSA), machine learning, pattern recognization, image processing, neural networks and quality control. Simple distribution forms such as Gaussian, exponential or Weibull distributions are often employed to represent the distributions of the random variables under consideration, as we are taught in universities. In engineering, physical and social science applications, however, the distributions of many random variables or random vectors are so complicated that they do not fit the simple distribution forms at al. Exact estimation of the probability distribution of a random variable is very important. Take stock market prediction for example. Gaussian distribution is often used to model the fluctuations of stock prices. If such fluctuations are not normally distributed, and we use the normal distribution to represent them, how could we expect our prediction of stock market is correct? Another case well exemplifying the necessity of exact estimation of probability distributions is reliability engineering. Failure of exact estimation of the probability distributions under consideration may lead to disastrous designs. There have been constant efforts to find appropriate methods to determine complicated distributions based on random samples, but this topic has never been systematically discussed in detail in a book or monograph. The present book is intended to fill the gap and documents the latest research in this subject. Determining a complicated distribution is not simply a multiple of the workload we use to determine a simple distribution, but it turns out to be a much harder task. Two important mathematical tools, function approximation and information theory, that are beyond traditional mathematical statistics, are often used. Several methods constructed based on the two mathematical tools for distribution estimation are detailed in this book. These methods have been applied by the author for several years to many cases. They are superior in the following senses: (1) No prior information of the distribution form to be determined is necessary. It can be determined automatically from the sample; (2) The sample size may be large or small; (3) They are particularly suitable for computers. It is the rapid development of computing technology that makes it possible for fast estimation of complicated distributions. The methods provided herein well demonstrate the significant cross influences between information theory and statistics, and showcase the fallacies of traditional statistics that, however, can be overcome by information theory. Key Features: - Density functions automatically determined from samples - Free of assuming density forms - Computation-effective methods suitable for PC - density functions automatically determined from samples - Free of assuming density forms - Computation-effective methods suitable for PC
Stellar Atmospheres: Beyond Classical Models by L. Crivellari,Ivan Hubeny,D. Hummer Pdf
The theory of stellar atmospheres is one of the most important branches of modern astrophysics. It is first of all a major tool for understanding all aspects of stars. As the physical properties of their outer layers can now be found with high precision, firm conclusions can be drawn about the internal structure and evolution of stars. Moreover, improvements in our knowledge of the chemical composition of stars is shedding new light on the chemical evolution of galaxies and of the Universe as a whole. Because the outer layers of stars are among the best-understood astrophysical objects, the theory of stellar atmospheres plays an important role in the study of many other types of objects. These include planetary nebulae, H II regions, interstellar matter, and objects of interest in high-energy astrophysics, such as accretion disks (close binaries, dwarf novae, cataclysmic variables, quasars, active galactic nuclei), pulsar magnetospheres, and Seyfert galaxies. Finally, as stars provide a laboratory in which plasmas can be studied under more extreme conditions than on earth, the study of stellar atmospheres has strong connections with modern physics. Astronomical observations provided a vital stimulus in the early stages of quantum theory and atomic physics; even today topics such as low-temperature dielectronic recombination develop hand in hand with the interpretation of stellar and nebular spectra. Early work on MHD was similiarly motivated. Many such connections remain to be explored.
Efficient Multirate Teletraffic Loss Models Beyond Erlang by Ioannis D. Moscholios,Michael D. Logothetis Pdf
A comprehensive study in efficient multi-rate teletraffic loss models used for designing, performance analysis, and optimization of systems and networks Efficient Multirate Teletraffic Loss Models Beyond Erlang is an easy-to-read book filled with numerous efficient teletraffic loss models. Presented in three sections—Teletraffic Models of Random Input, Teletraffic Models of Quasi-Random Input, and Teletraffic Models of Batched Poisson Input—it covers everything that a professional experienced with optimization and dimensioning of telecom networks could ever need to know. This unique book provides a detailed explanation on how efficient multirate teletraffic loss models are extracted and applied, and guides readers through almost all network technologies and services. Starting from the basics, it steadily increases in difficulty to keep the book self-contained and to provide a better understanding to those who might be new to the subject. It includes detailed explanations of the complex teletraffic models—many of which were developed by the authors. Tutorial examples, several backed by supplementary software, are accompanied by intermediate results and figures. Additionally, end-of-chapter applications describe the applicability of the models to modern network technologies, updating the incorporated teletraffic models of commercial packages/tools. Uses the classic EMLM (Erlang Multirate Loss Model) as its base to present a comprehensive range of teletraffic models through detailed explanation and numerical examples Filled with the authors’ own original teletraffic models—making for a wholly unique learning experience Offers a clear, self-contained presentation with a beginning, middle, and end Starts with simple models, then moves to more complex models, before finishing with complicated ones Supplemented by an accompanying website with computer implementation of the most important models Directed primarily at telecommunication engineers, Efficient Multirate Teletraffic Loss Models Beyond Erlang is also useful for telecom operators or managers on the higher and average levels, as well a Ph.D. students, researchers, and modelers.
UAV Communications for 5G and Beyond by Yong Zeng,Ismail Guvenc,Rui Zhang,Giovanni Geraci,David W. Matolak Pdf
To advantageously plan and design for the explosive near-future increase in the number of unmanned aerial vehicles (UAVs) and their demanding applications, integration of UAVs into cellular communication systems has seen increasing interest. This book provides a timely and comprehensive overview of the recent research efforts and results of unmanned aerial vehicles (UAVs)-integrated cellular network communications. The aim of the book is to provide a comprehensive coverage of the potential applications, networking architectures, latest research findings and key enabling technologies, experimental measurement results, as well as up-to-date industry standardizations for UAV communications in cellular systems, including the existing LTE as well as the future 5G-and-beyond systems.
