Maximum-Entropy Models in Science and Engineering

Size: px
Start display at page:

Download "Maximum-Entropy Models in Science and Engineering"

Transcription

1 Maximum-Entropy Models in Science and Engineering (Revised Edition) J. N. Kapur JOHN WILEY & SONS New York Chichester Brisbane Toronto Singapore

2 p Contents Preface iü 1. Maximum-Entropy Probability Distributions: Principles, Formalism and Techniques Measures of entropy Maximum-entropy principle Maximum-entropy formalism Proofs of some needed mathematical results Bibliographical and historical remarks Maximum-Entropy Discrete Univariate Probability Distributions When the discrete variate takes only a finite set of values When the discrete variate takes a countable infinite set of values When the prior probability distribution is given and mean is prescribed Lagrangian distributions Bibliographical and historical remarks Maximum-Entropy Continuous Univariate Probability Distributions When the ränge of the variate is ( oo, co) When the variate varies over the semi-infinite interval [0, oo) When the variate ranges over a finite interval [0, R] Bibliographical and historical Remarks Maximum-Entropy Discrete Multivariate Probability Distributions The Bose-Einstein, Fermi-Dirac and multinomial distributions A general class of discrete multivariate distributions Multivariate generalised geometrical, negative binomial, generalised negative binomial and Poisson distributions Multivariate Lagrangian distributions General discussion 110

3 viii Contents 4.6 Discrete multivariate distributions for queueing networks Bibliographical and historical remarks Maximum-Entropy Continuous Multivariate Probability Distributions Maximum-Entropy distributions obtained by specifying covariances Maximum-Entropy distributions when sumof variates is a constant Maximum-Entropy distributions obtained by also specifying expected values of functions of all variates Maximum-Entropy distribution obtained by finding distributions of function of given independent variates Some other multivariate distributions Bibliographical and historical remarks Maximum-Entropy Distributions in Statistical Mechanics Maxwell-Boltzmann distribution Bose-Einstein distribution Fermi-Dirac distribution Intermediate statistics distributions Bibliographical and historical remarks Minimum Discrepancy Measures Some general classes of measures of directed divergence or discrepancy Some special cases Minimum discriminationprobability distributions Properties of minimum discrimination functions Efficiency of minimum discrepancy estimators Generalised measures of generalised directed divergence Bibliographical and historical remarks Concavity (Convexity) of Maximum-Entropy (Minimum Information) Functions Concavity and convexity of functions Concavity and convexity of functions useful in Information theory Consequences of convexity or concavity of functions Concavity of S mix for Renyi's entropy of second order Extension of results to continuous variate distributions and density matrices Bibliographical and historical remarks 226

4 Contents ix 9. Eqaivalence of Maximum-Entropy Principle and Gauss's Principle of Density Estimation Minimum discrimination information principle Maximum likelihood estimators for the parameters of the minimum discrimination information distribution An alternative proof of equivalence and naturalness of measures Relations among six basic principles of Statistical inference Bibliographical and historical remarks Maximum-Entropy Principle and Contingency Tables Multidimensional contingency tables Contingency tables with elements as random variables The maximum-entropy principle and chi-square test Bibliographical and historical remarks Maximum-Entropy Principle and Statistics Statistical inference Jayne's entropy concentration theorem The role of MEP in statistics Non-parametric density estimation Bibliographical and historical remarks Entropy Maximization and Statistical Thermodynamics Thermodynamics of closed Systems Thermodynamics of open or diffusive systems Thermodynamic functions Bose-Einstein and Fermi-Dirac distributions Bibliographical and historical remarks Maximum-Entropy Models in Regional and Urban Planning Discrete population distribution modeis Transportation modeis Population distribution and transportation Systems (continuous modeis) Fermi-Dirac, Bose-Einstein and intermediate distributions for residential location and trip distribution Bibliographical and historical remarks Maximum-Entropy Models in Marketing and Elections Herniter's model for brand switching Generalisations of Herniter's model Maximum-Entropy brand switching and vote-switching modeis with different structures 378

5 x Contents 14.4 Vote-Switching among political parties Derivation of some purchase incidence stochastic modeis from maximum-entropy principle Bibliographical and historical remarks Maximum-Entropy Models in Economics, Finance, Insurance and Accountancy The effect of taxation on reduction of inequalities of income International trade modeis The maximum-entropy distribution of the future market price of a stock Maximum-entropy distributions in accounting and insurance Bibliographical and historical remarks Maximum-Entropy Spectral Analysis Maximum-Entropy probability distribution The spectral density function Relation of MESA with other methods of spectral analysis Multidimensional maximum-entropy spectral analysis Bibliographical and historical remarks Maximum-Entropy Image Reconstruction Some physical problems requiring image reconstruction The mathematical problems and discretisation Solutions of the problem of estimation Measures of entropy used in image reconstruction Entropiegray-level picture thresholding Bibliographical and historical remarks Maximum and Minimum-Entropy Models in Pattern Recognition Optimizing properties of Karhunen-Loeve expansion Use of measures of divergence in feature extraction Pattern recognition as a quest for minimumentropy Bibliographical and historical remarks Maximum-Entropy Principle in Operations Research Maximum-Entropy principle in search theory Maximum-Entropy principle in reliability theory 531' 19.3 Maximum-Entropy principle in queuing theory Maximum-Entropy principle in theory of games Optimal portfolio selection 544

6 Contents xi 19.6 Maximum-Entropy principle in risk sharing Maximum-Entropy principle and mathematical Programming Bibliographical and historical remarks Maximum-Entropy Models in Biology, Medicine and Agriculture Maximum-Entropy principle in pharmacokinetics (or in compartment analysis) Maximum-Entropy principle in stochastic prey-predator and epidemic modeis Maximum-Entropy principle in ecological modelling Maximum-Entropy principle in multispecies ecological modeis Maximum-Entropy estimation of missing data in design of experiments MEP derivation of logistic law of population growth Bibliographical and historical remarks 588 References Author Index Subject Index

