Springer Texts in Statistics

Size: px
Start display at page:

Download "Springer Texts in Statistics"

Transcription

1 Springer Texts in Statistics Series Editors: G. Casella S.E. Fienberg I. Olkin For further volumes:

2

3 Mary Kathryn Cowles Applied Bayesian Statistics With R and OpenBUGS Examples 123

4 Mary Kathryn Cowles Department of Statistics and Actuarial Science University of Iowa Iowa City, Iowa, USA ISSN X ISBN ISBN (ebook) DOI / Springer New York Heidelberg Dordrecht London Library of Congress Control Number: Springer Science+Business Media New York 2013 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. Exempted from this legal reservation are brief excerpts in connection with reviews or scholarly analysis or material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work. Duplication of this publication or parts thereof is permitted only under the provisions of the Copyright Law of the Publisher s location, in its current version, and permission for use must always be obtained from Springer. Permissions for use may be obtained through RightsLink at the Copyright Clearance Center. Violations are liable to prosecution under the respective Copyright Law. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. While the advice and information in this book are believed to be true and accurate at the date of publication, neither the authors nor the editors nor the publisher can accept any legal responsibility for any errors or omissions that may be made. The publisher makes no warranty, express or implied, with respect to the material contained herein. Printed on acid-free paper Springer is part of Springer Science+Business Media (

5 To Brendan, Lucy, and Donald.

6

7 Preface I have taught a course called Bayesian Statistics at the University of Iowa every academic year since This book is intended to fit the goals and audience addressed by my course. The Course Objectives section of my syllabus reads: Through hands-on experience with real data from a variety of applications, students will learn the basics of designing and carrying out Bayesian analyses, and interpreting and communicating the results. Students will learn to use software packages including R and OpenBUGS to fit Bayesian models. The course is intended to be intensely practical, focussing on building understanding of the concepts and procedures required to perform Bayesian analysis of real data to answer real questions. Emphasis is given to such issues as determining what data is needed to address a particular question; choosing an appropriate probability distribution for sample data; quantifying already-existing knowledge in the form of a prior distribution on model parameters; verifying that the posterior distribution will be proper if improper prior distributions are used; and when and how to specify hierarchical models. Interpretation and communication of results are stressed, including differences from, and similarities to, classical approaches to the same problems. WinBUGS and OpenBUGS currently are the dominant software in applied use of Bayesian methods. I have chosen to introduce OpenBUGS as the primary data analysis software in this textbook because, unlike WinBUGS, OpenBUGS is undergoing continuing development and has versions that run natively under Linux and Macintosh operating systems as well as Windows. Although some background is provided on the Markov chain Monte Carlo sampling procedures employed by WinBUGS and OpenBUGS, the emphasis is on those tasks that a user must carry out correctly for reasonably trustworthy inference. These include using appropriate tools to assess whether and when a sampler has converged to the target distribution, deciding how many iterations are needed for acceptable accuracy in estimation, and how to report results of a Bayesian analysis conducted with OpenBUGS. Caveats about the fallibility of convergence diagnostics are emphasized. vii

8 viii Preface Students of different levels and disciplines take the course, including: undergraduate mathematics and statistics majors; master s students in statistics, biostatistics, statistical genetics, educational testing and measurement, and engineering; and PhD students in economics, marketing, psychology, and geography as well as the previously listed fields. In addition, several practicing statisticians employed by the University of Iowa and American College Testing (ACT) have taken the course. The goal of the course, and of this book, is to provide an introduction to Bayesian principles and practice that is clear, useful, and unintimidating to motivated students even if they do not have an advanced background in mathematics and probability. I emphasize intuitive insight without sacrificing mathematical correctness. Prerequisites are one or two semesters of calculus-based probability and mathematical statistics (at least at the Hogg and Tannis level) and one or two semesters of classical statistical methods, including linear regression (David Moore s Basic Practice of Statistics level). Elementary integral and differential calculus is occasionally used in lectures and homework. Linear algebra is not required. Coralville, Iowa Mary Kathryn Cowles

9 Contents 1 What Is Bayesian Statistics? TheScientificMethod(ButItIsNotJustforScience...) A Bit of History Example of the Bayesian Method: Does My Friend Have Breast Cancer? Quantifying Uncertainty Using Probabilities Models and Prior Probabilities Data Likelihoods and Posterior Probabilities Bayesian Sequential Analysis Calibration Experiments for Assessing Subjective Probabilities What Is to Come? Problems Review of Probability Review of Probability Events and Sample Spaces Unions, Intersections, Complements The Addition Rule Marginal and Conditional Probabilities The Multiplication Rule Putting It All Together: Did Brendan Mail the Bill Payment? The Law of Total Probability Bayes Rule in the Discrete Case Random Variables and Probability Distributions Problems Introduction to One-Parameter Models: Estimating a Population Proportion What Proportion of Students Would Quit School If Tuition Were Raised 19%: Estimating a Population Proportion ix

10 x Contents 3.2 The First Stage of a Bayesian Model The Binomial Distribution for Our Survey Kernels and Normalizing Constants The Likelihood Function The Second Stage of the Bayesian Model: The Prior Other Possible Prior Distributions Prior Probability Intervals Using the Data to Update the Prior: The Posterior Distribution Conjugate Priors Computing the Posterior Distribution with a Conjugate Prior Choosing the Parameters of a Beta Distribution to Match Prior Beliefs Computing and Graphing the Posterior Distribution Plotting the Prior Density, the Likelihood, and the Posterior Density Introduction to R for Bayesian Analysis Functions and Objects in R Summarizing and Graphing Probability Distributions in R Printing and Saving R Graphics R Packages Useful in Bayesian Analysis Ending a Session Problems Inference for a Population Proportion Estimation and Testing: Frequentist Approach Maximum Likelihood Estimation Frequentist Confidence Intervals Frequentist Hypothesis Testing Bayesian Inference: Summarizing the Posterior Distribution The Posterior Mean Other Bayesian Point Estimates Bayesian Posterior Intervals Using the Posterior Distribution to Test Hypotheses Posterior Predictive Distributions Problems Special Considerations in Bayesian Inference Robustness to Prior Specifications Inference Using Nonconjugate Priors Discrete Priors A Histogram Prior Noninformative Priors Review of Proper and Improper Distributions A Noninformative Prior for the Binomial Likelihood... 73

