Ronald Christensen. University of New Mexico. Albuquerque, New Mexico. Wesley Johnson. University of California, Irvine. Irvine, California

Size: px
Start display at page:

Download "Ronald Christensen. University of New Mexico. Albuquerque, New Mexico. Wesley Johnson. University of California, Irvine. Irvine, California"

Transcription

1 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 of California, Irvine Irvine, California Adam Branscum Oregon State University Corvallis, Oregon Timothy E. Hanson University of South Carolina Columbia, South Carolina & CRC Press Taylor & Francis Group Boca Raton London New York CRC Press is an imprint of the Taylor St Francis Group an informa business A CHAPMAN & HALL BOOK

2 Contents Preface XV 1 Prologue Probability of a Defective: Binomial Data Brass Alloy Zinc Content: Normal Data Armadillo Hunting: Poisson Data Abortion in Dairy Cattle: Survival Data Ache Hunting with Age Trends Lung Cancer Treatment: Log-Normal Regression Survival with Random Effects: Ache Hunting 8 2 Fundamental Ideas I Simple Probability Computations Science, Priors, and Prediction Statistical Models Posterior Analysis Commonly Used Distributions 33 3 Integration Versus Simulation Introduction WinBUGS I: Getting Started Method of Composition Monte Carlo Integration* Posterior Computations in R 51 4 Fundamental Ideas II Statistical Testing Checking Bayesian Models Predictive P-Values Lindley-Jeffreys Paradox Exchangeability Likelihood Functions Sufficient Statistics Analysis Using Predictive Distributions Flat Priors Data Translated Likelihoods Jeffreys' Priors Multiple Parameter Jeffreys' Prior* Bayes Factors* General Parametric Testing Nested Models Simulating Bayes Factors 75 ix

3 CONTENTS 4.9 Other Model Selection Criteria Bayesian Information Criterion LPML Deviance Information Criterion Final Comments Normal Approximations to Posteriors* Bayesian Consistency and Inconsistency Hierarchical Models Some Final Comments on Likelihoods* Identiflability and Noninformative Data 94 Comparing Populations Inference for Proportions Prior Distributions Reference Priors Informative Beta Priors Rare Events Non-Beta Priors Effect Measures Independent Binomials Case-Control Sampling Inference for Normal Populations lit Reference Priors Conjugate Priors Independence Priors Some Curious Distributional Results* Two-Sample Normal Model Inference for Rates One-Sample Poisson Data Informative Priors Reference Priors Two-Sample Poisson Data Sample Size Determination* 136 Simulations Generating Random Samples Traditional Monte Carlo Methods Acceptance-Rejection Sampling Importance Sampling Markov Chain Monte Carlo Markov Chains Gibbs Sampling Proof that p(6) is the Stationary Distribution in the Two-Block Case* Metropolis Algorithm Proof that p(6) is the Stationary Distribution* Slice Sampling Checking MCMC Samples 159

4 CONTENTS xi 7 Basic Concepts of Regression Introduction Data Notation and Format Predictive Models: An Overview Modeling with Linear Structures Continuous Predictors Binary Predictors Multi-Category Predictors Predictor Selection Several Categorical Covariates Confounding Effect Modification/Interaction Two Categorical Predictors One Continuous and One Categorical Predictor Two Continuous Predictors Illustration: FEV Data Binomial Regression The Sampling Model Binomial Regression Analysis Predictive Probabilities Inference for Regression Coefficients Inference for LDa Model Checking Box's Method Link Selection Prior Distributions Simple Regression General Regression Prior Elicitation Data Augmentation Priors Standardized Variables Reference Priors Partial Prior Information Partial Priors: Theoretical Considerations* Mixed Models Prior Elicitation Mixed Model Likelihood Gibbs Sampling and Centering* Linear Regression The Sampling Model Reference Priors Least Squares Estimation Posterior Analysis A Proper Reference Prior Conjugate Priors Independence Priors Prior on j Prior on t Partial Prior Information Inference and Displays 238