Univariate Discrete Distributions

Univariate Discrete Distributions Univariate Discrete Distributions Second Edition NORMAN L. JOHNSON University of North Carolina Chapel Hill, North Carolina SAMUEL KOTZ University of Maryland College Park, Maryland ADRIENNE W. KEMP University

More information

Continuous Univariate Distributions

Continuous Univariate Distributions Continuous Univariate Distributions Volume 2 Second Edition NORMAN L. JOHNSON University of North Carolina Chapel Hill, North Carolina SAMUEL KOTZ University of Maryland College Park, Maryland N. BALAKRISHNAN

More information

COPYRIGHTED MATERIAL CONTENTS. Preface Preface to the First Edition

COPYRIGHTED MATERIAL CONTENTS. Preface Preface to the First Edition Preface Preface to the First Edition xi xiii 1 Basic Probability Theory 1 1.1 Introduction 1 1.2 Sample Spaces and Events 3 1.3 The Axioms of Probability 7 1.4 Finite Sample Spaces and Combinatorics 15

More information

Stat 5101 Lecture Notes

Stat 5101 Lecture Notes Stat 5101 Lecture Notes Charles J. Geyer Copyright 1998, 1999, 2000, 2001 by Charles J. Geyer May 7, 2001 ii Stat 5101 (Geyer) Course Notes Contents 1 Random Variables and Change of Variables 1 1.1 Random

More information

PATTERN CLASSIFICATION

PATTERN CLASSIFICATION PATTERN CLASSIFICATION Second Edition Richard O. Duda Peter E. Hart David G. Stork A Wiley-lnterscience Publication JOHN WILEY & SONS, INC. New York Chichester Weinheim Brisbane Singapore Toronto CONTENTS

More information

Applied Probability and Stochastic Processes

Applied Probability and Stochastic Processes Applied Probability and Stochastic Processes In Engineering and Physical Sciences MICHEL K. OCHI University of Florida A Wiley-Interscience Publication JOHN WILEY & SONS New York - Chichester Brisbane

More information

FUNDAMENTALS OF POLARIZED LIGHT

FUNDAMENTALS OF POLARIZED LIGHT FUNDAMENTALS OF POLARIZED LIGHT A STATISTICAL OPTICS APPROACH Christian Brosseau University of Brest, France A WILEY-INTERSCIENCE PUBLICATION JOHN WILEY & SONS, INC. New York - Chichester. Weinheim. Brisbane

More information

A User's Guide To Principal Components

A User's Guide To Principal Components A User's Guide To Principal Components J. EDWARD JACKSON A Wiley-Interscience Publication JOHN WILEY & SONS, INC. New York Chichester Brisbane Toronto Singapore Contents Preface Introduction 1. Getting

More information

Discriminant Analysis and Statistical Pattern Recognition

Discriminant Analysis and Statistical Pattern Recognition Discriminant Analysis and Statistical Pattern Recognition GEOFFREY J. McLACHLAN Department of Mathematics The University of Queensland St. Lucia, Queensland, Australia A Wiley-Interscience Publication

More information

Generalized, Linear, and Mixed Models

Generalized, Linear, and Mixed Models Generalized, Linear, and Mixed Models CHARLES E. McCULLOCH SHAYLER.SEARLE Departments of Statistical Science and Biometrics Cornell University A WILEY-INTERSCIENCE PUBLICATION JOHN WILEY & SONS, INC. New

More information

Monte Carlo Methods. Handbook of. University ofqueensland. Thomas Taimre. Zdravko I. Botev. Dirk P. Kroese. Universite de Montreal

Monte Carlo Methods. Handbook of. University ofqueensland. Thomas Taimre. Zdravko I. Botev. Dirk P. Kroese. Universite de Montreal Handbook of Monte Carlo Methods Dirk P. Kroese University ofqueensland Thomas Taimre University ofqueensland Zdravko I. Botev Universite de Montreal A JOHN WILEY & SONS, INC., PUBLICATION Preface Acknowledgments

More information

Mathematics for Economics and Finance

Mathematics for Economics and Finance Mathematics for Economics and Finance Michael Harrison and Patrick Waldron B 375482 Routledge Taylor & Francis Croup LONDON AND NEW YORK Contents List of figures ix List of tables xi Foreword xiii Preface

More information

Linear Models in Statistics

Linear Models in Statistics Linear Models in Statistics ALVIN C. RENCHER Department of Statistics Brigham Young University Provo, Utah A Wiley-Interscience Publication JOHN WILEY & SONS, INC. New York Chichester Weinheim Brisbane

More information

A Course in Time Series Analysis

A Course in Time Series Analysis A Course in Time Series Analysis Edited by DANIEL PENA Universidad Carlos III de Madrid GEORGE C. TIAO University of Chicago RUEY S. TSAY University of Chicago A Wiley-Interscience Publication JOHN WILEY

More information

Basic Mathematics for Chemists

Basic Mathematics for Chemists Basic Mathematics for Chemists Second Edition Peter Tebbutt JOHN WILEY & SONS Chichester. New York. Weinheim. Brisbane. Singapore. Toronto 2001 Contents Preface to the First Edition xii Preface to the

More information

HANDBOOK OF APPLICABLE MATHEMATICS

HANDBOOK OF APPLICABLE MATHEMATICS HANDBOOK OF APPLICABLE MATHEMATICS Chief Editor: Walter Ledermann Volume VI: Statistics PART A Edited by Emlyn Lloyd University of Lancaster A Wiley-Interscience Publication JOHN WILEY & SONS Chichester