11 Contents xi Jeffreys Prior Verifying the Propriety of the Posterior Distribution When Using an Improper Prior Problems Other One-Parameter Models and Their Conjugate Priors Poisson Normal: Unknown Mean, Variance Assumed Known Example: Mercury Concentration in the Tissue of Edible Fish Parametric Family for Likelihood Likelihood for μ Assuming that Population Variance Is Known Sufficient Statistics Finding a Conjugate Prior for μ Updating from Prior to Posterior in the Normal Normal Case Specifying Prior Parameters Mercury in Fish Tissue The Jeffreys Prior for the Normal Mean Posterior Predictive Density in the Normal Normal Model Normal: Unknown Variance, Mean Assumed Known Conjugate Prior for the Normal Variance, μ Assumed Known Obtaining the Posterior Density Jeffreys Prior for Normal Variance, Mean Assumed Known Normal: Unknown Precision, Mean Assumed Known Inference for the Variance in the Mercury Concentration Problem Problems More Realism Please: Introduction to Multiparameter Models Conventional Noninformative Prior for a Normal Likelihood with Both Mean and Variance Unknown Example: The Mercury Concentration Data Informative Priors for μ and σ A Conjugate Joint Prior Density for the Normal Mean and Variance Example: The Mercury Contamination Data The Standard Noninformative Joint Prior as a Limiting Form of the Conjugate Prior Problems

12 xii Contents 8 Fitting More Complex Bayesian Models: Markov Chain Monte Carlo Why Sampling-Based Methods Are Needed Single-Parameter Model Example Numeric Integration Monte Carlo Integration Sampling-Based Methods Independent Sampling Introduction to Markov Chain Monte Carlo Methods Markov Chains Markov Chains for Bayesian Inference Introduction to OpenBUGS and WinBUGS Using OpenBUGS for the Problem of Estimating a Binomial Success Parameter Model Specification Data and Initial Values Files Running the Model Assessing Convergence in OpenBUGS Posterior Inference Using OpenBUGS OpenBUGS for Normal Models Exercises Hierarchical Models and More on Convergence Assessment Specifying Bayesian Hierarchical Models Example: A Better Model for the College Softball Player s Batting Average The First Stage: The Likelihood The Second Stage: Priors on the Parameters That Appeared in the Likelihood The Third Stage: Priors on Any Parameters That Do Not Already Have Them The Joint Posterior Distribution in Hierarchical Models Higher-Order Hierarchical Models Fitting Bayesian Hierarchical Models Estimation Based on Hierarchical Models Prediction from Hierarchical Models More on Convergence Assessment in WinBUGS/OpenBUGS The Brooks Gelman and Rubin Diagnostic Convergence in the Hierarchical Softball Example with a Vague Prior Other Hierarchical Models Hierarchical Normal Means Directed Graphs for Hierarchical Models Parts of a DAG

13 Contents xiii 9.7 *Gibbs Sampling for Hierarchical Models Deriving Full Conditional Distributions Recommendations for Using MCMC to Fit Bayesian Models How Many Chains Initial Values General Advice Exercises Regression and Hierarchical Regression Models Review of Linear Regression Centering the Covariate Frequentist Estimation in Regression Example: Mercury Deposited by Precipitation Near the Brule River in Wisconsin Introduction to Bayesian Simple Linear Regression Standard Noninformative Prior Bayesian Analysis of the Brule River Mercury Concentration Data Informative Prior Densities for Regression Coefficients and Variance Generalized Linear Models Hierarchical Normal Linear Models Example: Estimating the Slope of Mean Log Mercury Concentration Throughout North America Using Data from Multiple MDN Sites Stages of a Hierarchical Normal Linear Model Univariate Formulation of the Second Stage Bivariate Formulation of the Second Stage Third Stage: Univariate Formulation Third Stage: Bivariate Formulation The Wishart Density WinBUGS Examples for Hierarchical Normal Linear Models Example with Univariate Formulation at Second and Third Stages Example with Bivariate Formulation at Second and Third Stages Problems Model Comparison, Model Checking, and Hypothesis Testing Bayes Factors for Model Comparison and Hypothesis Testing Bayes Factors in the Simple/Simple Case Interpreting a Bayes Factor The Bayes Factor in More General Models Bayes Factors and Bayesian Hypothesis Testing Obtaining Posterior Probabilities from WinBUGS/OpenBUGS Bayesian Viewpoint on Point Null Hypotheses

14 xiv Contents 11.3 The Deviance Information Criterion Posterior Predictive Checking Exercises Tables of Probability Distributions References Index

STA 225: Introductory Statistics (CT)

STA 225: Introductory Statistics (CT) Marshall University College of Science Mathematics Department STA 225: Introductory Statistics (CT) Course catalog description A critical thinking course in applied statistical reasoning covering basic

More information

International Series in Operations Research & Management Science

International Series in Operations Research & Management Science International Series in Operations Research & Management Science Volume 240 Series Editor Camille C. Price Stephen F. Austin State University, TX, USA Associate Series Editor Joe Zhu Worcester Polytechnic

More information

MARE Publication Series

MARE Publication Series MARE Publication Series Volume 8 Series Editors Maarten Bavinck University of Amsterdam, Amsterdam, The Netherlands Svein Jentoft Tromsø, Norway The MARE Publication Series is an initiative of the Centre

More information

Probability and Statistics Curriculum Pacing Guide

Probability and Statistics Curriculum Pacing Guide Unit 1 Terms PS.SPMJ.3 PS.SPMJ.5 Plan and conduct a survey to answer a statistical question. Recognize how the plan addresses sampling technique, randomization, measurement of experimental error and methods