Presents a survey of the history and evolution of the branch of mathematics that focuses on probability and statistics, including useful applications and notable mathematicians in this area.
Researchers and professionals in all walks of life need to use the many tools offered by the statistical world, but often do not have the necessary experience in both concept and application. No matter what your profession, sooner or later numbers need to be crunched, and often you need to understand how to do it, and why it is important. Quality c
Stock Analysis in the Twenty-First Century and Beyond by Thomas E. Berghage Pdf
Stock Analysis in the Twenty-First Century and Beyond For years, financial analysts have struggled with the fact that practically all the financial measures used to analyze corporate performance lack predictive power when it comes to forecasting the market performance of the company’s stock. Numerous academic studies have documented and reported this lack of predictability. Correlation coefficients close to zero have been reported for the relationship between stock market performance and such critical financial measures as earnings growth, sales growth, price/earnings ratio, return on equity, intrinsic value (models based on discounted cash flow or dividends), and many more. It is this disconnect between traditional financial measures and the performance of stocks in the marketplace that has led to the now-famous efficient market hypothesis, the cornerstone of modern portfolio theory. To accept the idea that the future performance of stocks is unpredictable is to say that nothing a company does will affect the future performance of its stock in the market, and that is absurd. It would be more accurate to say that everything a company does will affect the future performance of its stock in the market. The problem with this statement is that it makes the forecasting of future stock performance so complex that it removes it from the realm of human solution. Confident in the belief that something other than chance and irrational investors determine future stock prices, several research groups around the world have started exploring the use of intelligent computer programs (programs that self-organize based on environmental feedback). Early results are very promising and have provided a glimpse of the economic forces described by Adam Smith as the invisible hand that guides economic activity. Stock Analysis in the Twenty-First Century and Beyond describes the stock analysis problem and explores one of the more successful efforts to harness the new intelligent computer technology. Many people mistakenly classify Artificially Intelligent (AI) computer systems as a form of quantitative analysis. There are two distinct differences between advanced AI systems and traditional quantitative analysis. They are (1) who makes up the selection rules and weighting and (2) what information is used to discriminate between good- and poor-performing securities. In most quantitative systems, even in an advanced expert system form, humans make up the investment rules and mathematically derive the weightings associated with the rules. Computer systems that depend on outside human intelligence to program their actions are not inherently intelligent. In advanced AI systems, the computer makes up its own rules and weightings. The computer learns from examples of good- and poor-performing stocks and determines its own ways for discriminating between them. The procedures that are derived by the computer are often so complex that they defy human understanding. In addition to making up its own rules, advanced AI systems look at corporate financial data differently. Just like in the human brain, where information is not stored in the brain cells but rather in the connections and relationships between cells, so too is corporate performance information stored in the relationships between financial numbers. Assessing the performance of companies is not so much in the numbers as it is in the connections between the numbers. Financial analysts recognized this early on and have used first-order relational information in the form of financial ratios for many years (price/book, debt/equity, current assets / current liabilities, price/earnings, etc.). Now with advanced AI systems, we are finally able to look at and evaluate high-order interrelationships in financial data that have been far too complex to analyze with less sophisticated systems. These then are the fundamental differences between what has been used in the past and what will be used in the future. Cdr. Thomas E. Berghage
Probability Approximations via the Poisson Clumping Heuristic by David Aldous Pdf
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 and Measure by Patrick Billingsley Pdf
Now in its new third edition, Probability and Measure offers advanced students, scientists, and engineers an integrated introduction to measure theory and probability. Retaining the unique approach of the previous editions, this text interweaves material on probability and measure, so that probability problems generate an interest in measure theory and measure theory is then developed and applied to probability. Probability and Measure provides thorough coverage of probability, measure, integration, random variables and expected values, convergence of distributions, derivatives and conditional probability, and stochastic processes. The Third Edition features an improved treatment of Brownian motion and the replacement of queuing theory with ergodic theory.· Probability· Measure· Integration· Random Variables and Expected Values· Convergence of Distributions· Derivatives and Conditional Probability· Stochastic Processes
Beyond VoIP Protocols by Olivier Hersent,Jean-Pierre Petit,David Gurle Pdf
In 1999-2000, VoIP (Voice-over-IP) telephony was one of the most successful buzzwords of the telecom bubble era. However, in 2001-2003, VoIP faced a very tough reality check. Now, manufacturers and service providers are drawing on what they have learnt from past experience in order to prepare to participate in the next major challenge faced by the telecommunications industry. This book offers a comprehensive overview of the issues to solve in order to deploy global revenue-generating effective "multimedia" services. Drawing on extensive research and practical deployment experience in VoIP, the authors provide essential advice for those seeking to design and implement a post-bubble VoIP network. Beyond VoIP Protocols: Understanding Voice Technology and Networking Techniques for IP Telephony Introduces the basics of speech coding and voice quality Demonstrates how quality of service may be built into the network and deals with dimensioning aspects, e.g. multipoint communications and how to model call seizures. Explores the potential of multicast to turn an IP backbone into an optimized broadcast medium Includes amply illustrated, state-of-the-art practical advice for formulating a complete deployment strategy A companion volume to "IP Telephony: Deploying VoIP Protocols", this book takes the reader a stage deeper into how to prepare the network and exploit VoIP technology to its full potential.