More information

HANDBOOK OF APPLICABLE MATHEMATICS

HANDBOOK OF APPLICABLE MATHEMATICS HANDBOOK OF APPLICABLE MATHEMATICS Chief Editor: Walter Ledermann Volume II: Probability Emlyn Lloyd University oflancaster A Wiley-Interscience Publication JOHN WILEY & SONS Chichester - New York - Brisbane

More information

Stochastic Models. Edited by D.P. Heyman Bellcore. MJ. Sobel State University of New York at Stony Brook

Stochastic Models. Edited by D.P. Heyman Bellcore. MJ. Sobel State University of New York at Stony Brook Stochastic Models Edited by D.P. Heyman Bellcore MJ. Sobel State University of New York at Stony Brook 1990 NORTH-HOLLAND AMSTERDAM NEW YORK OXFORD TOKYO Contents Preface CHARTER 1 Point Processes R.F.

More information

Contents. Set Theory. Functions and its Applications CHAPTER 1 CHAPTER 2. Preface... (v)

Contents. Set Theory. Functions and its Applications CHAPTER 1 CHAPTER 2. Preface... (v) (vii) Preface... (v) CHAPTER 1 Set Theory Definition of Set... 1 Roster, Tabular or Enumeration Form... 1 Set builder Form... 2 Union of Set... 5 Intersection of Sets... 9 Distributive Laws of Unions and

More information

Principles of Equilibrium Statistical Mechanics

Principles of Equilibrium Statistical Mechanics Debashish Chowdhury, Dietrich Stauffer Principles of Equilibrium Statistical Mechanics WILEY-VCH Weinheim New York Chichester Brisbane Singapore Toronto Table of Contents Part I: THERMOSTATICS 1 1 BASIC

More information

Probability and Statistics

Probability and Statistics Probability and Statistics Probability and Statistics A.M. Mathai Associate Professor of Mathematics and Statistics McGill University, A-fontreal, Canada P. N. Rathie Professor of Statistics, Instituto

More information

The Fractional Fourier Transform with Applications in Optics and Signal Processing

The Fractional Fourier Transform with Applications in Optics and Signal Processing * The Fractional Fourier Transform with Applications in Optics and Signal Processing Haldun M. Ozaktas Bilkent University, Ankara, Turkey Zeev Zalevsky Tel Aviv University, Tel Aviv, Israel M. Alper Kutay

More information

Continuous Univariate Distributions

Continuous Univariate Distributions Continuous Univariate Distributions Volume 1 Second Edition NORMAN L. JOHNSON University of North Carolina Chapel Hill, North Carolina SAMUEL KOTZ University of Maryland College Park, Maryland N. BALAKRISHNAN

More information

A Guide to Modern Econometric:

A Guide to Modern Econometric: A Guide to Modern Econometric: 4th edition Marno Verbeek Rotterdam School of Management, Erasmus University, Rotterdam B 379887 )WILEY A John Wiley & Sons, Ltd., Publication Contents Preface xiii 1 Introduction

More information

Shigeji Fujita and Salvador V Godoy. Mathematical Physics WILEY- VCH. WILEY-VCH Verlag GmbH & Co. KGaA

Shigeji Fujita and Salvador V Godoy. Mathematical Physics WILEY- VCH. WILEY-VCH Verlag GmbH & Co. KGaA Shigeji Fujita and Salvador V Godoy Mathematical Physics WILEY- VCH WILEY-VCH Verlag GmbH & Co. KGaA Contents Preface XIII Table of Contents and Categories XV Constants, Signs, Symbols, and General Remarks

More information

Regression Analysis By Example

Regression Analysis By Example Regression Analysis By Example Third Edition SAMPRIT CHATTERJEE New York University ALI S. HADI Cornell University BERTRAM PRICE Price Associates, Inc. A Wiley-Interscience Publication JOHN WILEY & SONS,

More information

MESOSCOPIC QUANTUM OPTICS

MESOSCOPIC QUANTUM OPTICS MESOSCOPIC QUANTUM OPTICS by Yoshihisa Yamamoto Ata Imamoglu A Wiley-Interscience Publication JOHN WILEY & SONS, INC. New York Chichester Weinheim Brisbane Toronto Singapore Preface xi 1 Basic Concepts

More information

Statistical Methods in HYDROLOGY CHARLES T. HAAN. The Iowa State University Press / Ames

Statistical Methods in HYDROLOGY CHARLES T. HAAN. The Iowa State University Press / Ames Statistical Methods in HYDROLOGY CHARLES T. HAAN The Iowa State University Press / Ames Univariate BASIC Table of Contents PREFACE xiii ACKNOWLEDGEMENTS xv 1 INTRODUCTION 1 2 PROBABILITY AND PROBABILITY

More information

Contents. Part I: Fundamentals of Bayesian Inference 1

Contents. Part I: Fundamentals of Bayesian Inference 1 Contents Preface xiii Part I: Fundamentals of Bayesian Inference 1 1 Probability and inference 3 1.1 The three steps of Bayesian data analysis 3 1.2 General notation for statistical inference 4 1.3 Bayesian

More information

INTRODUCTION TO о JLXJLA Из А lv-/xvj_y JrJrl Y üv_>l3 Second Edition

INTRODUCTION TO о JLXJLA Из А lv-/xvj_y JrJrl Y üv_>l3 Second Edition INTRODUCTION TO о JLXJLA Из А lv-/xvj_y JrJrl Y üv_>l3 Second Edition Kerson Huang CRC Press Taylor & Francis Croup Boca Raton London New York CRC Press is an imprint of the Taylor & Francis Group an Informa

More information

MATHEMATICAL ANALYSIS

MATHEMATICAL ANALYSIS MATHEMATICAL ANALYSIS S. C. Malik Savita Arora Department of Mathematics S.G.T.B. Khalsa College University of Delhi Delhi, India JOHN WILEY & SONS NEW YORK CHICHESTER BRISBANE TORONTO SINGAPORE Preface

More information

INFORMATION THEORY AND STATISTICS

INFORMATION THEORY AND STATISTICS INFORMATION THEORY AND STATISTICS Solomon Kullback DOVER PUBLICATIONS, INC. Mineola, New York Contents 1 DEFINITION OF INFORMATION 1 Introduction 1 2 Definition 3 3 Divergence 6 4 Examples 7 5 Problems...''.