More information

Guide to Teaching Computer Science

Guide to Teaching Computer Science Guide to Teaching Computer Science Orit Hazzan Tami Lapidot Noa Ragonis Guide to Teaching Computer Science An Activity-Based Approach Dr. Orit Hazzan Associate Professor Technion - Israel Institute of

More information

Hierarchical Linear Modeling with Maximum Likelihood, Restricted Maximum Likelihood, and Fully Bayesian Estimation

Hierarchical Linear Modeling with Maximum Likelihood, Restricted Maximum Likelihood, and Fully Bayesian Estimation A peer-reviewed electronic journal. Copyright is retained by the first or sole author, who grants right of first publication to Practical Assessment, Research & Evaluation. Permission is granted to distribute

More information

Pre-vocational Education in Germany and China

Pre-vocational Education in Germany and China Pre-vocational Education in Germany and China Jun Li Pre-vocational Education in Germany and China A Comparison of Curricula and Its Implications Jun Li Tongji University, Shanghai, People s Republic of

More information

ACTL5103 Stochastic Modelling For Actuaries. Course Outline Semester 2, 2014

ACTL5103 Stochastic Modelling For Actuaries. Course Outline Semester 2, 2014 UNSW Australia Business School School of Risk and Actuarial Studies ACTL5103 Stochastic Modelling For Actuaries Course Outline Semester 2, 2014 Part A: Course-Specific Information Please consult Part B

More information

Advances in Mathematics Education

Advances in Mathematics Education Advances in Mathematics Education Series Editors: Gabriele Kaiser, University of Hamburg, Hamburg, Germany Bharath Sriraman, The University of Montana, Missoula, MT, USA International Editorial Board:

More information

CS/SE 3341 Spring 2012

CS/SE 3341 Spring 2012 CS/SE 3341 Spring 2012 Probability and Statistics in Computer Science & Software Engineering (Section 001) Instructor: Dr. Pankaj Choudhary Meetings: TuTh 11 30-12 45 p.m. in ECSS 2.412 Office: FO 2.408-B

More information

Python Machine Learning

Python Machine Learning Python Machine Learning Unlock deeper insights into machine learning with this vital guide to cuttingedge predictive analytics Sebastian Raschka [ PUBLISHING 1 open source I community experience distilled

More information

Lecture Notes on Mathematical Olympiad Courses

Lecture Notes on Mathematical Olympiad Courses Lecture Notes on Mathematical Olympiad Courses For Junior Section Vol. 2 Mathematical Olympiad Series ISSN: 1793-8570 Series Editors: Lee Peng Yee (Nanyang Technological University, Singapore) Xiong Bin

More information

Introduction to the Practice of Statistics

Introduction to the Practice of Statistics Chapter 1: Looking at Data Distributions Introduction to the Practice of Statistics Sixth Edition David S. Moore George P. McCabe Bruce A. Craig Statistics is the science of collecting, organizing and

More information

Perspectives of Information Systems

Perspectives of Information Systems Perspectives of Information Systems Springer-Science+ Business Media, LLC Vesa Savolainen Editor and Main Author Perspectives of Information Systems Springer Vesa Savolainen Department of Computer Science

More information

Algebra 1, Quarter 3, Unit 3.1. Line of Best Fit. Overview

Algebra 1, Quarter 3, Unit 3.1. Line of Best Fit. Overview Algebra 1, Quarter 3, Unit 3.1 Line of Best Fit Overview Number of instructional days 6 (1 day assessment) (1 day = 45 minutes) Content to be learned Analyze scatter plots and construct the line of best

More information

S T A T 251 C o u r s e S y l l a b u s I n t r o d u c t i o n t o p r o b a b i l i t y

S T A T 251 C o u r s e S y l l a b u s I n t r o d u c t i o n t o p r o b a b i l i t y Department of Mathematics, Statistics and Science College of Arts and Sciences Qatar University S T A T 251 C o u r s e S y l l a b u s I n t r o d u c t i o n t o p r o b a b i l i t y A m e e n A l a

More information

Sociology 521: Social Statistics and Quantitative Methods I Spring Wed. 2 5, Kap 305 Computer Lab. Course Website

Sociology 521: Social Statistics and Quantitative Methods I Spring Wed. 2 5, Kap 305 Computer Lab. Course Website Sociology 521: Social Statistics and Quantitative Methods I Spring 2012 Wed. 2 5, Kap 305 Computer Lab Instructor: Tim Biblarz Office hours (Kap 352): W, 5 6pm, F, 10 11, and by appointment (213) 740 3547;

More information

Spring 2014 SYLLABUS Michigan State University STT 430: Probability and Statistics for Engineering

Spring 2014 SYLLABUS Michigan State University STT 430: Probability and Statistics for Engineering Spring 2014 SYLLABUS Michigan State University STT 430: Probability and Statistics for Engineering Time and Place: MW 3:00-4:20pm, A126 Wells Hall Instructor: Dr. Marianne Huebner Office: A-432 Wells Hall

More information

A Model of Knower-Level Behavior in Number Concept Development

A Model of Knower-Level Behavior in Number Concept Development Cognitive Science 34 (2010) 51 67 Copyright Ó 2009 Cognitive Science Society, Inc. All rights reserved. ISSN: 0364-0213 print / 1551-6709 online DOI: 10.1111/j.1551-6709.2009.01063.x A Model of Knower-Level

More information

Cal s Dinner Card Deals

Cal s Dinner Card Deals Cal s Dinner Card Deals Overview: In this lesson students compare three linear functions in the context of Dinner Card Deals. Students are required to interpret a graph for each Dinner Card Deal to help

More information

Theory of Probability

Theory of Probability Theory of Probability Class code MATH-UA 9233-001 Instructor Details Prof. David Larman Room 806,25 Gordon Street (UCL Mathematics Department). Class Details Fall 2013 Thursdays 1:30-4-30 Location to be

More information

MGT/MGP/MGB 261: Investment Analysis

MGT/MGP/MGB 261: Investment Analysis UNIVERSITY OF CALIFORNIA, DAVIS GRADUATE SCHOOL OF MANAGEMENT SYLLABUS for Fall 2014 MGT/MGP/MGB 261: Investment Analysis Daytime MBA: Tu 12:00p.m. - 3:00 p.m. Location: 1302 Gallagher (CRN: 51489) Sacramento

