Exploring Monte Carlo Methods
|
|
|
- Anis Fox
- 5 years ago
- Views:
Transcription
1 Exploring Monte Carlo Methods William L Dunn J. Kenneth Shultis AMSTERDAM BOSTON HEIDELBERG LONDON NEW YORK OXFORD PARIS SAN DIEGO SAN FRANCISCO SINGAPORE SYDNEY TOKYO ELSEVIER Academic Press Is an imprint of Elsevier
2 Preface xv 1 Introduction What Is Monte Carlo? A Brief History of Monte Carlo Monte Carlo as Quadrature Monte Carlo as Simulation Preview of Things to Come IS 1.6 Summary 16 2 The Basis of Monte Carlo Single Continuous Random Variables Probability Density Function Cumulative Distribution Function Some Example Distributions Population Mean, Variance, and Standard Deviation Sample Mean, Variance, and Standard Deviation Discrete Random Variables Multiple Random Variables Two Random Variables More Than Two Random Variables Sums of Random Variables The Law of Large Numbers The Central Limit Theorem Monte Carlo Quadrature Monte Carlo Simulation Summary 44 3 Pseudorandom Number Generators Linear Congruential Generators Structure of the Generated Random Numbers Characteristics of Good Random Number Generators Tests for Congruential Generators Spectral Test Number of HyperpJanes Distance between Points Other Tests 53
3 viii Contents 3.5 Practical Multiplicative Congruential Generators Generators with m = 2" Prime Modulus Generators A Minimal Standard Congruential Generator Coding the Minimal Standard Deficiencies of the Minimal Standard Generator Optimum Multipliers for Prime Modulus Generators Shuffling a Generator's Output Skipping Ahead Combining Generators Bit Mixing The Wichmann-Hill Generator The L'Ecuyer Generator Other Random Number Generators Multiple Recursive Generators Lagged Fibonacci Generators Add-with-Carry Generators Inversive Congruential Generators Nonlinear Congruential Generators Summary 65 4 Sampling, Scoring, and Precision Sampling Inverse CDF Method for Continuous Variables Inverse CDF Method for Discrete Variables Rejection Method Composition Method Rectangle-Wedge-Tail Decomposition Method Sampling from a Nearly Linear PDF Composition-Rejection Method Ratio of Uniforms Method Sampling from a Joint Distribution Sampling from Specific Distributions Scoring Statistical Tests to Assess Results Scoring for "Successes-Over-Trials" Simulation Use of Weights in Scoring Scoring for Multidimensional Integrals Accuracy and Precision Factors Affecting Accuracy Factors Affecting Precision Summary 93 5 Variance Reduction Techniques Use of Transformations 100
4 ix 5.2 Importance Sampling Application to Monte Carlo Integration Systematic Sampling Comparison to Straightforward Sampling Systematic Sampling to Evaluate an Integral Systematic Sampling as Importance Sampling Stratified Sampling Comparison to Straightforward Sampling Importance Sampling Versus Stratified Sampling Correlated Sampling Correlated Sampling With One Known Expected Value Antithetic Variates Partition of the Integration Volume Reduction of Dimensionality Russian Roulette and Splitting Application to Monte Carlo Simulation Combinations of Different Variance Reduction Techniques Biased Estimators Improved Monte Carlo Integration Schemes Weighted Monte Carlo Integration Monte Carlo Integration with Quasirandom Numbers Summary Markov Chain Monte Carlo Markov Chains to the Rescue Ergodic Markov Chains The Metropolis-Hastings Algorithm The Myth of Burn-in The Proposal Distribution Multidimensional Sampling The Gibbs Sampler Brief Review of Probability Concepts Bayes Theorem Inference and Decision Applications Implementing MCMC with Data Summary Inverse Monte Carlo Formulation of the Inverse Problem Integral Formulation Practical Formulation Optimization Formulation Monte Carlo Approaches to Solving Inverse Problems Inverse Monte Carlo by Iteration Symbolic Monte Carlo Uncertainties in Retrieved Values 179