More information

Handbook of Regression Analysis

Handbook of Regression Analysis Handbook of Regression Analysis Samprit Chatterjee New York University Jeffrey S. Simonoff New York University WILEY A JOHN WILEY & SONS, INC., PUBLICATION CONTENTS Preface xi PARTI THE MULTIPLE LINEAR

More information

Subjective and Objective Bayesian Statistics

Subjective and Objective Bayesian Statistics Subjective and Objective Bayesian Statistics Principles, Models, and Applications Second Edition S. JAMES PRESS with contributions by SIDDHARTHA CHIB MERLISE CLYDE GEORGE WOODWORTH ALAN ZASLAVSKY \WILEY-

More information

Contents. Preface to Second Edition Preface to First Edition Abbreviations PART I PRINCIPLES OF STATISTICAL THINKING AND ANALYSIS 1

Contents. Preface to Second Edition Preface to First Edition Abbreviations PART I PRINCIPLES OF STATISTICAL THINKING AND ANALYSIS 1 Contents Preface to Second Edition Preface to First Edition Abbreviations xv xvii xix PART I PRINCIPLES OF STATISTICAL THINKING AND ANALYSIS 1 1 The Role of Statistical Methods in Modern Industry and Services

More information

STATISTICS; An Introductory Analysis. 2nd hidition TARO YAMANE NEW YORK UNIVERSITY A HARPER INTERNATIONAL EDITION

STATISTICS; An Introductory Analysis. 2nd hidition TARO YAMANE NEW YORK UNIVERSITY A HARPER INTERNATIONAL EDITION 2nd hidition TARO YAMANE NEW YORK UNIVERSITY STATISTICS; An Introductory Analysis A HARPER INTERNATIONAL EDITION jointly published by HARPER & ROW, NEW YORK, EVANSTON & LONDON AND JOHN WEATHERHILL, INC.,

More information

Kernel-based Approximation. Methods using MATLAB. Gregory Fasshauer. Interdisciplinary Mathematical Sciences. Michael McCourt.

Kernel-based Approximation. Methods using MATLAB. Gregory Fasshauer. Interdisciplinary Mathematical Sciences. Michael McCourt. SINGAPORE SHANGHAI Vol TAIPEI - Interdisciplinary Mathematical Sciences 19 Kernel-based Approximation Methods using MATLAB Gregory Fasshauer Illinois Institute of Technology, USA Michael McCourt University

More information

APPLIED FUNCTIONAL ANALYSIS

APPLIED FUNCTIONAL ANALYSIS APPLIED FUNCTIONAL ANALYSIS Second Edition JEAN-PIERRE AUBIN University of Paris-Dauphine Exercises by BERNARD CORNET and JEAN-MICHEL LASRY Translated by CAROLE LABROUSSE A Wiley-Interscience Publication

More information

STOCHASTIC PROCESSES FOR PHYSICISTS. Understanding Noisy Systems

STOCHASTIC PROCESSES FOR PHYSICISTS. Understanding Noisy Systems STOCHASTIC PROCESSES FOR PHYSICISTS Understanding Noisy Systems Stochastic processes are an essential part of numerous branches of physics, as well as biology, chemistry, and finance. This textbook provides

More information

TABLE OF CONTENTS CHAPTER 1 COMBINATORIAL PROBABILITY 1

TABLE OF CONTENTS CHAPTER 1 COMBINATORIAL PROBABILITY 1 TABLE OF CONTENTS CHAPTER 1 COMBINATORIAL PROBABILITY 1 1.1 The Probability Model...1 1.2 Finite Discrete Models with Equally Likely Outcomes...5 1.2.1 Tree Diagrams...6 1.2.2 The Multiplication Principle...8

More information

Economic Foundations of Symmetric Programming

Economic Foundations of Symmetric Programming Economic Foundations of Symmetric Programming QUIRINO PARIS University of California, Davis B 374309 CAMBRIDGE UNIVERSITY PRESS Foreword by Michael R. Caputo Preface page xv xvii 1 Introduction 1 Duality,

More information

Prerequisite: STATS 7 or STATS 8 or AP90 or (STATS 120A and STATS 120B and STATS 120C). AP90 with a minimum score of 3

Prerequisite: STATS 7 or STATS 8 or AP90 or (STATS 120A and STATS 120B and STATS 120C). AP90 with a minimum score of 3 University of California, Irvine 2017-2018 1 Statistics (STATS) Courses STATS 5. Seminar in Data Science. 1 Unit. An introduction to the field of Data Science; intended for entering freshman and transfers.