More information

Lecture 1: Machine Learning Basics

Lecture 1: Machine Learning Basics 1/69 Lecture 1: Machine Learning Basics Ali Harakeh University of Waterloo WAVE Lab ali.harakeh@uwaterloo.ca May 1, 2017 2/69 Overview 1 Learning Algorithms 2 Capacity, Overfitting, and Underfitting 3

More information

Sociology 521: Social Statistics and Quantitative Methods I Spring 2013 Mondays 2 5pm Kap 305 Computer Lab. Course Website

Sociology 521: Social Statistics and Quantitative Methods I Spring 2013 Mondays 2 5pm Kap 305 Computer Lab. Course Website Sociology 521: Social Statistics and Quantitative Methods I Spring 2013 Mondays 2 5pm Kap 305 Computer Lab Instructor: Tim Biblarz Office: Hazel Stanley Hall (HSH) Room 210 Office hours: Mon, 5 6pm, F,

More information

Lecture Notes in Artificial Intelligence 4343

Lecture Notes in Artificial Intelligence 4343 Lecture Notes in Artificial Intelligence 4343 Edited by J. G. Carbonell and J. Siekmann Subseries of Lecture Notes in Computer Science Christian Müller (Ed.) Speaker Classification I Fundamentals, Features,

More information

Physics 270: Experimental Physics

Physics 270: Experimental Physics 2017 edition Lab Manual Physics 270 3 Physics 270: Experimental Physics Lecture: Lab: Instructor: Office: Email: Tuesdays, 2 3:50 PM Thursdays, 2 4:50 PM Dr. Uttam Manna 313C Moulton Hall umanna@ilstu.edu

More information

Course Content Concepts

Course Content Concepts CS 1371 SYLLABUS, Fall, 2017 Revised 8/6/17 Computing for Engineers Course Content Concepts The students will be expected to be familiar with the following concepts, either by writing code to solve problems,

More information

Office Hours: Mon & Fri 10:00-12:00. Course Description

Office Hours: Mon & Fri 10:00-12:00. Course Description 1 State University of New York at Buffalo INTRODUCTION TO STATISTICS PSC 408 4 credits (3 credits lecture, 1 credit lab) Fall 2016 M/W/F 1:00-1:50 O Brian 112 Lecture Dr. Michelle Benson mbenson2@buffalo.edu

More information

Mathematics subject curriculum

Mathematics subject curriculum Mathematics subject curriculum Dette er ei omsetjing av den fastsette læreplanteksten. Læreplanen er fastsett på Nynorsk Established as a Regulation by the Ministry of Education and Research on 24 June

More information

Self Study Report Computer Science

Self Study Report Computer Science Computer Science undergraduate students have access to undergraduate teaching, and general computing facilities in three buildings. Two large classrooms are housed in the Davis Centre, which hold about

More information

EGRHS Course Fair. Science & Math AP & IB Courses

EGRHS Course Fair. Science & Math AP & IB Courses EGRHS Course Fair Science & Math AP & IB Courses Science Courses: AP Physics IB Physics SL IB Physics HL AP Biology IB Biology HL AP Physics Course Description Course Description AP Physics C (Mechanics)

More information

DIDACTIC MODEL BRIDGING A CONCEPT WITH PHENOMENA

DIDACTIC MODEL BRIDGING A CONCEPT WITH PHENOMENA DIDACTIC MODEL BRIDGING A CONCEPT WITH PHENOMENA Beba Shternberg, Center for Educational Technology, Israel Michal Yerushalmy University of Haifa, Israel The article focuses on a specific method of constructing

More information

Mathematics Program Assessment Plan

Mathematics Program Assessment Plan Mathematics Program Assessment Plan Introduction This assessment plan is tentative and will continue to be refined as needed to best fit the requirements of the Board of Regent s and UAS Program Review

More information

University of Cincinnati College of Medicine. DECISION ANALYSIS AND COST-EFFECTIVENESS BE-7068C: Spring 2016

University of Cincinnati College of Medicine. DECISION ANALYSIS AND COST-EFFECTIVENESS BE-7068C: Spring 2016 1 DECISION ANALYSIS AND COST-EFFECTIVENESS BE-7068C: Spring 2016 Instructor Name: Mark H. Eckman, MD, MS Office:, Division of General Internal Medicine (MSB 7564) (ML#0535) Cincinnati, Ohio 45267-0535

More information

US and Cross-National Policies, Practices, and Preparation

US and Cross-National Policies, Practices, and Preparation US and Cross-National Policies, Practices, and Preparation Studies in Educational Leadership VOLUME 12 Series Editor Kenneth A. Leithwood, OISE, University of Toronto, Canada Editorial Board Christopher

More information

Math 96: Intermediate Algebra in Context

Math 96: Intermediate Algebra in Context : Intermediate Algebra in Context Syllabus Spring Quarter 2016 Daily, 9:20 10:30am Instructor: Lauri Lindberg Office Hours@ tutoring: Tutoring Center (CAS-504) 8 9am & 1 2pm daily STEM (Math) Center (RAI-338)

More information

Developing Language Teacher Autonomy through Action Research

Developing Language Teacher Autonomy through Action Research Developing Language Teacher Autonomy through Action Research Helping teachers engage autonomously in action research is a very worthwhile enterprise. Beneficiaries are likely to include learners, schools

More information

BENG Simulation Modeling of Biological Systems. BENG 5613 Syllabus: Page 1 of 9. SPECIAL NOTE No. 1:

BENG Simulation Modeling of Biological Systems. BENG 5613 Syllabus: Page 1 of 9. SPECIAL NOTE No. 1: BENG 5613 Syllabus: Page 1 of 9 BENG 5613 - Simulation Modeling of Biological Systems SPECIAL NOTE No. 1: Class Syllabus BENG 5613, beginning in 2014, is being taught in the Spring in both an 8- week term