5 X Contents The PDF Is Fully Known The PDF Is Unknown Unknown Parameter in Domain of x Inverse Monte Carlo by Simulation A Simple Two-Dimensional World General Applications of IMC Summary Linear Operator Equations 8.1 Linear 203 Algebraic Equations Solution of Linear Equations by Random Walks Solution of the Adjoint Linear Equations by Random Walks Solution of Linear Equations by Finite Random Walks Linear Integral Equations Monte Carlo Solution of a Simple Integral Equation A More General Procedure for Integral Equations Linear Differential Equations Monte Carlo Solutions of Linear Differential Equations Continuous Monte Carlo for Laplace's Equation Generalization to Three Dimensions Continuous Monte Carlo for Poisson's Equation The Two-dimensional Helmholtz Equation The Three-dimensional Helmholtz Equation Eigenvalue Problems Summary The Fundamentals of Neutral Particle Transport Description of the Radiation Field Directions and Solid Angles Particle Density Flux Density Fluence Current Vector Radiation Interactions with the Medium Interaction Coefficient Macroscopic Cross Section Attenuation of Uncollided Radiation Average Travel Distance Before an Interaction Scattering Interaction Coefficients Microscopic Cross Sections Reaction Rate Density Transport Equation Integral Forms of the Transport Equation Adjoint Transport Equation Derivation of the Adjoint Transport Equation 262
6 xi Utility of the Adjoint Solution Summary Monte Carlo Simulation of Neutral Particle Transport Basic Approach for Monte Carlo Transport Simulations Geometry Combinatorial Geometry Sources Isotropic Sources Path-Length Estimation Travel Distance in Each Cell Convex versus Concave Cells Effect of Computer Precision Purely Absorbing Media Type of Collision Scattering Interactions Photon Scattering from a Free Electron Neutron Scattering Time Dependence Particle Weights Scoring and Tallies Fluence Averaged Over a Surface Average Fluence in a Volume: Path-Length Estimator Average Fluence in a Volume: Reaction-Density Estimator Average Current Through a Surface Fluence at a Point: Next-Event Estimator Flow Through a Surface: Leakage Estimator An Example of One-Speed Particle Transport Monte Carlo Based on the Integral Transport Equation Integral Transport Equation Integral Equation Method as Simulation Variance Reduction and Nonanalog Methods Importance Sampling Truncation Methods Splitting and Russian Roulette Implicit Absorption Interaction Forcing Exponential Transformation Summary 304 A Some Common Probability Distributions 307 A.l Continuous Distributions 307 A. 1.1 Uniform Distribution 308 A. 1.2 Exponential Distribution 310 A. 1.3 Gamma Distribution 312
7 xii Contents A. 1.4 Beta Distribution 314 A. 1.5 Weibull Distribution 316 A. 1.6 Normal Distribution 317 A. 1.7 Lognormal Distribution 319 A. 1.8 Cauchy Distribution 319 A. 1.9 Chi-Squared Distribution 321 A.1.10 Student's t Distribution 322 A Pareto Distribution 323 A.2 Discrete Distributions 324 A.2.1 Bernoulli Distribution 325 A.2.2 Binomial Distribution 326 A.2.3 Geometric Distribution 329 A.2.4 Negative Binomial Distribution 329 A.2.5 Poisson Distribution 330 A. 3 Joint Distributions 333 A.3.1 Multivariate Normal Distribution 333 A. 3.2 Multinomial Distribution 334 B The Weak and Strong Laws of Large Numbers 337 B. 1 The Weak Law of Large Numbers 337 B. 2 The Strong Law of Large Numbers 339 B. 2.1 Difference Between the Weak and Strong Laws 339 B. 2.2 Other Subtleties 340 C Central Limit Theorem 341 C. l Moment Generating Functions 341 C. l.l Central Moments 342 C. 1.2 Some Properties of the MGF 342 C. 1.3 Uniqueness of the MGF 344 C. 2 Central Limit Theorem 344 D Some Popular Monte Carlo Codes for Particle Transport 347 D. l COG 347 D. l.l Current Version 347 D.1.2 Principal Authors 347 D.1.3 Operating Systems 347 D.1.4 Availability 347 D. 1.5 Applications 348 D.l.6 Significant Features 348 D.2 EGSnrc 349 D.2.1 Acronym and Current Version 349 D.2.2 Principal Authors 349 D.2.3 Operating Systems 349 D.2.4 Availability 349 D.2.5 Applications 349 D.2.6 Significant Features 350