More information

Fundamentals of Probability Theory and Mathematical Statistics

Fundamentals of Probability Theory and Mathematical Statistics Fundamentals of Probability Theory and Mathematical Statistics Gerry Del Fiacco Math Center Metropolitan State University St. Paul, Minnesota June 6, 2016 1 Preface This collection of material was researched,

More information

Modern Urban and Regional Economics

Modern Urban and Regional Economics Modern Urban and Regional Economics SECOND EDITION Philip McCann OXFORD UNIVERSITY PRESS Contents List of figures List of tables Introduction xii xiv xvii Part I Urban and Regional Economic Models and

More information

Supermodular ordering of Poisson arrays

Supermodular ordering of Poisson arrays Supermodular ordering of Poisson arrays Bünyamin Kızıldemir Nicolas Privault Division of Mathematical Sciences School of Physical and Mathematical Sciences Nanyang Technological University 637371 Singapore

More information

CALCULUS GARRET J. ETGEN SALAS AND HILLE'S. ' MiIIIIIIH. I '////I! li II ii: ONE AND SEVERAL VARIABLES SEVENTH EDITION REVISED BY \

CALCULUS GARRET J. ETGEN SALAS AND HILLE'S. ' MiIIIIIIH. I '////I! li II ii: ONE AND SEVERAL VARIABLES SEVENTH EDITION REVISED BY \ / / / ' ' ' / / ' '' ' - -'/-' yy xy xy' y- y/ /: - y/ yy y /'}' / >' // yy,y-' 'y '/' /y , I '////I! li II ii: ' MiIIIIIIH IIIIII!l ii r-i: V /- A' /; // ;.1 " SALAS AND HILLE'S

More information

CALCULUS SALAS AND HILLE'S REVISED BY GARRET J. ETGEI ONE VARIABLE SEVENTH EDITION ' ' ' ' i! I! I! 11 ' ;' 1 ::: T.

CALCULUS SALAS AND HILLE'S REVISED BY GARRET J. ETGEI ONE VARIABLE SEVENTH EDITION ' ' ' ' i! I! I! 11 ' ;' 1 ::: T. ' ' ' ' i! I! I! 11 ' SALAS AND HILLE'S CALCULUS I ;' 1 1 ONE VARIABLE SEVENTH EDITION REVISED BY GARRET J. ETGEI y.-'' ' / ' ' ' / / // X / / / /-.-.,

More information

Location Theory and Decision Analysis

Location Theory and Decision Analysis Location Theory and Decision Analysis Analytics of Spatial Information Second Edition Yupo Chan Professor & Founding Chair Department of Systems Engineering Donaghey College of Engineering and Information

More information

PRINCIPLES OF STATISTICAL INFERENCE

PRINCIPLES OF STATISTICAL INFERENCE Advanced Series on Statistical Science & Applied Probability PRINCIPLES OF STATISTICAL INFERENCE from a Neo-Fisherian Perspective Luigi Pace Department of Statistics University ofudine, Italy Alessandra

More information

Matrix Differential Calculus with Applications in Statistics and Econometrics

Matrix Differential Calculus with Applications in Statistics and Econometrics Matrix Differential Calculus with Applications in Statistics and Econometrics Revised Edition JAN. R. MAGNUS CentERjor Economic Research, Tilburg University and HEINZ NEUDECKER Cesaro, Schagen JOHN WILEY

More information

Finite Population Sampling and Inference

Finite Population Sampling and Inference Finite Population Sampling and Inference A Prediction Approach RICHARD VALLIANT ALAN H. DORFMAN RICHARD M. ROYALL A Wiley-Interscience Publication JOHN WILEY & SONS, INC. New York Chichester Weinheim Brisbane

More information

PART I INTRODUCTION The meaning of probability Basic definitions for frequentist statistics and Bayesian inference Bayesian inference Combinatorics

PART I INTRODUCTION The meaning of probability Basic definitions for frequentist statistics and Bayesian inference Bayesian inference Combinatorics Table of Preface page xi PART I INTRODUCTION 1 1 The meaning of probability 3 1.1 Classical definition of probability 3 1.2 Statistical definition of probability 9 1.3 Bayesian understanding of probability

More information

PRINCIPLES OF PHYSICS. \Hp. Ni Jun TSINGHUA. Physics. From Quantum Field Theory. to Classical Mechanics. World Scientific. Vol.2. Report and Review in

PRINCIPLES OF PHYSICS. \Hp. Ni Jun TSINGHUA. Physics. From Quantum Field Theory. to Classical Mechanics. World Scientific. Vol.2. Report and Review in LONDON BEIJING HONG TSINGHUA Report and Review in Physics Vol2 PRINCIPLES OF PHYSICS From Quantum Field Theory to Classical Mechanics Ni Jun Tsinghua University, China NEW JERSEY \Hp SINGAPORE World Scientific

More information

PROBABILITY AND STOCHASTIC PROCESSES A Friendly Introduction for Electrical and Computer Engineers

PROBABILITY AND STOCHASTIC PROCESSES A Friendly Introduction for Electrical and Computer Engineers PROBABILITY AND STOCHASTIC PROCESSES A Friendly Introduction for Electrical and Computer Engineers Roy D. Yates Rutgers, The State University ofnew Jersey David J. Goodman Rutgers, The State University

More information

Use of Eigen values and eigen vectors to calculate higher transition probabilities

Use of Eigen values and eigen vectors to calculate higher transition probabilities The Lecture Contains : Markov-Bernoulli Chain Note Assignments Random Walks which are correlated Actual examples of Markov Chains Examples Use of Eigen values and eigen vectors to calculate higher transition

More information

Mathematical Methods and Economic Theory

Mathematical Methods and Economic Theory Mathematical Methods and Economic Theory Anjan Mukherji Subrata Guha C 263944 OXTORD UNIVERSITY PRESS Contents Preface SECTION I 1 Introduction 3 1.1 The Objective 3 1.2 The Tools for Section I 4 2 Basic