5 xii CONTENTS Gibbs Sampling* WinBUGS and R Code ANOVA Independence Prior Allocation and Diagnosis Hierarchical Priors and Models Model Diagnostics Model Selection Nonlinear Regression* Correlated Data Introduction Mixed Models Random Intercept Model Random Slopes and Random Intercepts Multivariate Normal Models Parameterized Covariance Matrices Analytic Formulas for CS and AR(1) Precision Matrices Multivariate Normal Regression Posterior Sampling and Missing Data Count Data Poisson Regression Poisson Regression for Rates Over-Dispersion and Mixtures of Poissons Zero-Inflated Poisson Data SAS Analysis of Foot-and-Mouth Disease Data Longitudinal Data Time to Event Data Introduction Survival and Hazard Functions Censoring The Likelihood One-Sample Models Distributional Models Posterior Analysis Log-Normal Data Exponential Data WinBUGS for Censored Data WeibullData Prediction Interval Censoring Two-Sample Data Two-Sample Exponential Model Two-Sample Weibull Model Two-Sample Log-Normal Model Plotting Survival and Hazard Functions' 322

6 CONTENTS xiii 13 Time to Event Regression Accelerated Failure Time Models Abortion Data Prior Elicitation for AFTs Specifying the Marginal Prior for j Partial Prior Information for/ Uncertainty About t Case Deletion Diagnostics for AFT Models Predictive Influence Bayes Factor Model Selection Sensitivity Analysis Final Comments Proportional Hazards Modeling The Proportional Hazards (PH) Model A Baseline Hazard Model The Likelihood NoninformativeData* Priors for J Priors for X Our Data Model WinBUGSCode Posterior Analysis for Leukemia Data SAS Analysis of Leukemia Data Another Example Survival with Random Effects Binary Diagnostic Tests Basic Ideas One Test, One Population Gold-Standard Data No Gold-Standard Data Two Tests, Two Populations Methods for Conditionally Independent Tests Prevalence Distributions Nonparametric Models Flexible Density Shapes Finite Mixtures Identifiability Issues* Dirichlet Process Mixtures: Infinite Mixtures Mixtures of Polya Trees Flexible Regression Functions Proportional Hazards Modeling 414 Appendix A: Matrices and Vectors 419 A.l Matrix Addition and Subtraction 420 A.2 Scalar Multiplication 420 A.3 Matrix Multiplication 420 A.4 Special Matrices 422 A.5 Linear Dependence and Rank 423 A.6 Inverse Matrices 424 A.7 A List of Useful Properties 426

7 xiv CONTENTS A.8 Eigenvalues and Eigenvectors 426 A.9 Properties of Determinants 428 A. 10 Calculus and Taylor's Theorem 428 A. 11 Partitioned Matrices 428 Appendix B: Probability 431 B. 1 Univariate Probability 431 B.2 Multivariate Probability 432 B.2.1 Joint Distribution of Two Vectors 434 B.2.2 Conditional Distributions 434 B.2.3 Independence 436 B.2.4 Moment Generating Functions 437 B.2.5 Change of Variables 437 B. 3 Models and Conditional Independence 438 Appendix C: Getting Started in R 443 C. l Getting R 443 C.2 Some R Basics 443 C.3 User-Contributed Packages 446 C.4 Reading Data 447 C.5 Graphing 447 C.6 Interface Between R and WinBUGS 456 C.7 Writing New R Functions 456 References 459 Author Index 467 Subject Index 473

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

Generalized Linear. Mixed Models. Methods and Applications. Modern Concepts, Walter W. Stroup. Texts in Statistical Science.

Generalized Linear. Mixed Models. Methods and Applications. Modern Concepts, Walter W. Stroup. Texts in Statistical Science. Texts in Statistical Science Generalized Linear Mixed Models Modern Concepts, Methods and Applications Walter W. Stroup CRC Press Taylor & Francis Croup Boca Raton London New York CRC Press is an imprint

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

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

The Bayesian Choice. Christian P. Robert. From Decision-Theoretic Foundations to Computational Implementation. Second Edition.