More information

The University of Texas at Tyler College of Business and Technology Department of Management and Marketing SPRING 2015

The University of Texas at Tyler College of Business and Technology Department of Management and Marketing SPRING 2015 The University of Texas at Tyler College of Business and Technology Department of Management and Marketing SPRING 2015 COURSE NUMBER MANA 1300.001 COURSE TITLE Introduction to Business COURSE MEETINGS

More information

Instrumentation, Control & Automation Staffing. Maintenance Benchmarking Study

Instrumentation, Control & Automation Staffing. Maintenance Benchmarking Study Electronic Document Instrumentation, Control & Automation Staffing Prepared by ITA Technical Committee, Maintenance Subcommittee, Task Force on IC&A Staffing John Petito, Chair Richard Haugh, Vice-Chair

More information

content First Introductory book to cover CAPM First to differentiate expected and required returns First to discuss the intrinsic value of stocks

content First Introductory book to cover CAPM First to differentiate expected and required returns First to discuss the intrinsic value of stocks content First Introductory book to cover CAPM First to differentiate expected and required returns First to discuss the intrinsic value of stocks presentation First timelines to explain TVM First financial

More information

Second Language Learning and Teaching. Series editor Mirosław Pawlak, Kalisz, Poland

Second Language Learning and Teaching. Series editor Mirosław Pawlak, Kalisz, Poland Second Language Learning and Teaching Series editor Mirosław Pawlak, Kalisz, Poland About the Series The series brings together volumes dealing with different aspects of learning and teaching second and

More information

AGS THE GREAT REVIEW GAME FOR PRE-ALGEBRA (CD) CORRELATED TO CALIFORNIA CONTENT STANDARDS

AGS THE GREAT REVIEW GAME FOR PRE-ALGEBRA (CD) CORRELATED TO CALIFORNIA CONTENT STANDARDS AGS THE GREAT REVIEW GAME FOR PRE-ALGEBRA (CD) CORRELATED TO CALIFORNIA CONTENT STANDARDS 1 CALIFORNIA CONTENT STANDARDS: Chapter 1 ALGEBRA AND WHOLE NUMBERS Algebra and Functions 1.4 Students use algebraic

More information

The University of Iceland

The University of Iceland The University of Iceland By Eziama Alvan C. www.freetuitionuniversities.com 1 Student Visa Preparation Guide: Copyright Information The information contained in this document remains the property of www.freetuitionuniversities.com

More information

Math 181, Calculus I

Math 181, Calculus I Math 181, Calculus I [Semester] [Class meeting days/times] [Location] INSTRUCTOR INFORMATION: Name: Office location: Office hours: Mailbox: Phone: Email: Required Material and Access: Textbook: Stewart,

More information

MMOG Subscription Business Models: Table of Contents

MMOG Subscription Business Models: Table of Contents DFC Intelligence DFC Intelligence Phone 858-780-9680 9320 Carmel Mountain Rd Fax 858-780-9671 Suite C www.dfcint.com San Diego, CA 92129 MMOG Subscription Business Models: Table of Contents November 2007

More information

GDP Falls as MBA Rises?

GDP Falls as MBA Rises? Applied Mathematics, 2013, 4, 1455-1459 http://dx.doi.org/10.4236/am.2013.410196 Published Online October 2013 (http://www.scirp.org/journal/am) GDP Falls as MBA Rises? T. N. Cummins EconomicGPS, Aurora,

More information

Hierarchical Linear Models I: Introduction ICPSR 2015

Hierarchical Linear Models I: Introduction ICPSR 2015 Hierarchical Linear Models I: Introduction ICPSR 2015 Instructor: Teaching Assistant: Aline G. Sayer, University of Massachusetts Amherst sayer@psych.umass.edu Holly Laws, Yale University holly.laws@yale.edu

More information

Green Belt Curriculum (This workshop can also be conducted on-site, subject to price change and number of participants)

Green Belt Curriculum (This workshop can also be conducted on-site, subject to price change and number of participants) Green Belt Curriculum (This workshop can also be conducted on-site, subject to price change and number of participants) Notes: 1. We use Mini-Tab in this workshop. Mini-tab is available for free trail

More information

Business Analytics and Information Tech COURSE NUMBER: 33:136:494 COURSE TITLE: Data Mining and Business Intelligence

Business Analytics and Information Tech COURSE NUMBER: 33:136:494 COURSE TITLE: Data Mining and Business Intelligence Business Analytics and Information Tech COURSE NUMBER: 33:136:494 COURSE TITLE: Data Mining and Business Intelligence COURSE DESCRIPTION This course presents computing tools and concepts for all stages

More information

CHALLENGES FACING DEVELOPMENT OF STRATEGIC PLANS IN PUBLIC SECONDARY SCHOOLS IN MWINGI CENTRAL DISTRICT, KENYA

CHALLENGES FACING DEVELOPMENT OF STRATEGIC PLANS IN PUBLIC SECONDARY SCHOOLS IN MWINGI CENTRAL DISTRICT, KENYA CHALLENGES FACING DEVELOPMENT OF STRATEGIC PLANS IN PUBLIC SECONDARY SCHOOLS IN MWINGI CENTRAL DISTRICT, KENYA By Koma Timothy Mutua Reg. No. GMB/M/0870/08/11 A Research Project Submitted In Partial Fulfilment

More information

Course Name: Elementary Calculus Course Number: Math 2103 Semester: Fall Phone:

Course Name: Elementary Calculus Course Number: Math 2103 Semester: Fall Phone: Course Name: Elementary Calculus Course Number: Math 2103 Semester: Fall 2011 Instructor s Name: Ricky Streight Hours Credit: 3 Phone: 405-945-6794 email: ricky.streight@okstate.edu 1. COURSE: Math 2103

More information

PROFESSIONAL TREATMENT OF TEACHERS AND STUDENT ACADEMIC ACHIEVEMENT. James B. Chapman. Dissertation submitted to the Faculty of the Virginia