More information

Probabilistic Graphical Models

Probabilistic Graphical Models Probabilistic Graphical Models Lecture 11 CRFs, Exponential Family CS/CNS/EE 155 Andreas Krause Announcements Homework 2 due today Project milestones due next Monday (Nov 9) About half the work should

More information

Wolfgang Karl Härdle Leopold Simar. Applied Multivariate. Statistical Analysis. Fourth Edition. ö Springer

Wolfgang Karl Härdle Leopold Simar. Applied Multivariate. Statistical Analysis. Fourth Edition. ö Springer Wolfgang Karl Härdle Leopold Simar Applied Multivariate Statistical Analysis Fourth Edition ö Springer Contents Part I Descriptive Techniques 1 Comparison of Batches 3 1.1 Boxplots 4 1.2 Histograms 11

More information

STOCHASTIC MODELS OF CONTROL AND ECONOMIC DYNAMICS

STOCHASTIC MODELS OF CONTROL AND ECONOMIC DYNAMICS STOCHASTIC MODELS OF CONTROL AND ECONOMIC DYNAMICS V. I. ARKIN I. V. EVSTIGNEEV Central Economic Mathematics Institute Academy of Sciences of the USSR Moscow, Vavilova, USSR Translated and Edited by E.

More information

Elementary Lie Group Analysis and Ordinary Differential Equations

Elementary Lie Group Analysis and Ordinary Differential Equations Elementary Lie Group Analysis and Ordinary Differential Equations Nail H. Ibragimov University of North-West Mmabatho, South Africa JOHN WILEY & SONS Chichester New York Weinheim Brisbane Singapore Toronto

More information

From Practical Data Analysis with JMP, Second Edition. Full book available for purchase here. About This Book... xiii About The Author...

From Practical Data Analysis with JMP, Second Edition. Full book available for purchase here. About This Book... xiii About The Author... From Practical Data Analysis with JMP, Second Edition. Full book available for purchase here. Contents About This Book... xiii About The Author... xxiii Chapter 1 Getting Started: Data Analysis with JMP...

More information

Malvin H. Kalos, Paula A. Whitlock. Monte Carlo Methods. Second Revised and Enlarged Edition WILEY- BLACKWELL. WILEY-VCH Verlag GmbH & Co.

Malvin H. Kalos, Paula A. Whitlock. Monte Carlo Methods. Second Revised and Enlarged Edition WILEY- BLACKWELL. WILEY-VCH Verlag GmbH & Co. Malvin H. Kalos, Paula A. Whitlock Monte Carlo Methods Second Revised and Enlarged Edition WILEY- BLACKWELL WILEY-VCH Verlag GmbH & Co. KGaA v I Contents Preface to the Second Edition IX Preface to the

More information

An Introduction to Stochastic Modeling

An Introduction to Stochastic Modeling F An Introduction to Stochastic Modeling Fourth Edition Mark A. Pinsky Department of Mathematics Northwestern University Evanston, Illinois Samuel Karlin Department of Mathematics Stanford University Stanford,

More information

Irr. Statistical Methods in Experimental Physics. 2nd Edition. Frederick James. World Scientific. CERN, Switzerland

Irr. Statistical Methods in Experimental Physics. 2nd Edition. Frederick James. World Scientific. CERN, Switzerland Frederick James CERN, Switzerland Statistical Methods in Experimental Physics 2nd Edition r i Irr 1- r ri Ibn World Scientific NEW JERSEY LONDON SINGAPORE BEIJING SHANGHAI HONG KONG TAIPEI CHENNAI CONTENTS

More information

Contents Quantum-like Paradigm Classical (Kolmogorovian) and Quantum (Born) Probability

Contents Quantum-like Paradigm Classical (Kolmogorovian) and Quantum (Born) Probability 1 Quantum-like Paradigm... 1 1.1 Applications of Mathematical Apparatus of QM Outside ofphysics... 1 1.2 Irreducible Quantum Randomness, Copenhagen Interpretation... 2 1.3 Quantum Reductionism in Biology

More information

Institute of Actuaries of India

Institute of Actuaries of India Institute of Actuaries of India Subject CT3 Probability and Mathematical Statistics For 2018 Examinations Subject CT3 Probability and Mathematical Statistics Core Technical Syllabus 1 June 2017 Aim The

More information

Time Series: Theory and Methods

Time Series: Theory and Methods Peter J. Brockwell Richard A. Davis Time Series: Theory and Methods Second Edition With 124 Illustrations Springer Contents Preface to the Second Edition Preface to the First Edition vn ix CHAPTER 1 Stationary

More information

A SIGNAL THEORETIC INTRODUCTION TO RANDOM PROCESSES

A SIGNAL THEORETIC INTRODUCTION TO RANDOM PROCESSES A SIGNAL THEORETIC INTRODUCTION TO RANDOM PROCESSES ROY M. HOWARD Department of Electrical Engineering & Computing Curtin University of Technology Perth, Australia WILEY CONTENTS Preface xiii 1 A Signal

More information

COSMOLOGY The Origin and Evolution of Cosmic Structure

COSMOLOGY The Origin and Evolution of Cosmic Structure COSMOLOGY The Origin and Evolution of Cosmic Structure Peter COLES Astronomy Unit, Queen Mary & Westfield College, University of London, United Kingdom Francesco LUCCHIN Dipartimento di Astronomia, Universita

More information

The Bayes classifier

The Bayes classifier The Bayes classifier Consider where is a random vector in is a random variable (depending on ) Let be a classifier with probability of error/risk given by The Bayes classifier (denoted ) is the optimal

More information

Probability via Expectation

Probability via Expectation Peter Whittle Probability via Expectation Fourth Edition With 22 Illustrations Springer Contents Preface to the Fourth Edition Preface to the Third Edition Preface to the Russian Edition of Probability