8 xiii D.3 GEANT4 351 D.3.1 Current Version 351 D.3.2 Principal Author 351 D.3.3 Operating Systems 351 D.3.4 Availability 351 D.3.5 Applications 352 D.3.6 Significant Features 352 D.4 MCNP and MCNPX 353 D.4.1 Current Version and Availability 354 D.4.2 Principal Authors 354 D.4.3 Operating Systems 354 D.4.4 Applications 354 D.4.5 Significant Features 355 D.4.6 Additional Information 356 D.5 MCSHAPE 356 D.5.1 Acronyms 356 D.5.2 Current Version and Availability 356 D.5.3 Principal Authors 357 D.5.4 Operating Systems 357 D.5.5 Applications 357 D.5.6 Significant Features 358 D.6 PENELOPE 359 D.6.1 Acronyms and Current Version 359 D.6.2 Principal Authors 359 D.6.3 Operating Systems 359 D.6.4 Availability 359 D.6.5 Applications 359 D.6.6 Significant Features 361 D.7 SCALE 361 D.7.1 Acronyms 361 D.7.2 Current Version 362 D.7.3 Principal Author 362 D.7.4 Operating Systems 362 D.7.5 Availability 362 D.7.6 Applications 362 D.7.7 Significant Features 363 D.8 SRIM 364 D.8.1 Acronyms 364 D.8.2 Principal Authors 364 D.8.3 Operating Systems 364 D.8.4 Availability 364 D.8.5 Applications 364 D.8.6 Significant Features 365 D.9 TRIPOLI 365 D.9.1 Acronym and Current Version 365
9 D.9.2 Principal Authors 365 D.9.3 Operating Systems 366 D.9.4 Availability 366 D.9.5 Applications 366 D.9.6 Significant Features 366 E Minimal Standard Pseudorandom Number Generator 373 E.l FORTRAN E.2 FORTRAN E.3 Pascal 374 E.4 C and C E.5 Programming Considerations 375 Index 377
Fundamentals of Applied Probability and Random Processes
Fundamentals of Applied Probability and Random Processes,nd 2 na Edition Oliver C. Ibe University of Massachusetts, LoweLL, Massachusetts ip^ W >!^ AMSTERDAM BOSTON HEIDELBERG LONDON NEW YORK OXFORD PARIS
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
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,
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
Notation Precedence Diagram
Notation Precedence Diagram xix xxi CHAPTER 1 Introduction 1 1.1. Systems, Models, and Simulation 1 1.2. Verification, Approximation, and Validation 8 1.2.1. Verifying a Program 9 1.2.2. Approximation
Numerical Analysis for Statisticians
Kenneth Lange Numerical Analysis for Statisticians Springer Contents Preface v 1 Recurrence Relations 1 1.1 Introduction 1 1.2 Binomial CoefRcients 1 1.3 Number of Partitions of a Set 2 1.4 Horner's Method
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
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
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
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
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
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
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
Geophysical Data Analysis: Discrete Inverse Theory
Geophysical Data Analysis: Discrete Inverse Theory MATLAB Edition William Menke Lamont-Doherty Earth Observatory and Department of Earth and Environmental Sciences Columbia University. ' - Palisades, New
GEOPHYSICAL INVERSE THEORY AND REGULARIZATION PROBLEMS
Methods in Geochemistry and Geophysics, 36 GEOPHYSICAL INVERSE THEORY AND REGULARIZATION PROBLEMS Michael S. ZHDANOV University of Utah Salt Lake City UTAH, U.S.A. 2OO2 ELSEVIER Amsterdam - Boston - London
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
Digital Control Engineering Analysis and Design
Digital Control Engineering Analysis and Design M. Sami Fadali Antonio Visioli AMSTERDAM BOSTON HEIDELBERG LONDON NEW YORK OXFORD PARIS SAN DIEGO SAN FRANCISCO SINGAPORE SYDNEY TOKYO Academic Press is
Fundamentals of Nuclear Reactor Physics
Fundamentals of Nuclear Reactor Physics E. E. Lewis Professor of Mechanical Engineering McCormick School of Engineering and Applied Science Northwestern University AMSTERDAM BOSTON HEIDELBERG LONDON NEW