PROFESSIONAL TREATMENT OF TEACHERS AND STUDENT ACADEMIC ACHIEVEMENT. James B. Chapman. Dissertation submitted to the Faculty of the Virginia PROFESSIONAL TREATMENT OF TEACHERS AND STUDENT ACADEMIC ACHIEVEMENT by James B. Chapman Dissertation submitted to the Faculty of the Virginia Polytechnic Institute and State University in partial fulfillment

More information

Grade 6: Module 3B: Unit 2: Overview

Grade 6: Module 3B: Unit 2: Overview Grade 6: Module 3B: Unit 2: Overview This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License. Exempt third-party content is indicated by the footer: (name

More information

10.2. Behavior models

10.2. Behavior models User behavior research 10.2. Behavior models Overview Why do users seek information? How do they seek information? How do they search for information? How do they use libraries? These questions are addressed

More information

Economics 201 Principles of Microeconomics Fall 2010 MWF 10:00 10:50am 160 Bryan Building

Economics 201 Principles of Microeconomics Fall 2010 MWF 10:00 10:50am 160 Bryan Building Economics 201 Principles of Microeconomics Fall 2010 MWF 10:00 10:50am 160 Bryan Building Professor: Dr. Michelle Sheran Office: 445 Bryan Building Phone: 256-1192 E-mail: mesheran@uncg.edu Office Hours:

More information

PRODUCT PLATFORM AND PRODUCT FAMILY DESIGN

PRODUCT PLATFORM AND PRODUCT FAMILY DESIGN PRODUCT PLATFORM AND PRODUCT FAMILY DESIGN PRODUCT PLATFORM AND PRODUCT FAMILY DESIGN Methods and Applications Edited by Timothy W. Simpson 1, Zahed Siddique 2, and Jianxin (Roger) Jiao 3 1 The Pennsylvania

More information

Class Meeting Time and Place: Section 3: MTWF10:00-10:50 TILT 221

Class Meeting Time and Place: Section 3: MTWF10:00-10:50 TILT 221 Math 155. Calculus for Biological Scientists Fall 2017 Website https://csumath155.wordpress.com Please review the course website for details on the schedule, extra resources, alternate exam request forms,

More information

Excel Formulas & Functions

Excel Formulas & Functions Microsoft Excel Formulas & Functions 4th Edition Microsoft Excel Formulas & Functions 4th Edition by Ken Bluttman Microsoft Excel Formulas & Functions For Dummies, 4th Edition Published by: John Wiley

More information

THE INFLUENCE OF COOPERATIVE WRITING TECHNIQUE TO TEACH WRITING SKILL VIEWED FROM STUDENTS CREATIVITY

THE INFLUENCE OF COOPERATIVE WRITING TECHNIQUE TO TEACH WRITING SKILL VIEWED FROM STUDENTS CREATIVITY THE INFLUENCE OF COOPERATIVE WRITING TECHNIQUE TO TEACH WRITING SKILL VIEWED FROM STUDENTS CREATIVITY (An Experimental Research at the Fourth Semester of English Department of Slamet Riyadi University,

More information

STA2023 Introduction to Statistics (Hybrid) Spring 2013

STA2023 Introduction to Statistics (Hybrid) Spring 2013 STA2023 Introduction to Statistics (Hybrid) Spring 2013 Course Description This course introduces the student to the concepts of a statistical design and data analysis with emphasis on introductory descriptive

More information

Analysis of Enzyme Kinetic Data

Analysis of Enzyme Kinetic Data Analysis of Enzyme Kinetic Data To Marilú Analysis of Enzyme Kinetic Data ATHEL CORNISH-BOWDEN Directeur de Recherche Émérite, Centre National de la Recherche Scientifique, Marseilles OXFORD UNIVERSITY

More information

State University of New York at Buffalo INTRODUCTION TO STATISTICS PSC 408 Fall 2015 M,W,F 1-1:50 NSC 210

State University of New York at Buffalo INTRODUCTION TO STATISTICS PSC 408 Fall 2015 M,W,F 1-1:50 NSC 210 1 State University of New York at Buffalo INTRODUCTION TO STATISTICS PSC 408 Fall 2015 M,W,F 1-1:50 NSC 210 Dr. Michelle Benson mbenson2@buffalo.edu Office: 513 Park Hall Office Hours: Mon & Fri 10:30-12:30

More information

A THESIS. By: IRENE BRAINNITA OKTARIN S

A THESIS. By: IRENE BRAINNITA OKTARIN S THE EFFECTIVENESS OF BLENDED LEARNING TO TEACH WRITING VIEWED FROM STUDENTS CREATIVITY (An Experimental Study at the English Education Department of Slamet Riyadi University in the Academic Year of 2014/2015)

More information

Probability and Game Theory Course Syllabus

Probability and Game Theory Course Syllabus Probability and Game Theory Course Syllabus DATE ACTIVITY CONCEPT Sunday Learn names; introduction to course, introduce the Battle of the Bismarck Sea as a 2-person zero-sum game. Monday Day 1 Pre-test

More information

Knowledge-Based - Systems

Knowledge-Based - Systems Knowledge-Based - Systems ; Rajendra Arvind Akerkar Chairman, Technomathematics Research Foundation and Senior Researcher, Western Norway Research institute Priti Srinivas Sajja Sardar Patel University

More information

Level 6. Higher Education Funding Council for England (HEFCE) Fee for 2017/18 is 9,250*

Level 6. Higher Education Funding Council for England (HEFCE) Fee for 2017/18 is 9,250* Programme Specification: Undergraduate For students starting in Academic Year 2017/2018 1. Course Summary Names of programme(s) and award title(s) Award type Mode of study Framework of Higher Education

More information

AUTONOMY. in the Law

AUTONOMY. in the Law AUTONOMY in the Law Ius Gentium Comparative Perspectives on Law and Justice VOLUME 1 Series Editor Mortimer Sellers (University of Baltimore) Board of Editors Myroslava Antonovych (Kyiv-Mohyla Academy)

More information

Julia Smith. Effective Classroom Approaches to.