More information

Testing Statistical Hypotheses

Testing Statistical Hypotheses E.L. Lehmann Joseph P. Romano Testing Statistical Hypotheses Third Edition 4y Springer Preface vii I Small-Sample Theory 1 1 The General Decision Problem 3 1.1 Statistical Inference and Statistical Decisions

More information

Mechanics of Viscoelastic Solids

Mechanics of Viscoelastic Solids Mechanics of Viscoelastic Solids Aleksey D. Drozdov Institute for Industrial Mathematics, Beersheba, Israel JOHN WILEY & SONS Chichester New York Weinheim Brisbane Toronto Singapore Contents Preface xi

More information

FINITE MIXTURE DISTRIBUTIONS

FINITE MIXTURE DISTRIBUTIONS MONOGRAPHS ON APPLl~[) PROBABILITY AND STATISTICS FINITE MIXTURE DISTRIBUTIONS MONOGRAPHS ON APPLIED PROBABILITY AND STATISTICS General Editor D.R. COX, FRS Also available in the series Probability, Statistics

More information

Platzhalter für Bild, Bild auf Titelfolie hinter das Logo einsetzen

Platzhalter für Bild, Bild auf Titelfolie hinter das Logo einsetzen Platzhalter für Bild, Bild auf Titelfolie hinter das Logo einsetzen PARAMetric UNCertainties, Budapest STOCHASTIC PROCESSES AND FIELDS Noémi Friedman Institut für Wissenschaftliches Rechnen, wire@tu-bs.de

More information

Information Dynamics Foundations and Applications

Information Dynamics Foundations and Applications Gustavo Deco Bernd Schürmann Information Dynamics Foundations and Applications With 89 Illustrations Springer PREFACE vii CHAPTER 1 Introduction 1 CHAPTER 2 Dynamical Systems: An Overview 7 2.1 Deterministic

More information

Applied Regression Modeling

Applied Regression Modeling Applied Regression Modeling A Business Approach Iain Pardoe University of Oregon Charles H. Lundquist College of Business Eugene, Oregon WILEY- INTERSCIENCE A JOHN WILEY & SONS, INC., PUBLICATION CONTENTS

More information

1 Introduction Overview of the Book How to Use this Book Introduction to R 10

1 Introduction Overview of the Book How to Use this Book Introduction to R 10 List of Tables List of Figures Preface xiii xv xvii 1 Introduction 1 1.1 Overview of the Book 3 1.2 How to Use this Book 7 1.3 Introduction to R 10 1.3.1 Arithmetic Operations 10 1.3.2 Objects 12 1.3.3

More information

THERMODYNAMICS THERMOSTATISTICS AND AN INTRODUCTION TO SECOND EDITION. University of Pennsylvania

THERMODYNAMICS THERMOSTATISTICS AND AN INTRODUCTION TO SECOND EDITION. University of Pennsylvania THERMODYNAMICS AND AN INTRODUCTION TO THERMOSTATISTICS SECOND EDITION HERBERT B. University of Pennsylvania CALLEN JOHN WILEY & SONS New York Chichester Brisbane Toronto Singapore CONTENTS PART I GENERAL

More information

Information theoretic solutions for correlated bivariate processes

Information theoretic solutions for correlated bivariate processes Economics Letters 97 (2007) 201 207 www.elsevier.com/locate/econbase Information theoretic solutions for correlated bivariate processes Wendy K. Tam Cho a,, George G. Judge b a Departments of Political

More information

Stochastic Processes. Theory for Applications. Robert G. Gallager CAMBRIDGE UNIVERSITY PRESS

Stochastic Processes. Theory for Applications. Robert G. Gallager CAMBRIDGE UNIVERSITY PRESS Stochastic Processes Theory for Applications Robert G. Gallager CAMBRIDGE UNIVERSITY PRESS Contents Preface page xv Swgg&sfzoMj ybr zmjfr%cforj owf fmdy xix Acknowledgements xxi 1 Introduction and review

More information

Introduction to the Mathematical and Statistical Foundations of Econometrics Herman J. Bierens Pennsylvania State University

Introduction to the Mathematical and Statistical Foundations of Econometrics Herman J. Bierens Pennsylvania State University Introduction to the Mathematical and Statistical Foundations of Econometrics 1 Herman J. Bierens Pennsylvania State University November 13, 2003 Revised: March 15, 2004 2 Contents Preface Chapter 1: Probability

More information

Probability Models in Electrical and Computer Engineering Mathematical models as tools in analysis and design Deterministic models Probability models

Probability Models in Electrical and Computer Engineering Mathematical models as tools in analysis and design Deterministic models Probability models Probability Models in Electrical and Computer Engineering Mathematical models as tools in analysis and design Deterministic models Probability models Statistical regularity Properties of relative frequency

More information

DESIGN AND ANALYSIS OF EXPERIMENTS Third Edition

DESIGN AND ANALYSIS OF EXPERIMENTS Third Edition DESIGN AND ANALYSIS OF EXPERIMENTS Third Edition Douglas C. Montgomery ARIZONA STATE UNIVERSITY JOHN WILEY & SONS New York Chichester Brisbane Toronto Singapore Contents Chapter 1. Introduction 1-1 What

More information

fiziks Institute for NET/JRF, GATE, IIT-JAM, JEST, TIFR and GRE in PHYSICAL SCIENCES

fiziks Institute for NET/JRF, GATE, IIT-JAM, JEST, TIFR and GRE in PHYSICAL SCIENCES Content-Thermodynamics & Statistical Mechanics 1. Kinetic theory of gases..(1-13) 1.1 Basic assumption of kinetic theory 1.1.1 Pressure exerted by a gas 1.2 Gas Law for Ideal gases: 1.2.1 Boyle s Law 1.2.2

More information

STA 4273H: Statistical Machine Learning

STA 4273H: Statistical Machine Learning STA 4273H: Statistical Machine Learning Russ Salakhutdinov Department of Statistics! rsalakhu@utstat.toronto.edu! http://www.utstat.utoronto.ca/~rsalakhu/ Sidney Smith Hall, Room 6002 Lecture 3 Linear

More information

AN INTRODUCTION TO PROBABILITY AND STATISTICS

AN INTRODUCTION TO PROBABILITY AND STATISTICS AN INTRODUCTION TO PROBABILITY AND STATISTICS WILEY SERIES IN PROBABILITY AND STATISTICS Established by WALTER A. SHEWHART and SAMUEL S. WILKS Editors: David J. Balding, Noel A. C. Cressie, Garrett M.