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

More information

Pattern Recognition and Machine Learning

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

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

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

A general mixed model approach for spatio-temporal regression data

A general mixed model approach for spatio-temporal regression data A general mixed model approach for spatio-temporal regression data Thomas Kneib, Ludwig Fahrmeir & Stefan Lang Department of Statistics, Ludwig-Maximilians-University Munich 1. Spatio-temporal regression

More information

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 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

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

Experimental Design and Data Analysis for Biologists

Experimental Design and Data Analysis for Biologists Experimental Design and Data Analysis for Biologists Gerry P. Quinn Monash University Michael J. Keough University of Melbourne CAMBRIDGE UNIVERSITY PRESS Contents Preface page xv I I Introduction 1 1.1

More information

Wiley. Methods and Applications of Linear Models. Regression and the Analysis. of Variance. Third Edition. Ishpeming, Michigan RONALD R.

Wiley. Methods and Applications of Linear Models. Regression and the Analysis. of Variance. Third Edition. Ishpeming, Michigan RONALD R. Methods and Applications of Linear Models Regression and the Analysis of Variance Third Edition RONALD R. HOCKING PenHock Statistical Consultants Ishpeming, Michigan Wiley Contents Preface to the Third

More information

Numerical Analysis for Statisticians

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

More information

Modelling geoadditive survival data

Modelling geoadditive survival data Modelling geoadditive survival data Thomas Kneib & Ludwig Fahrmeir Department of Statistics, Ludwig-Maximilians-University Munich 1. Leukemia survival data 2. Structured hazard regression 3. Mixed model

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

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

Linear Algebra and Probability

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

More information

Sample Size Calculations for ROC Studies: Parametric Robustness and Bayesian Nonparametrics

Sample Size Calculations for ROC Studies: Parametric Robustness and Bayesian Nonparametrics Baylor Health Care System From the SelectedWorks of unlei Cheng Spring January 30, 01 Sample Size Calculations for ROC Studies: Parametric Robustness and Bayesian Nonparametrics unlei Cheng, Baylor Health

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

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

Modelling Operational Risk Using Bayesian Inference

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

More information

Bayesian Inference. Chapter 4: Regression and Hierarchical Models

Bayesian Inference. Chapter 4: Regression and Hierarchical Models Bayesian Inference Chapter 4: Regression and Hierarchical Models Conchi Ausín and Mike Wiper Department of Statistics Universidad Carlos III de Madrid Master in Business Administration and Quantitative

More information

Chapter 4 Multi-factor Treatment Designs with Multiple Error Terms 93

Chapter 4 Multi-factor Treatment Designs with Multiple Error Terms 93 Contents Preface ix Chapter 1 Introduction 1 1.1 Types of Models That Produce Data 1 1.2 Statistical Models 2 1.3 Fixed and Random Effects 4 1.4 Mixed Models 6 1.5 Typical Studies and the Modeling Issues

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

Review. Timothy Hanson. Department of Statistics, University of South Carolina. Stat 770: Categorical Data Analysis

Review. Timothy Hanson. Department of Statistics, University of South Carolina. Stat 770: Categorical Data Analysis Review Timothy Hanson Department of Statistics, University of South Carolina Stat 770: Categorical Data Analysis 1 / 22 Chapter 1: background Nominal, ordinal, interval data. Distributions: Poisson, binomial,

More information

Penalized Loss functions for Bayesian Model Choice

Penalized Loss functions for Bayesian Model Choice Penalized Loss functions for Bayesian Model Choice Martyn International Agency for Research on Cancer Lyon, France 13 November 2009 The pure approach For a Bayesian purist, all uncertainty is represented

More information

Mixture modelling of recurrent event times with long-term survivors: Analysis of Hutterite birth intervals. John W. Mac McDonald & Alessandro Rosina

Mixture modelling of recurrent event times with long-term survivors: Analysis of Hutterite birth intervals. John W. Mac McDonald & Alessandro Rosina Mixture modelling of recurrent event times with long-term survivors: Analysis of Hutterite birth intervals John W. Mac McDonald & Alessandro Rosina Quantitative Methods in the Social Sciences Seminar -

More information

Markov Chain Monte Carlo in Practice

Markov Chain Monte Carlo in Practice Markov Chain Monte Carlo in Practice Edited by W.R. Gilks Medical Research Council Biostatistics Unit Cambridge UK S. Richardson French National Institute for Health and Medical Research Vilejuif France