J. MEDHI STOCHASTIC MODELS IN QUEUEING THEORY
J. MEDHI STOCHASTIC MODELS IN QUEUEING THEORY SECOND EDITION ACADEMIC PRESS An imprint of Elsevier Science Amsterdam Boston London New York Oxford Paris San Diego San Francisco Singapore Sydney Tokyo Contents
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
System Dynamics for Engineering Students Concepts and Applications
System Dynamics for Engineering Students Concepts and Applications Nicolae Lobontiu University of Alaska Anchorage "Ж AMSTERDAM BOSTON HEIDELBERG LONDON NEW YORK OXFORD PARIS SAN DIEGO SAN FRANCISCO SINGAPORE
Modelling Operational Risk Using Bayesian Inference
Pavel V. Shevchenko Modelling Operational Risk Using Bayesian Inference 4y Springer 1 Operational Risk and Basel II 1 1.1 Introduction to Operational Risk 1 1.2 Defining Operational Risk 4 1.3 Basel II
APPLIED PARTIAL DIFFERENTIAL EQUATIONS
APPLIED PARTIAL DIFFERENTIAL EQUATIONS AN I N T R O D U C T I O N ALAN JEFFREY University of Newcastle-upon-Tyne ACADEMIC PRESS An imprint of Elsevier Science Amsterdam Boston London New York Oxford Paris
CONTENTS. Preface List of Symbols and Notation
CONTENTS Preface List of Symbols and Notation xi xv 1 Introduction and Review 1 1.1 Deterministic and Stochastic Models 1 1.2 What is a Stochastic Process? 5 1.3 Monte Carlo Simulation 10 1.4 Conditional
The Bayesian Choice. Christian P. Robert. From Decision-Theoretic Foundations to Computational Implementation. Second Edition.
Christian P. Robert The Bayesian Choice From Decision-Theoretic Foundations to Computational Implementation Second Edition With 23 Illustrations ^Springer" Contents Preface to the Second Edition Preface
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
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
Ronald Christensen. University of New Mexico. Albuquerque, New Mexico. Wesley Johnson. University of California, Irvine. Irvine, California
Texts in Statistical Science Bayesian Ideas and Data Analysis An Introduction for Scientists and Statisticians Ronald Christensen University of New Mexico Albuquerque, New Mexico Wesley Johnson University
Numerical Methods with MATLAB
Numerical Methods with MATLAB A Resource for Scientists and Engineers G. J. BÖRSE Lehigh University PWS Publishing Company I(T)P AN!NTERNATIONAL THOMSON PUBLISHING COMPANY Boston Albany Bonn Cincinnati
GAME PHYSICS ENGINE DEVELOPMENT
GAME PHYSICS ENGINE DEVELOPMENT IAN MILLINGTON i > AMSTERDAM BOSTON HEIDELBERG fpf l LONDON. NEW YORK. OXFORD ^. PARIS SAN DIEGO SAN FRANCISCO втс^н Г^ 4.«Mt-fSSKHbe. SINGAPORE. SYDNEY. TOKYO ELSEVIER
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.,
Monte-Carlo Methods and Stochastic Processes
Monte-Carlo Methods and Stochastic Processes From Linear to Non-Linear EMMANUEL GOBET ECOLE POLYTECHNIQUE - UNIVERSITY PARIS-SACLAY CMAP, PALAISEAU CEDEX, FRANCE CRC Press Taylor & Francis Group 6000 Broken
Differential Equations with Mathematica
Differential Equations with Mathematica THIRD EDITION Martha L. Abell James P. Braselton ELSEVIER ACADEMIC PRESS Amsterdam Boston Heidelberg London New York Oxford Paris San Diego San Francisco Singapore
EEC 686/785 Modeling & Performance Evaluation of Computer Systems. Lecture 19
EEC 686/785 Modeling & Performance Evaluation of Computer Systems Lecture 19 Department of Electrical and Computer Engineering Cleveland State University wenbing@ieee.org (based on Dr. Raj Jain s lecture
Foundations of Probability and Statistics
Foundations of Probability and Statistics William C. Rinaman Le Moyne College Syracuse, New York Saunders College Publishing Harcourt Brace College Publishers Fort Worth Philadelphia San Diego New York
Karl-Rudolf Koch Introduction to Bayesian Statistics Second Edition
Karl-Rudolf Koch Introduction to Bayesian Statistics Second Edition Karl-Rudolf Koch Introduction to Bayesian Statistics Second, updated and enlarged Edition With 17 Figures Professor Dr.-Ing., Dr.-Ing.
