Introduction to Bayesian Statistics - 3rd Edition

Informationen zum Autor WILLIAM M. BOLSTAD, PhD, is a retired Senior Lecturer in the Department of Statistics at The University of Waikato, New Zealand. Dr. Bolstad's research interests include Bayesian statistics, MCMC methods, recursive estimation techniques, multiprocess dynamic time series models, and forecasting. He is author of Understanding Computational Bayesian Statistics, also published by Wiley. JAMES M. CURRAN is a Professor of Statistics in the Department of Statistics at the University of Auckland, New Zealand. Professor Curran's research interests include the statistical interpretation of forensic evidence, statistical computing, experimental design, and Bayesian statistics. He is the author of two other books including Introduction to Data Analysis with R for Forensic Scientists, published by Taylor and Francis through its CRC brand. Klappentext "...this edition is useful and effective in teaching Bayesian inference at both elementary and intermediate levels. It is a well-written book on elementary Bayesian inference, and the material is easily accessible. It is both concise and timely, and provides a good collection of overviews and reviews of important tools used in Bayesian statistical methods."There is a strong upsurge in the use of Bayesian methods in applied statistical analysis, yet most introductory statistics texts only present frequentist methods. Bayesian statistics has many important advantages that students should learn about if they are going into fields where statistics will be used. In this third Edition, four newly-added chapters address topics that reflect the rapid advances in the field of Bayesian statistics. The authors continue to provide a Bayesian treatment of introductory statistical topics, such as scientific data gathering, discrete random variables, robust Bayesian methods, and Bayesian approaches to inference for discrete random variables, binomial proportions, Poisson, and normal means, and simple linear regression. In addition, more advanced topics in the field are presented in four new chapters: Bayesian inference for a normal with unknown mean and variance; Bayesian inference for a Multivariate Normal mean vector; Bayesian inference for the Multiple Linear Regression Model; and Computational Bayesian Statistics including Markov Chain Monte Carlo. The inclusion of these topics will facilitate readers' ability to advance from a minimal understanding of Statistics to the ability to tackle topics in more applied, advanced level books. Minitab macros and R functions are available on the book's related website to assist with chapter exercises. Introduction to Bayesian Statistics, Third Edition also features:* Topics including the Joint Likelihood function and inference using independent Jeffreys priors and join conjugate prior* The cutting-edge topic of computational Bayesian Statistics in a new chapter, with a unique focus on Markov Chain Monte Carlo methods* Exercises throughout the book that have been updated to reflect new applications and the latest software applications* Detailed appendices that guide readers through the use of R and Minitab software for Bayesian analysis and Monte Carlo simulations, with all related macros available on the book's websiteIntroduction to Bayesian Statistics, Third Edition is a textbook for upper-undergraduate or first-year graduate level courses on introductory statistics course with a Bayesian emphasis. It can also be used as a reference work for statisticians who require a working knowledge of Bayesian statistics. Zusammenfassung ". this edition is useful and effective in teaching Bayesian inference at both elementary and intermediate levels. It is a well-written book on elementary Bayesian inference, and the material is easily accessible. Inhaltsverzeichnis Preface xiii 1 Introduction to Statistical Science 1 1.1 The Scientic Method: A Pr...