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

Bayesian Inference. Chapter 4: Regression and Hierarchical Models

Bayesian Inference. Chapter 4: Regression and Hierarchical Models Bayesian Inference Chapter 4: Regression and Hierarchical Models Conchi Ausín and Mike Wiper Department of Statistics Universidad Carlos III de Madrid Advanced Statistics and Data Mining Summer School

More information

STA 4273H: Statistical Machine Learning

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

More information

BAYESIAN METHODS FOR VARIABLE SELECTION WITH APPLICATIONS TO HIGH-DIMENSIONAL DATA

BAYESIAN METHODS FOR VARIABLE SELECTION WITH APPLICATIONS TO HIGH-DIMENSIONAL DATA BAYESIAN METHODS FOR VARIABLE SELECTION WITH APPLICATIONS TO HIGH-DIMENSIONAL DATA Intro: Course Outline and Brief Intro to Marina Vannucci Rice University, USA PASI-CIMAT 04/28-30/2010 Marina Vannucci

More information

Bayesian Methods for Machine Learning

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),

More information

CPSC 540: Machine Learning

CPSC 540: Machine Learning CPSC 540: Machine Learning MCMC and Non-Parametric Bayes Mark Schmidt University of British Columbia Winter 2016 Admin I went through project proposals: Some of you got a message on Piazza. No news is

More information

DESIGNING EXPERIMENTS AND ANALYZING DATA A Model Comparison Perspective

DESIGNING EXPERIMENTS AND ANALYZING DATA A Model Comparison Perspective DESIGNING EXPERIMENTS AND ANALYZING DATA A Model Comparison Perspective Second Edition Scott E. Maxwell Uniuersity of Notre Dame Harold D. Delaney Uniuersity of New Mexico J,t{,.?; LAWRENCE ERLBAUM ASSOCIATES,

More information

Elements of Multivariate Time Series Analysis

Elements of Multivariate Time Series Analysis Gregory C. Reinsel Elements of Multivariate Time Series Analysis Second Edition With 14 Figures Springer Contents Preface to the Second Edition Preface to the First Edition vii ix 1. Vector Time Series

More information

Non-Parametric Bayes

Non-Parametric Bayes Non-Parametric Bayes Mark Schmidt UBC Machine Learning Reading Group January 2016 Current Hot Topics in Machine Learning Bayesian learning includes: Gaussian processes. Approximate inference. Bayesian

More information

Bayesian Prediction of Code Output. ASA Albuquerque Chapter Short Course October 2014

Bayesian Prediction of Code Output. ASA Albuquerque Chapter Short Course October 2014 Bayesian Prediction of Code Output ASA Albuquerque Chapter Short Course October 2014 Abstract This presentation summarizes Bayesian prediction methodology for the Gaussian process (GP) surrogate representation

More information

Econometric Analysis of Cross Section and Panel Data

Econometric Analysis of Cross Section and Panel Data Econometric Analysis of Cross Section and Panel Data Jeffrey M. Wooldridge / The MIT Press Cambridge, Massachusetts London, England Contents Preface Acknowledgments xvii xxiii I INTRODUCTION AND BACKGROUND

More information

Bayesian non-parametric model to longitudinally predict churn

Bayesian non-parametric model to longitudinally predict churn Bayesian non-parametric model to longitudinally predict churn Bruno Scarpa Università di Padova Conference of European Statistics Stakeholders Methodologists, Producers and Users of European Statistics

More information

Bayesian Linear Regression

Bayesian Linear Regression Bayesian Linear Regression Sudipto Banerjee 1 Biostatistics, School of Public Health, University of Minnesota, Minneapolis, Minnesota, U.S.A. September 15, 2010 1 Linear regression models: a Bayesian perspective

More information

Introduction to. Process Control. Ahmet Palazoglu. Second Edition. Jose A. Romagnoli. CRC Press. Taylor & Francis Group. Taylor & Francis Group,

Introduction to. Process Control. Ahmet Palazoglu. Second Edition. Jose A. Romagnoli. CRC Press. Taylor & Francis Group. Taylor & Francis Group, Introduction to Process Control Second Edition Jose A. Romagnoli Ahmet Palazoglu CRC Press Taylor & Francis Group Boca Raton London NewYork CRC Press is an imprint of the Taylor & Francis Group, an informa