( ) ( ) Monte Carlo Methods Interested in. E f X = f x d x. Examples:
Monte Carlo Methods Interested in Examples: µ E f X = f x d x Type I error rate of a hypothesis test Mean width of a confidence interval procedure Evaluating a likelihood Finding posterior mean and variance
DIFFERENTIAL EQUATIONS, DYNAMICAL SYSTEMS, AND AN INTRODUCTION TO CHAOS
DIFFERENTIAL EQUATIONS, DYNAMICAL SYSTEMS, AND AN INTRODUCTION TO CHAOS Morris W. Hirsch University of California, Berkeley Stephen Smale University of California, Berkeley Robert L. Devaney Boston University
Outline. Simulation of a Single-Server Queueing System. EEC 686/785 Modeling & Performance Evaluation of Computer Systems.
EEC 686/785 Modeling & Performance Evaluation of Computer Systems Lecture 19 Outline Simulation of a Single-Server Queueing System Review of midterm # Department of Electrical and Computer Engineering
Pattern Recognition and Machine Learning
Christopher M. Bishop Pattern Recognition and Machine Learning ÖSpri inger Contents Preface Mathematical notation Contents vii xi xiii 1 Introduction 1 1.1 Example: Polynomial Curve Fitting 4 1.2 Probability
Probability Distributions Columns (a) through (d)
Discrete Probability Distributions Columns (a) through (d) Probability Mass Distribution Description Notes Notation or Density Function --------------------(PMF or PDF)-------------------- (a) (b) (c)
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
Table of Contents [ntc]
![Table of Contents [ntc]](/thumbs/93/114200514.jpg "Table of Contents [ntc]")
Table of Contents [ntc] 1. Introduction: Contents and Maps Table of contents [ntc] Equilibrium thermodynamics overview [nln6] Thermal equilibrium and nonequilibrium [nln1] Levels of description in statistical
The Finite Element Method for Solid and Structural Mechanics
The Finite Element Method for Solid and Structural Mechanics Sixth edition O.C. Zienkiewicz, CBE, FRS UNESCO Professor of Numerical Methods in Engineering International Centre for Numerical Methods in
DIFFERENTIAL EQUATIONS, DYNAMICAL SYSTEMS, AND AN INTRODUCTION TO CHAOS
DIFFERENTIAL EQUATIONS, DYNAMICAL SYSTEMS, AND AN INTRODUCTION TO CHAOS Morris W. Hirsch University of California, Berkeley Stephen Smale University of California, Berkeley Robert L. Devaney Boston University
Introduction to Bayesian Statistics and Markov Chain Monte Carlo Estimation. EPSY 905: Multivariate Analysis Spring 2016 Lecture #10: April 6, 2016
Introduction to Bayesian Statistics and Markov Chain Monte Carlo Estimation EPSY 905: Multivariate Analysis Spring 2016 Lecture #10: April 6, 2016 EPSY 905: Intro to Bayesian and MCMC Today s Class An
Mathematics for Engineers and Scientists
Mathematics for Engineers and Scientists Fourth edition ALAN JEFFREY University of Newcastle-upon-Tyne B CHAPMAN & HALL University and Professional Division London New York Tokyo Melbourne Madras Contents
IDL Advanced Math & Stats Module
IDL Advanced Math & Stats Module Regression List of Routines and Functions Multiple Linear Regression IMSL_REGRESSORS IMSL_MULTIREGRESS IMSL_MULTIPREDICT Generates regressors for a general linear model.