Julia Smith. Effective Classroom Approaches to. Julia Smith @tessmaths Effective Classroom Approaches to GCSE Maths resits julia.smith@writtle.ac.uk Agenda The context of GCSE resit in a post-16 setting An overview of the new GCSE Key features of a

More information

Math Techniques of Calculus I Penn State University Summer Session 2017

Math Techniques of Calculus I Penn State University Summer Session 2017 Math 110 - Techniques of Calculus I Penn State University Summer Session 2017 Instructor: Sergio Zamora Barrera Office: 018 McAllister Bldg E-mail: sxz38@psu.edu Office phone: 814-865-4291 Office Hours:

More information

SAMPLE SYLLABUS. Master of Health Care Administration Academic Center 3rd Floor Des Moines, Iowa 50312

SAMPLE SYLLABUS. Master of Health Care Administration Academic Center 3rd Floor Des Moines, Iowa 50312 Master of Health Care Administration Academic Center 3rd Floor Des Moines, Iowa 50312 MHA Curriculum Committee Approval Date: August 16, 2012 CHS Curriculum Committee Approval Date: July 10, 2012 COURSE

More information

Lahore University of Management Sciences. FINN 321 Econometrics Fall Semester 2017

Lahore University of Management Sciences. FINN 321 Econometrics Fall Semester 2017 Instructor Syed Zahid Ali Room No. 247 Economics Wing First Floor Office Hours Email szahid@lums.edu.pk Telephone Ext. 8074 Secretary/TA TA Office Hours Course URL (if any) Suraj.lums.edu.pk FINN 321 Econometrics

More information

THE PROMOTION OF SOCIAL AWARENESS

THE PROMOTION OF SOCIAL AWARENESS THE PROMOTION OF SOCIAL AWARENESS Powerful Lessons from the Partnership of Developmental Theory and Classroom Practice Robert L. Selman Russell Sage Foundation New York The Russell Sage Foundation The

More information

EPI BIO 446 DESIGN, CONDUCT, and ANALYSIS of CLINICAL TRIALS 1.0 Credit SPRING QUARTER 2014

EPI BIO 446 DESIGN, CONDUCT, and ANALYSIS of CLINICAL TRIALS 1.0 Credit SPRING QUARTER 2014 EPI BIO 446 DESIGN, CONDUCT, and ANALYSIS of CLINICAL TRIALS 1.0 Credit SPRING QUARTER 2014 Time: March 31, 2014 June 13, 2014 Tuesdays and Thursdays 10:00am-11:30am Location: Lurie Center Gray Conference

More information

AP Statistics Summer Assignment 17-18

AP Statistics Summer Assignment 17-18 AP Statistics Summer Assignment 17-18 Welcome to AP Statistics. This course will be unlike any other math class you have ever taken before! Before taking this course you will need to be competent in basic

More information

Statistical Analysis of Climate Change, Renewable Energies, and Sustainability An Independent Investigation for Introduction to Statistics

Statistical Analysis of Climate Change, Renewable Energies, and Sustainability An Independent Investigation for Introduction to Statistics 5/22/2012 Statistical Analysis of Climate Change, Renewable Energies, and Sustainability An Independent Investigation for Introduction to Statistics College of Menominee Nation & University of Wisconsin

More information

Mathematics. Mathematics

Mathematics. Mathematics Mathematics Program Description Successful completion of this major will assure competence in mathematics through differential and integral calculus, providing an adequate background for employment in

More information

Statewide Framework Document for:

Statewide Framework Document for: Statewide Framework Document for: 270301 Standards may be added to this document prior to submission, but may not be removed from the framework to meet state credit equivalency requirements. Performance

More information

What is a Mental Model?

What is a Mental Model? Mental Models for Program Understanding Dr. Jonathan I. Maletic Computer Science Department Kent State University What is a Mental Model? Internal (mental) representation of a real system s behavior,

More information

Honors Mathematics. Introduction and Definition of Honors Mathematics

Honors Mathematics. Introduction and Definition of Honors Mathematics Honors Mathematics Introduction and Definition of Honors Mathematics Honors Mathematics courses are intended to be more challenging than standard courses and provide multiple opportunities for students

More information

Edexcel GCSE. Statistics 1389 Paper 1H. June Mark Scheme. Statistics Edexcel GCSE

Edexcel GCSE. Statistics 1389 Paper 1H. June Mark Scheme. Statistics Edexcel GCSE Edexcel GCSE Statistics 1389 Paper 1H June 2007 Mark Scheme Edexcel GCSE Statistics 1389 NOTES ON MARKING PRINCIPLES 1 Types of mark M marks: method marks A marks: accuracy marks B marks: unconditional

More information

NCEO Technical Report 27

NCEO Technical Report 27 Home About Publications Special Topics Presentations State Policies Accommodations Bibliography Teleconferences Tools Related Sites Interpreting Trends in the Performance of Special Education Students

More information

How the Guppy Got its Spots:

How the Guppy Got its Spots: This fall I reviewed the Evobeaker labs from Simbiotic Software and considered their potential use for future Evolution 4974 courses. Simbiotic had seven labs available for review. I chose to review the

More information

TABLE OF CONTENTS TABLE OF CONTENTS COVER PAGE HALAMAN PENGESAHAN PERNYATAAN NASKAH SOAL TUGAS AKHIR ACKNOWLEDGEMENT FOREWORD

TABLE OF CONTENTS TABLE OF CONTENTS COVER PAGE HALAMAN PENGESAHAN PERNYATAAN NASKAH SOAL TUGAS AKHIR ACKNOWLEDGEMENT FOREWORD TABLE OF CONTENTS TABLE OF CONTENTS COVER PAGE HALAMAN PENGESAHAN PERNYATAAN NASKAH SOAL TUGAS AKHIR ACKNOWLEDGEMENT FOREWORD TABLE OF CONTENTS LIST OF FIGURES LIST OF TABLES LIST OF APPENDICES LIST OF

More information

MODULE 4 Data Collection and Hypothesis Development. Trainer Outline

MODULE 4 Data Collection and Hypothesis Development. Trainer Outline MODULE 4 Data Collection and Hypothesis Development Trainer Outline The following trainer guide includes estimated times for each section of the module, an overview of the information to be presented,