More information

3 Joint Distributions 71

3 Joint Distributions 71 2.2.3 The Normal Distribution 54 2.2.4 The Beta Density 58 2.3 Functions of a Random Variable 58 2.4 Concluding Remarks 64 2.5 Problems 64 3 Joint Distributions 71 3.1 Introduction 71 3.2 Discrete Random

More information

Exploring Monte Carlo Methods

Exploring Monte Carlo Methods 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

More information

Analysing geoadditive regression data: a mixed model approach

Analysing geoadditive regression data: a mixed model approach Analysing geoadditive regression data: a mixed model approach Institut für Statistik, Ludwig-Maximilians-Universität München Joint work with Ludwig Fahrmeir & Stefan Lang 25.11.2005 Spatio-temporal regression

More information

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 Edition Karl-Rudolf Koch Introduction to Bayesian Statistics Second, updated and enlarged Edition With 17 Figures Professor Dr.-Ing., Dr.-Ing.

More information

Contents. Acknowledgments. xix

Contents. Acknowledgments. xix Table of Preface Acknowledgments page xv xix 1 Introduction 1 The Role of the Computer in Data Analysis 1 Statistics: Descriptive and Inferential 2 Variables and Constants 3 The Measurement of Variables

More information

Log Gaussian Cox Processes. Chi Group Meeting February 23, 2016

Log Gaussian Cox Processes. Chi Group Meeting February 23, 2016 Log Gaussian Cox Processes Chi Group Meeting February 23, 2016 Outline Typical motivating application Introduction to LGCP model Brief overview of inference Applications in my work just getting started

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

Part 8: GLMs and Hierarchical LMs and GLMs

Part 8: GLMs and Hierarchical LMs and GLMs Part 8: GLMs and Hierarchical LMs and GLMs 1 Example: Song sparrow reproductive success Arcese et al., (1992) provide data on a sample from a population of 52 female song sparrows studied over the course

More information

Bayesian inference. Fredrik Ronquist and Peter Beerli. October 3, 2007

Bayesian inference. Fredrik Ronquist and Peter Beerli. October 3, 2007 Bayesian inference Fredrik Ronquist and Peter Beerli October 3, 2007 1 Introduction The last few decades has seen a growing interest in Bayesian inference, an alternative approach to statistical inference.

More information

Bagging During Markov Chain Monte Carlo for Smoother Predictions

Bagging During Markov Chain Monte Carlo for Smoother Predictions Bagging During Markov Chain Monte Carlo for Smoother Predictions Herbert K. H. Lee University of California, Santa Cruz Abstract: Making good predictions from noisy data is a challenging problem. Methods

More information

Index. Regression Models for Time Series Analysis. Benjamin Kedem, Konstantinos Fokianos Copyright John Wiley & Sons, Inc. ISBN.

Index. Regression Models for Time Series Analysis. Benjamin Kedem, Konstantinos Fokianos Copyright John Wiley & Sons, Inc. ISBN. Regression Models for Time Series Analysis. Benjamin Kedem, Konstantinos Fokianos Copyright 0 2002 John Wiley & Sons, Inc. ISBN. 0-471-36355-3 Index Adaptive rejection sampling, 233 Adjacent categories

More information

PROBABILITY DISTRIBUTIONS. J. Elder CSE 6390/PSYC 6225 Computational Modeling of Visual Perception

PROBABILITY DISTRIBUTIONS. J. Elder CSE 6390/PSYC 6225 Computational Modeling of Visual Perception PROBABILITY DISTRIBUTIONS Credits 2 These slides were sourced and/or modified from: Christopher Bishop, Microsoft UK Parametric Distributions 3 Basic building blocks: Need to determine given Representation:

More information

Theory and Methods of Statistical Inference

Theory and Methods of Statistical Inference PhD School in Statistics cycle XXIX, 2014 Theory and Methods of Statistical Inference Instructors: B. Liseo, L. Pace, A. Salvan (course coordinator), N. Sartori, A. Tancredi, L. Ventura Syllabus Some prerequisites:

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

Subject CS1 Actuarial Statistics 1 Core Principles

Subject CS1 Actuarial Statistics 1 Core Principles Institute of Actuaries of India Subject CS1 Actuarial Statistics 1 Core Principles For 2019 Examinations Aim The aim of the Actuarial Statistics 1 subject is to provide a grounding in mathematical and

More information

PATTERN RECOGNITION AND MACHINE LEARNING CHAPTER 2: PROBABILITY DISTRIBUTIONS

PATTERN RECOGNITION AND MACHINE LEARNING CHAPTER 2: PROBABILITY DISTRIBUTIONS PATTERN RECOGNITION AND MACHINE LEARNING CHAPTER 2: PROBABILITY DISTRIBUTIONS Parametric Distributions Basic building blocks: Need to determine given Representation: or? Recall Curve Fitting Binary Variables

More information

Multivariate Survival Analysis

Multivariate Survival Analysis Multivariate Survival Analysis Previously we have assumed that either (X i, δ i ) or (X i, δ i, Z i ), i = 1,..., n, are i.i.d.. This may not always be the case. Multivariate survival data can arise in

More information

Markov Chain Monte Carlo

Markov Chain Monte Carlo Markov Chain Monte Carlo Recall: To compute the expectation E ( h(y ) ) we use the approximation E(h(Y )) 1 n n h(y ) t=1 with Y (1),..., Y (n) h(y). Thus our aim is to sample Y (1),..., Y (n) from f(y).

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

Introduction to Statistical Analysis

Introduction to Statistical Analysis Introduction to Statistical Analysis Changyu Shen Richard A. and Susan F. Smith Center for Outcomes Research in Cardiology Beth Israel Deaconess Medical Center Harvard Medical School Objectives Descriptive

More information

Statistícal Methods for Spatial Data Analysis

Statistícal Methods for Spatial Data Analysis Texts in Statistícal Science Statistícal Methods for Spatial Data Analysis V- Oliver Schabenberger Carol A. Gotway PCT CHAPMAN & K Contents Preface xv 1 Introduction 1 1.1 The Need for Spatial Analysis

More information

7. Estimation and hypothesis testing. Objective. Recommended reading

7. Estimation and hypothesis testing. Objective. Recommended reading 7. Estimation and hypothesis testing Objective In this chapter, we show how the election of estimators can be represented as a decision problem. Secondly, we consider the problem of hypothesis testing

More information

Local Polynomial Modelling and Its Applications

Local Polynomial Modelling and Its Applications Local Polynomial Modelling and Its Applications J. Fan Department of Statistics University of North Carolina Chapel Hill, USA and I. Gijbels Institute of Statistics Catholic University oflouvain Louvain-la-Neuve,

More information

10. Exchangeability and hierarchical models Objective. Recommended reading

10. Exchangeability and hierarchical models Objective. Recommended reading 10. Exchangeability and hierarchical models Objective Introduce exchangeability and its relation to Bayesian hierarchical models. Show how to fit such models using fully and empirical Bayesian methods.

More information

Nonparametric Bayesian Methods (Gaussian Processes)

Nonparametric Bayesian Methods (Gaussian Processes) [70240413 Statistical Machine Learning, Spring, 2015] Nonparametric Bayesian Methods (Gaussian Processes) Jun Zhu dcszj@mail.tsinghua.edu.cn http://bigml.cs.tsinghua.edu.cn/~jun State Key Lab of Intelligent

More information

Survival Analysis Math 434 Fall 2011

Survival Analysis Math 434 Fall 2011 Survival Analysis Math 434 Fall 2011 Part IV: Chap. 8,9.2,9.3,11: Semiparametric Proportional Hazards Regression Jimin Ding Math Dept. www.math.wustl.edu/ jmding/math434/fall09/index.html Basic Model Setup

More information

Technical Vignette 5: Understanding intrinsic Gaussian Markov random field spatial models, including intrinsic conditional autoregressive models

Technical Vignette 5: Understanding intrinsic Gaussian Markov random field spatial models, including intrinsic conditional autoregressive models Technical Vignette 5: Understanding intrinsic Gaussian Markov random field spatial models, including intrinsic conditional autoregressive models Christopher Paciorek, Department of Statistics, University