MATHEMATICAL HANDBOOK. Formulas and Tables
SCHAUM'S OUTLINE SERIES MATHEMATICAL HANDBOOK of Formulas and Tables Second Edition MURRAY R. SPIEGEL, Ph.D. Former Professor and Chairman Mathematics Department Rensselaer Polytechnic Institute Hartford
Probability for Statistics and Machine Learning
~Springer Anirban DasGupta Probability for Statistics and Machine Learning Fundamentals and Advanced Topics Contents Suggested Courses with Diffe~ent Themes........................... xix 1 Review of Univariate
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
GAME PHYSICS SECOND EDITION. дяййтаййг 1 *
GAME PHYSICS SECOND EDITION DAVID H. EBERLY дяййтаййг 1 * К AMSTERDAM BOSTON HEIDELBERG LONDON NEW YORK OXFORD PARIS SAN DIEGO SAN FRANCISCO SINGAPORE SYDNEY TOKYO MORGAN ELSEVIER Morgan Kaufmann Publishers
Review for the previous lecture
Lecture 1 and 13 on BST 631: Statistical Theory I Kui Zhang, 09/8/006 Review for the previous lecture Definition: Several discrete distributions, including discrete uniform, hypergeometric, Bernoulli,
Computational Fluid Dynamics
Computational Fluid Dynamics A Practical Approach Jiyuan Tu RMIT University, Australia Guan Heng Yeoh Australian Nuclear Science and Technology Organisation Chaoqun Liu University of Texas, Arlington ^fl
Linear Algebra and Probability
Linear Algebra and Probability for Computer Science Applications Ernest Davis CRC Press Taylor!* Francis Group Boca Raton London New York CRC Press is an imprint of the Taylor Sc Francis Croup, an informa
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
Markov Chain Monte Carlo (MCMC)
Markov Chain Monte Carlo (MCMC Dependent Sampling Suppose we wish to sample from a density π, and we can evaluate π as a function but have no means to directly generate a sample. Rejection sampling can
Three-Dimensional Electron Microscopy of Macromolecular Assemblies
Three-Dimensional Electron Microscopy of Macromolecular Assemblies Joachim Frank Wadsworth Center for Laboratories and Research State of New York Department of Health The Governor Nelson A. Rockefeller
Bayesian Methods for Machine Learning
Bayesian Methods for Machine Learning CS 584: Big Data Analytics Material adapted from Radford Neal s tutorial (http://ftp.cs.utoronto.ca/pub/radford/bayes-tut.pdf), Zoubin Ghahramni (http://hunch.net/~coms-4771/zoubin_ghahramani_bayesian_learning.pdf),
Appendix F. Computational Statistics Toolbox. The Computational Statistics Toolbox can be downloaded from:
Appendix F Computational Statistics Toolbox The Computational Statistics Toolbox can be downloaded from: http://www.infinityassociates.com http://lib.stat.cmu.edu. Please review the readme file for installation
STA 4273H: Statistical Machine Learning
STA 4273H: Statistical Machine Learning Russ Salakhutdinov Department of Computer Science! Department of Statistical Sciences! rsalakhu@cs.toronto.edu! h0p://www.cs.utoronto.ca/~rsalakhu/ Lecture 7 Approximate
Preface Introduction to Statistics and Data Analysis Overview: Statistical Inference, Samples, Populations, and Experimental Design The Role of
Preface Introduction to Statistics and Data Analysis Overview: Statistical Inference, Samples, Populations, and Experimental Design The Role of Probability Sampling Procedures Collection of Data Measures
Markov Chain Monte Carlo Using the Ratio-of-Uniforms Transformation. Luke Tierney Department of Statistics & Actuarial Science University of Iowa
Markov Chain Monte Carlo Using the Ratio-of-Uniforms Transformation Luke Tierney Department of Statistics & Actuarial Science University of Iowa Basic Ratio of Uniforms Method Introduced by Kinderman and
Parameter Estimation. William H. Jefferys University of Texas at Austin Parameter Estimation 7/26/05 1
Parameter Estimation William H. Jefferys University of Texas at Austin bill@bayesrules.net Parameter Estimation 7/26/05 1 Elements of Inference Inference problems contain two indispensable elements: Data
Machine Learning using Bayesian Approaches
Machine Learning using Bayesian Approaches Sargur N. Srihari University at Buffalo, State University of New York 1 Outline 1. Progress in ML and PR 2. Fully Bayesian Approach 1. Probability theory Bayes
Fundamental Probability and Statistics
Fundamental Probability and Statistics "There are known knowns. These are things we know that we know. There are known unknowns. That is to say, there are things that we know we don't know. But there are
Probability and Stochastic Processes
Probability and Stochastic Processes A Friendly Introduction Electrical and Computer Engineers Third Edition Roy D. Yates Rutgers, The State University of New Jersey David J. Goodman New York University
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
Part IA Probability. Definitions. Based on lectures by R. Weber Notes taken by Dexter Chua. Lent 2015
Part IA Probability Definitions Based on lectures by R. Weber Notes taken by Dexter Chua Lent 2015 These notes are not endorsed by the lecturers, and I have modified them (often significantly) after lectures.