List of contents

Preface xiii
 
1 Introduction to Statistical Science 1
 
1.1 The Scientic Method: A Process for Learning 3
 
1.2 The Role of Statistics in the Scientic Method 5
 
1.3 Main Approaches to Statistics 5
 
1.4 Purpose and Organization of This Text 8
 
2 Scientic Data Gathering 13
 
2.1 Sampling from a Real Population 14
 
2.2 Observational Studies and Designed Experiments 17
 
Monte Carlo Exercises 23
 
3 Displaying and Summarizing Data 31
 
3.1 Graphically Displaying a Single Variable 32
 
3.2 Graphically Comparing Two Samples 39
 
3.3 Measures of Location 41
 
3.4 Measures of Spread 44
 
3.5 Displaying Relationships Between Two or More Variables 46
 
3.6 Measures of Association for Two or More Variables 49
 
Exercises 52
 
4 Logic, Probability, and Uncertainty 59
 
4.1 Deductive Logic and Plausible Reasoning 60
 
4.2 Probability 62
 
4.3 Axioms of Probability 64
 
4.4 Joint Probability and Independent Events 65
 
4.5 Conditional Probability 66
 
4.6 Bayes' Theorem 68
 
4.7 Assigning Probabilities 74
 
4.8 Odds and Bayes Factor 75
 
4.9 Beat the Dealer 76
 
Exercises 80
 
5 Discrete Random Variables 83
 
5.1 Discrete Random Variables 84
 
5.2 Probability Distribution of a Discrete Random Variable 86
 
5.3 Binomial Distribution 90
 
5.4 Hypergeometric Distribution 92
 
5.5 Poisson Distribution 93
 
5.6 Joint Random Variables 96
 
5.7 Conditional Probability for Joint Random Variables 100
 
Exercises 104
 
6 Bayesian Inference for Discrete Random Variables 109
 
6.1 Two Equivalent Ways of Using Bayes' Theorem 114
 
6.2 Bayes' Theorem for Binomial with Discrete Prior 116
 
6.3 Important Consequences of Bayes' Theorem 119
 
6.4 Bayes' Theorem for Poisson with Discrete Prior 120
 
Exercises 122
 
Computer Exercises 126
 
7 Continuous Random Variables 129
 
7.1 Probability Density Function 131
 
7.2 Some Continuous Distributions 135
 
7.3 Joint Continuous Random Variables 143
 
7.4 Joint Continuous and Discrete Random Variables 144
 
Exercises 147
 
8 Bayesian Inference for Binomial Proportion 149
 
8.1 Using a Uniform Prior 150
 
8.2 Using a Beta Prior 151
 
8.3 Choosing Your Prior 154
 
8.4 Summarizing the Posterior Distribution 158
 
8.5 Estimating the Proportion 161
 
8.6 Bayesian Credible Interval 162
 
Exercises 164
 
Computer Exercises 167
 
9 Comparing Bayesian and Frequentist Inferences for Proportion 169
 
9.1 Frequentist Interpretation of Probability and Parameters 170
 
9.2 Point Estimation 171
 
9.3 Comparing Estimators for Proportion 174
 
9.4 Interval Estimation 175
 
9.5 Hypothesis Testing 178
 
9.6 Testing a One-Sided Hypothesis 179
 
9.7 Testing a Two-Sided Hypothesis 182
 
Exercises 187
 
Monte Carlo Exercises 190
 
10 Bayesian Inference for Poisson 193
 
10.1 Some Prior Distributions for Poisson 194
 
10.2 Inference for Poisson Parameter 200
 
Exercises 207
 
Computer Exercises 208
 
11 Bayesian Inference for Normal Mean 211
 
11.1 Bayes' Theorem for Normal Mean with a Discrete Prior 211
 
11.2 Bayes' Theorem for Normal Mean with a Continuous Prior 218
 
11.3 Choosing Your Normal Prior 222
 
11.4 Bayesian Credible Interval for Normal Mean 224
 
11.5 Pred

Product details

• Authors: Bolstad, William Bolstad, William M Bolstad, William M. Bolstad, William M. Curran Bolstad, Bolstad William M., James M Curran, James M. Curran, James Michael Curran
• Publisher: Blackwell Scientific Publishers Ltd
• Languages: English
• Product format: Hardback
• Released: 01.12.2016
• EAN: 9781118091562
• ISBN: 978-1-118-09156-2
• Dimensions: 162 mm x 242 mm x 32 mm
• Subjects: Natural sciences, medicine, IT, technology > Mathematics > Probability theory, stochastic theory, mathematical statistics; Statistik, Statistics, Bayes-Verfahren, Bayesian Analysis, Statistics - Text & Reference, Statistik / Lehr- u. Nachschlagewerke, Spezialthemen Statistik, Statistics Special Topics, Bayessches Verfahren