More information

eqr094: Hierarchical MCMC for Bayesian System Reliability

eqr094: Hierarchical MCMC for Bayesian System Reliability eqr094: Hierarchical MCMC for Bayesian System Reliability Alyson G. Wilson Statistical Sciences Group, Los Alamos National Laboratory P.O. Box 1663, MS F600 Los Alamos, NM 87545 USA Phone: 505-667-9167

More information

The Mixture Approach for Simulating New Families of Bivariate Distributions with Specified Correlations

The Mixture Approach for Simulating New Families of Bivariate Distributions with Specified Correlations The Mixture Approach for Simulating New Families of Bivariate Distributions with Specified Correlations John R. Michael, Significance, Inc. and William R. Schucany, Southern Methodist University The mixture

More information

Supplement to A Hierarchical Approach for Fitting Curves to Response Time Measurements

Supplement to A Hierarchical Approach for Fitting Curves to Response Time Measurements Supplement to A Hierarchical Approach for Fitting Curves to Response Time Measurements Jeffrey N. Rouder Francis Tuerlinckx Paul L. Speckman Jun Lu & Pablo Gomez May 4 008 1 The Weibull regression model

More information

Bayesian Inference on Joint Mixture Models for Survival-Longitudinal Data with Multiple Features. Yangxin Huang

Bayesian Inference on Joint Mixture Models for Survival-Longitudinal Data with Multiple Features. Yangxin Huang Bayesian Inference on Joint Mixture Models for Survival-Longitudinal Data with Multiple Features Yangxin Huang Department of Epidemiology and Biostatistics, COPH, USF, Tampa, FL yhuang@health.usf.edu January

More information

General Regression Model

General Regression Model Scott S. Emerson, M.D., Ph.D. Department of Biostatistics, University of Washington, Seattle, WA 98195, USA January 5, 2015 Abstract Regression analysis can be viewed as an extension of two sample statistical

More information

Stat 451 Lecture Notes Markov Chain Monte Carlo. Ryan Martin UIC

Stat 451 Lecture Notes Markov Chain Monte Carlo. Ryan Martin UIC Stat 451 Lecture Notes 07 12 Markov Chain Monte Carlo Ryan Martin UIC www.math.uic.edu/~rgmartin 1 Based on Chapters 8 9 in Givens & Hoeting, Chapters 25 27 in Lange 2 Updated: April 4, 2016 1 / 42 Outline

More information

ST440/540: Applied Bayesian Statistics. (9) Model selection and goodness-of-fit checks

ST440/540: Applied Bayesian Statistics. (9) Model selection and goodness-of-fit checks (9) Model selection and goodness-of-fit checks Objectives In this module we will study methods for model comparisons and checking for model adequacy For model comparisons there are a finite number of candidate

More information

Markov Chain Monte Carlo methods

Markov Chain Monte Carlo methods Markov Chain Monte Carlo methods Tomas McKelvey and Lennart Svensson Signal Processing Group Department of Signals and Systems Chalmers University of Technology, Sweden November 26, 2012 Today s learning

More information

Bayes methods for categorical data. April 25, 2017

Bayes methods for categorical data. April 25, 2017 Bayes methods for categorical data April 25, 2017 Motivation for joint probability models Increasing interest in high-dimensional data in broad applications Focus may be on prediction, variable selection,

More information

University of California at Berkeley TRUNbTAM THONG TIN.THirVlEN

University of California at Berkeley TRUNbTAM THONG TIN.THirVlEN DECISION MAKING AND FORECASTING With Emphasis on Model Building and Policy Analysis Kneale T. Marshall U.S. Naval Postgraduate School Robert M. Oliver )A1 HOC OUOC GIA HA NO! University of California at

More information

DETAILED CONTENTS PART I INTRODUCTION AND DESCRIPTIVE STATISTICS. 1. Introduction to Statistics

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

More information

An Algorithm for Bayesian Variable Selection in High-dimensional Generalized Linear Models

An Algorithm for Bayesian Variable Selection in High-dimensional Generalized Linear Models Proceedings 59th ISI World Statistics Congress, 25-30 August 2013, Hong Kong (Session CPS023) p.3938 An Algorithm for Bayesian Variable Selection in High-dimensional Generalized Linear Models Vitara Pungpapong