Feature Extraction and Image Processing
Feature Extraction and Image Processing Second edition Mark S. Nixon Alberto S. Aguado :*авш JBK IIP AMSTERDAM BOSTON HEIDELBERG LONDON NEW YORK OXFORD PARIS SAN DIEGO SAN FRANCISCO SINGAPORE SYDNEY TOKYO
Distributions of Functions of Random Variables. 5.1 Functions of One Random Variable
Distributions of Functions of Random Variables 5.1 Functions of One Random Variable 5.2 Transformations of Two Random Variables 5.3 Several Random Variables 5.4 The Moment-Generating Function Technique
Boundary. DIFFERENTIAL EQUATIONS with Fourier Series and. Value Problems APPLIED PARTIAL. Fifth Edition. Richard Haberman PEARSON
APPLIED PARTIAL DIFFERENTIAL EQUATIONS with Fourier Series and Boundary Value Problems Fifth Edition Richard Haberman Southern Methodist University PEARSON Boston Columbus Indianapolis New York San Francisco
Contents LIST OF TABLES... LIST OF FIGURES... xvii. LIST OF LISTINGS... xxi PREFACE. ...xxiii
LIST OF TABLES... xv LIST OF FIGURES... xvii LIST OF LISTINGS... xxi PREFACE...xxiii CHAPTER 1. PERFORMANCE EVALUATION... 1 1.1. Performance evaluation... 1 1.2. Performance versus resources provisioning...
Integrated Arithmetic and Basic Algebra
211 771 406 III T H I R D E D I T I O N Integrated Arithmetic and Basic Algebra Bill E. Jordan Seminole Community College William P. Palow Miami-Dade College Boston San Francisco New York London Toronto
in Computer Simulations for Bioinformatics
Bi04a_ Unit 04a: Stochastic Processes and their Applications in Computer Simulations for Bioinformatics Stochastic Processes and their Applications in Computer Simulations for Bioinformatics Basic Probability
LINEAR AND NONLINEAR PROGRAMMING
LINEAR AND NONLINEAR PROGRAMMING Stephen G. Nash and Ariela Sofer George Mason University The McGraw-Hill Companies, Inc. New York St. Louis San Francisco Auckland Bogota Caracas Lisbon London Madrid Mexico
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-
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
2 Random Variable Generation
2 Random Variable Generation Most Monte Carlo computations require, as a starting point, a sequence of i.i.d. random variables with given marginal distribution. We describe here some of the basic methods
The Boltzmann Equation and Its Applications
Carlo Cercignani The Boltzmann Equation and Its Applications With 42 Illustrations Springer-Verlag New York Berlin Heidelberg London Paris Tokyo CONTENTS PREFACE vii I. BASIC PRINCIPLES OF THE KINETIC
Generating the Sample
STAT 80: Mathematical Statistics Monte Carlo Suppose you are given random variables X,..., X n whose joint density f (or distribution) is specified and a statistic T (X,..., X n ) whose distribution you
Simulating Random Variables
Simulating Random Variables Timothy Hanson Department of Statistics, University of South Carolina Stat 740: Statistical Computing 1 / 23 R has many built-in random number generators... Beta, gamma (also
Wave Propagation in Anisotropic, Anelastic, Porous and Electromagnetic Media
SECTION I. SEISMIC EXPLORATION Volume 38 WAVE FIELDS IN REAL MEDIA: Wave Propagation in Anisotropic, Anelastic, Porous and Electromagnetic Media (SECOND EDITION, REVISED AND EXTENDED) by Jose M. CARCIONE
Contents. 1 Basic Equations 1. Acknowledgment. 1.1 The Maxwell Equations Constitutive Relations 11
Preface Foreword Acknowledgment xvi xviii xix 1 Basic Equations 1 1.1 The Maxwell Equations 1 1.1.1 Boundary Conditions at Interfaces 4 1.1.2 Energy Conservation and Poynting s Theorem 9 1.2 Constitutive
STAT 302 Introduction to Probability Learning Outcomes. Textbook: A First Course in Probability by Sheldon Ross, 8 th ed.