More information

Introduction to Spatial Analysis. Spatial Analysis. Session organization. Learning objectives. Module organization. GIS and spatial analysis

Introduction to Spatial Analysis. Spatial Analysis. Session organization. Learning objectives. Module organization. GIS and spatial analysis Introduction to Spatial Analysis I. Conceptualizing space Session organization Module : Conceptualizing space Module : Spatial analysis of lattice data Module : Spatial analysis of point patterns Module

More information

Self-Organization in Nonequilibrium Systems

Self-Organization in Nonequilibrium Systems Self-Organization in Nonequilibrium Systems From Dissipative Structures to Order through Fluctuations G. Nicolis Universite Libre de Bruxelles Belgium I. Prigogine Universite Libre de Bruxelles Belgium

More information

Multilevel Statistical Models: 3 rd edition, 2003 Contents

Multilevel Statistical Models: 3 rd edition, 2003 Contents Multilevel Statistical Models: 3 rd edition, 2003 Contents Preface Acknowledgements Notation Two and three level models. A general classification notation and diagram Glossary Chapter 1 An introduction

More information

Mathematics for Economics

Mathematics for Economics Mathematics for Economics third edition Michael Hoy John Livernois Chris McKenna Ray Rees Thanasis Stengos The MIT Press Cambridge, Massachusetts London, England c 2011 Massachusetts Institute of Technology

More information

Generalized Linear Models (GLZ)

Generalized Linear Models (GLZ) Generalized Linear Models (GLZ) Generalized Linear Models (GLZ) are an extension of the linear modeling process that allows models to be fit to data that follow probability distributions other than the

More information

Testing Statistical Hypotheses

Testing Statistical Hypotheses E.L. Lehmann Joseph P. Romano, 02LEu1 ttd ~Lt~S Testing Statistical Hypotheses Third Edition With 6 Illustrations ~Springer 2 The Probability Background 28 2.1 Probability and Measure 28 2.2 Integration.........

More information

STOCHASTIC PROCESSES IN PHYSICS AND CHEMISTRY

STOCHASTIC PROCESSES IN PHYSICS AND CHEMISTRY STOCHASTIC PROCESSES IN PHYSICS AND CHEMISTRY Third edition N.G. VAN KAMPEN Institute for Theoretical Physics of the University at Utrecht ELSEVIER Amsterdam Boston Heidelberg London New York Oxford Paris

More information

Uncertainty Per Krusell & D. Krueger Lecture Notes Chapter 6

Uncertainty Per Krusell & D. Krueger Lecture Notes Chapter 6 1 Uncertainty Per Krusell & D. Krueger Lecture Notes Chapter 6 1 A Two-Period Example Suppose the economy lasts only two periods, t =0, 1. The uncertainty arises in the income (wage) of period 1. Not that

More information

> DEPARTMENT OF MATHEMATICS AND COMPUTER SCIENCE GRAVIS 2016 BASEL. Logistic Regression. Pattern Recognition 2016 Sandro Schönborn University of Basel

> DEPARTMENT OF MATHEMATICS AND COMPUTER SCIENCE GRAVIS 2016 BASEL. Logistic Regression. Pattern Recognition 2016 Sandro Schönborn University of Basel Logistic Regression Pattern Recognition 2016 Sandro Schönborn University of Basel Two Worlds: Probabilistic & Algorithmic We have seen two conceptual approaches to classification: data class density estimation

More information

Evolutionary Theory. Sinauer Associates, Inc. Publishers Sunderland, Massachusetts U.S.A.

Evolutionary Theory. Sinauer Associates, Inc. Publishers Sunderland, Massachusetts U.S.A. Evolutionary Theory Mathematical and Conceptual Foundations Sean H. Rice Sinauer Associates, Inc. Publishers Sunderland, Massachusetts U.S.A. Contents Preface ix Introduction 1 CHAPTER 1 Selection on One

More information

Controlled Markov Processes and Viscosity Solutions

Controlled Markov Processes and Viscosity Solutions Controlled Markov Processes and Viscosity Solutions Wendell H. Fleming, H. Mete Soner Controlled Markov Processes and Viscosity Solutions Second Edition Wendell H. Fleming H.M. Soner Div. Applied Mathematics

More information

Linear Statistical Models

Linear Statistical Models Linear Statistical Models JAMES H. STAPLETON Michigan State University A Wiley-Interscience Publication JOHN WILEY & SONS, INC. New York 0 Chichester 0 Brisbane 0 Toronto 0 Singapore This Page Intentionally

More information

STATISTICAL ANALYSIS WITH MISSING DATA

STATISTICAL ANALYSIS WITH MISSING DATA STATISTICAL ANALYSIS WITH MISSING DATA SECOND EDITION Roderick J.A. Little & Donald B. Rubin WILEY SERIES IN PROBABILITY AND STATISTICS Statistical Analysis with Missing Data Second Edition WILEY SERIES

More information