More information

Micro Syllabus for Statistics (B.Sc. CSIT) program

Micro Syllabus for Statistics (B.Sc. CSIT) program Micro Syllabus for Statistics (B.Sc. CSIT) program Tribhuvan University Institute of Science & Technology(IOST) Level: B.Sc. Course Title: Statistics I Full Marks: 60 + 0 + 0 Course Code: STA 64 Pass Marks:

More information

Probability for Statistics and Machine Learning

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

More information

Bayesian Models in Machine Learning

Bayesian Models in Machine Learning Bayesian Models in Machine Learning Lukáš Burget Escuela de Ciencias Informáticas 2017 Buenos Aires, July 24-29 2017 Frequentist vs. Bayesian Frequentist point of view: Probability is the frequency of

More information

Machine Learning Overview

Machine Learning Overview Machine Learning Overview Sargur N. Srihari University at Buffalo, State University of New York USA 1 Outline 1. What is Machine Learning (ML)? 2. Types of Information Processing Problems Solved 1. Regression

More information

Linear Models 1. Isfahan University of Technology Fall Semester, 2014

Linear Models 1. Isfahan University of Technology Fall Semester, 2014 Linear Models 1 Isfahan University of Technology Fall Semester, 2014 References: [1] G. A. F., Seber and A. J. Lee (2003). Linear Regression Analysis (2nd ed.). Hoboken, NJ: Wiley. [2] A. C. Rencher and

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

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

Report and Opinion 2016;8(6) Analysis of bivariate correlated data under the Poisson-gamma model

Report and Opinion 2016;8(6)   Analysis of bivariate correlated data under the Poisson-gamma model Analysis of bivariate correlated data under the Poisson-gamma model Narges Ramooz, Farzad Eskandari 2. MSc of Statistics, Allameh Tabatabai University, Tehran, Iran 2. Associate professor of Statistics,

More information

Approximate Normality, Newton-Raphson, & Multivariate Delta Method

Approximate Normality, Newton-Raphson, & Multivariate Delta Method Approximate Normality, Newton-Raphson, & Multivariate Delta Method Timothy Hanson Department of Statistics, University of South Carolina Stat 740: Statistical Computing 1 / 39 Statistical models come in

More information

Bayesian Inference. Chapter 9. Linear models and regression

Bayesian Inference. Chapter 9. Linear models and regression Bayesian Inference Chapter 9. Linear models and regression M. Concepcion Ausin Universidad Carlos III de Madrid Master in Business Administration and Quantitative Methods Master in Mathematical Engineering

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

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 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

More information

Probability and Stochastic Processes

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

More information

Bayesian Nonparametrics for Speech and Signal Processing

Bayesian Nonparametrics for Speech and Signal Processing Bayesian Nonparametrics for Speech and Signal Processing Michael I. Jordan University of California, Berkeley June 28, 2011 Acknowledgments: Emily Fox, Erik Sudderth, Yee Whye Teh, and Romain Thibaux Computer

More information

Index. Pagenumbersfollowedbyf indicate figures; pagenumbersfollowedbyt indicate tables.

Index. Pagenumbersfollowedbyf indicate figures; pagenumbersfollowedbyt indicate tables. Index Pagenumbersfollowedbyf indicate figures; pagenumbersfollowedbyt indicate tables. Adaptive rejection metropolis sampling (ARMS), 98 Adaptive shrinkage, 132 Advanced Photo System (APS), 255 Aggregation

More information

An Introduction to Multivariate Statistical Analysis

An Introduction to Multivariate Statistical Analysis An Introduction to Multivariate Statistical Analysis Third Edition T. W. ANDERSON Stanford University Department of Statistics Stanford, CA WILEY- INTERSCIENCE A JOHN WILEY & SONS, INC., PUBLICATION Contents

More information

A THEORETICAL INTRODUCTION TO NUMERICAL ANALYSIS

A THEORETICAL INTRODUCTION TO NUMERICAL ANALYSIS A THEORETICAL INTRODUCTION TO NUMERICAL ANALYSIS Victor S. Ryaben'kii Semyon V. Tsynkov Chapman &. Hall/CRC Taylor & Francis Group Boca Raton London New York Chapman & Hall/CRC is an imprint of the Taylor

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