STAT 302 Introduction to Probability Learning Outcomes Textbook: A First Course in Probability by Sheldon Ross, 8 th ed. Chapter 1: Combinatorial Analysis Demonstrate the ability to solve combinatorial
Basics of Monte Carlo Simulation
Basics of Monte Carlo Simulation condensed from a presentation by M. Asai Dennis Wright Geant4 Tutorial at Lund University 3 September 2018 Contents Historical review of Monte Carlo methods Basics of Monte
Cheng Soon Ong & Christian Walder. Canberra February June 2018
Cheng Soon Ong & Christian Walder Research Group and College of Engineering and Computer Science Canberra February June 2018 Outlines Overview Introduction Linear Algebra Probability Linear Regression
Markov chain Monte Carlo
Markov chain Monte Carlo Feng Li feng.li@cufe.edu.cn School of Statistics and Mathematics Central University of Finance and Economics Revised on April 24, 2017 Today we are going to learn... 1 Markov Chains
DETAILED CONTENTS PART I INTRODUCTION AND DESCRIPTIVE STATISTICS. 1. Introduction to Statistics
DETAILED CONTENTS About the Author Preface to the Instructor To the Student How to Use SPSS With This Book PART I INTRODUCTION AND DESCRIPTIVE STATISTICS 1. Introduction to Statistics 1.1 Descriptive and
Probability Distribution Summary Dr. Mohammed Hawa October 2007
Probability Distribution Summary Dr. Mohammed Hawa October 2007 There are many probability distributions that have been studied over the years. Each of which was developed based on observations of a particular
Introduction to Machine Learning CMU-10701
Introduction to Machine Learning CMU-10701 Markov Chain Monte Carlo Methods Barnabás Póczos & Aarti Singh Contents Markov Chain Monte Carlo Methods Goal & Motivation Sampling Rejection Importance Markov
F denotes cumulative density. denotes probability density function; (.)
BAYESIAN ANALYSIS: FOREWORDS Notation. System means the real thing and a model is an assumed mathematical form for the system.. he probability model class M contains the set of the all admissible models
College Algebra. Third Edition. Concepts Through Functions. Michael Sullivan. Michael Sullivan, III. Chicago State University. Joliet Junior College
College Algebra Concepts Through Functions Third Edition Michael Sullivan Chicago State University Michael Sullivan, III Joliet Junior College PEARSON Boston Columbus Indianapolis New York San Francisco
Distribution Fitting (Censored Data)
Distribution Fitting (Censored Data) Summary... 1 Data Input... 2 Analysis Summary... 3 Analysis Options... 4 Goodness-of-Fit Tests... 6 Frequency Histogram... 8 Comparison of Alternative Distributions...
16 : Markov Chain Monte Carlo (MCMC)
10-708: Probabilistic Graphical Models 10-708, Spring 2014 16 : Markov Chain Monte Carlo MCMC Lecturer: Matthew Gormley Scribes: Yining Wang, Renato Negrinho 1 Sampling from low-dimensional distributions
An Introduction to Computer Simulation Methods
An Introduction to Computer Simulation Methods Applications to Physical Systems Second Edition Harvey Gould Department of Physics Clark University Jan Tobochnik Department of Physics Kalamazoo College
INVERTED KUMARASWAMY DISTRIBUTION: PROPERTIES AND ESTIMATION
Pak. J. Statist. 2017 Vol. 33(1), 37-61 INVERTED KUMARASWAMY DISTRIBUTION: PROPERTIES AND ESTIMATION A. M. Abd AL-Fattah, A.A. EL-Helbawy G.R. AL-Dayian Statistics Department, Faculty of Commerce, AL-Azhar
Stream Ciphers and Number Theory
Stream Ciphers and Number Theory Revised Edition Thomas W. Cusick The State University of New York at Buffalo, NY, U.S.A. Cunsheng Ding The Hong Kong University of Science and Technology China Ari Renvall
Probability and Estimation. Alan Moses
Probability and Estimation Alan Moses Random variables and probability A random variable is like a variable in algebra (e.g., y=e x ), but where at least part of the variability is taken to be stochastic.
Principles of Bayesian Inference
Principles of Bayesian Inference Sudipto Banerjee University of Minnesota July 20th, 2008 1 Bayesian Principles Classical statistics: model parameters are fixed and unknown. A Bayesian thinks of parameters