More information

To link to this article: PLEASE SCROLL DOWN FOR ARTICLE

To link to this article:  PLEASE SCROLL DOWN FOR ARTICLE This article was downloaded by: [Dr Brian Winkel] On: 19 November 2014, At: 04:59 Publisher: Taylor & Francis Informa Ltd Registered in England and Wales Registered Number: 1072954 Registered office: Mortimer

More information

Introduction. Chem 110: Chemical Principles 1 Sections 40-52

Introduction. Chem 110: Chemical Principles 1 Sections 40-52 Introduction Chem 110: Chemical Principles 1 Sections 40-52 Instructor: Dr. Squire J. Booker 302 Chemistry Building 814-865-8793 squire@psu.edu (sjb14@psu.edu) Lectures: Monday (M), Wednesday (W), Friday

More information

JONATHAN H. WRIGHT Department of Economics, Johns Hopkins University, 3400 N. Charles St., Baltimore MD (410)

JONATHAN H. WRIGHT Department of Economics, Johns Hopkins University, 3400 N. Charles St., Baltimore MD (410) JONATHAN H. WRIGHT Department of Economics, Johns Hopkins University, 3400 N. Charles St., Baltimore MD 21218. (410) 516 5728 wrightj@jhu.edu EDUCATION Harvard University 1993-1997. Ph.D., Economics (1997).

More information

MTH 141 Calculus 1 Syllabus Spring 2017

MTH 141 Calculus 1 Syllabus Spring 2017 Instructor: Section/Meets Office Hrs: Textbook: Calculus: Single Variable, by Hughes-Hallet et al, 6th ed., Wiley. Also needed: access code to WileyPlus (included in new books) Calculator: Not required,

More information

San José State University Department of Marketing and Decision Sciences BUS 90-06/ Business Statistics Spring 2017 January 26 to May 16, 2017

San José State University Department of Marketing and Decision Sciences BUS 90-06/ Business Statistics Spring 2017 January 26 to May 16, 2017 San José State University Department of Marketing and Decision Sciences BUS 90-06/30174- Business Statistics Spring 2017 January 26 to May 16, 2017 Course and Contact Information Instructor: Office Location:

More information

A Case-Based Approach To Imitation Learning in Robotic Agents

A Case-Based Approach To Imitation Learning in Robotic Agents A Case-Based Approach To Imitation Learning in Robotic Agents Tesca Fitzgerald, Ashok Goel School of Interactive Computing Georgia Institute of Technology, Atlanta, GA 30332, USA {tesca.fitzgerald,goel}@cc.gatech.edu

More information

PM tutor. Estimate Activity Durations Part 2. Presented by Dipo Tepede, PMP, SSBB, MBA. Empowering Excellence. Powered by POeT Solvers Limited

PM tutor. Estimate Activity Durations Part 2. Presented by Dipo Tepede, PMP, SSBB, MBA. Empowering Excellence. Powered by POeT Solvers Limited PM tutor Empowering Excellence Estimate Activity Durations Part 2 Presented by Dipo Tepede, PMP, SSBB, MBA This presentation is copyright 2009 by POeT Solvers Limited. All rights reserved. This presentation

More information

Math Placement at Paci c Lutheran University

Math Placement at Paci c Lutheran University Math Placement at Paci c Lutheran University The Art of Matching Students to Math Courses Professor Je Stuart Math Placement Director Paci c Lutheran University Tacoma, WA 98447 USA je rey.stuart@plu.edu

More information

Course Syllabus for Math

Course Syllabus for Math Course Syllabus for Math 1090-003 Instructor: Stefano Filipazzi Class Time: Mondays, Wednesdays and Fridays, 9.40 a.m. - 10.30 a.m. Class Place: LCB 225 Office hours: Wednesdays, 2.00 p.m. - 3.00 p.m.,

More information

Accounting 380K.6 Accounting and Control in Nonprofit Organizations (#02705) Spring 2013 Professors Michael H. Granof and Gretchen Charrier

Accounting 380K.6 Accounting and Control in Nonprofit Organizations (#02705) Spring 2013 Professors Michael H. Granof and Gretchen Charrier Accounting 380K.6 Accounting and Control in Nonprofit Organizations (#02705) Spring 2013 Professors Michael H. Granof and Gretchen Charrier 1. Office: Prof Granof: CBA 4M.246; Prof Charrier: GSB 5.126D

More information

BIOL 2402 Anatomy & Physiology II Course Syllabus:

BIOL 2402 Anatomy & Physiology II Course Syllabus: BIOL 2402 Anatomy & Physiology II Course Syllabus: Northeast Texas Community College exists to provide responsible, exemplary learning opportunities. Dr. Brenda Deming Office: Math/Science Building, Office

More information

CAAP. Content Analysis Report. Sample College. Institution Code: 9011 Institution Type: 4-Year Subgroup: none Test Date: Spring 2011

CAAP. Content Analysis Report. Sample College. Institution Code: 9011 Institution Type: 4-Year Subgroup: none Test Date: Spring 2011 CAAP Content Analysis Report Institution Code: 911 Institution Type: 4-Year Normative Group: 4-year Colleges Introduction This report provides information intended to help postsecondary institutions better

More information

EDUCATION IN THE INDUSTRIALISED COUNTRIES

EDUCATION IN THE INDUSTRIALISED COUNTRIES EDUCATION IN THE INDUSTRIALISED COUNTRIES PLAN EUROPE 2000 PUBLISHED UNDER THE AUSPICES OF THE EUROPEAN CULTURAL FOUNDATION PROJECT 1 EDUCATING MAN FOR THE XXIst CENTURY Volume 5 "EDUCATION IN THE INDUSTRIALISED

More information

Why Did My Detector Do That?!

Why Did My Detector Do That?! Why Did My Detector Do That?! Predicting Keystroke-Dynamics Error Rates Kevin Killourhy and Roy Maxion Dependable Systems Laboratory Computer Science Department Carnegie Mellon University 5000 Forbes Ave,

More information