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Introduction to Bayesian Statistics Bolstad, William M.

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EAN
9780471270201
ISBN
9780471270201
Kategorie

Über dieses Produkt

Product Identifiers

Publisher
Wiley & Sons, Incorporated, John
ISBN-10
0471270202
ISBN-13
9780471270201
eBay Product ID (ePID)
30287036

Product Key Features

Number of Pages
376 Pages
Language
English
Publication Name
Introduction to Bayesian Statistics
Subject
Probability & Statistics / General, Probability & Statistics / Bayesian Analysis
Publication Year
2004
Type
Textbook
Author
William M. Bolstad
Subject Area
Mathematics
Format
Hardcover

Dimensions

Item Height
1 in
Item Weight
22.8 Oz
Item Length
9.5 in
Item Width
6.5 in

Additional Product Features

Intended Audience
Scholarly & Professional
LCCN
2003-057660
Reviews
"I would recommend this book if you are interested in teaching an introductory in Bayesian statistics..."  ( The American Statistician , February 2006) "...a very useful undergraduate text presenting a novel approach to an introductory statistics course." ( Biometrics , September 2005) "I cannot think of a better book for teachers of introductory statistics who want a readable and pedagogically sound text to introduce Bayesian statistics." ( Statistics in Medical Research , October 2005) "...this book fills a gap for teaching elementary Bayesian statistics...it could easily serve as a self-learning text..." ( Technometrics , May 2005) [In a review comparing Bolstad with another book,] "I will keep both of these books on my shelf, but I expect that Bolstad will be the one most borrowed by my colleagues."( significance , December 2004) "...does an excellent job of presenting Bayesian Statistics as a perfectly reasonable approach to elementary problems of statistics...I must heartily recommend this book..." ( STATS: The Magazine for Students of Statistics , Fall 2004)
Dewey Edition
22
Illustrated
Yes
Dewey Decimal
519.542
Table Of Content
Preface.1.  Introduction to Statistical Science.1.1 The Scientific Method: A Process for Learning.1.2 The Role of Statistics in the Scientific Method.1.3 Main Approaches to Statistics.1.4 Purpose and Organization of This Text.2.  Scientific Data Gathering.2.1 Sampling from a Real Population.2.2 Observational Studies and Designed Experiments.Monte Carlo Exercises.3.  Displaying and Summarizing Data.3.1 Graphically Displaying a Single Variable.3.2 Graphically Comparing Two Samples.3.3 Measures of Location.3.4 Measures of Spread.3.5 Displaying Relationships Between Two or More Variables.3.6 Measures of Association for Two or More Variables.Exercises.4.  Logic, Probability, and Uncertainty.4.1 Deductive Logic and Plausible Reasoning.4.2 Probability.4.3 Axioms of Probability.4.4 Joint Probability and Independent Event s.4.5 Conditional Probability.4.6 Bayes' Theorem.4.7 Assigning Probabilities.4.8 Odds Ratios and Bayes Factor.Exercises.5.  Discrete Random Variables.5.1 Discrete Random Variables.5.2 Probability Distribution of a Discrete Random Variable.5.3 Binomial Distribution.5.4 Hypergeometric Distribution.5.5 Joint Random Variables.5.6 Conditional Probability for Joint Random Variables.Exercises.6.  Bayesian Inference for Discrete Random Variables.6.1 Two Equivalent Ways of Using Bayes' Theorem.6.2 Bayes' Theorem for Binomial with Discrete Prior.6.3 Important Consequences of Bayes' Theorem.Exercises.Computer Exercises.7.  Continuous Random Variables.7.1 Probability Density Function.7.2 Some Continuous Distributions.7.3 Joint Continuous Random Variables.7.4 Joint Continuous and Discrete Random Variables.Exercises.8.  Bayesian Inference for Binomial Proportion.8.1 Using a Uniform Prior.8.2 Using a Beta Prior.8.3 Choosing Your Prior.8.4 Summarizing the Posterior Distribution.8.5 Estimating the Proportion.8.6 Bayesian Credible Interval.Exercises.Computer Exercises.9.  Comparing Bayesian and Frequentist Inferences for Proportion.9.1 Frequentist Interpretation of Probability and Parameters.9.2 Point Estimation.9.3 Comparing Estimators for Proportion.9.4 Interval Estimation.9.5 Hypothesis Testing.9.6 Testing a OneSided Hypothesis.9.7 Testing a TwoSided Hypothesis.Exercises.Monte Carlo Exercises.10.  Bayesian Inference for Normal Mean.10.1 Bayes' Theorem for Normal Mean with a Discrete Prior.10.2 Bayes' Theorem for Normal Mean with a Continuous Prior.10.3 Choosing Your Normal Prior.10.4 Bayesian Credible Interval for Normal Mean.10.5 Predictive Density for Next Observation.Exercises.Computer Exercises.11.  Comparing Bayesian and Frequentist Inferences for Mean.11.1 Comparing Frequentist and Bayesian Point Estimators.11.2 Comparing Confidence and Credible Intervals for Mean.11.3 Testing a OneSided Hypothesis about a Normal Mean.11.4 Testing a TwoSided Hypothesis about a Normal Mean.Exercises.12.  Bayesian Inference for Difference between Means.12.1 Independent Random Samples from Two Normal Distributions.12.2 Case 1: Equal Variances.12.3 Case 2: Unequal Variances.12.4 Bayesian Inference for Difference Between Two Proportions Using Normal Approximation.12.5 Normal Random Samples from Paired Experiments.Exercises.13.  Bayesian Inference for Simple Linear Regression.13.1 Least Squares Regression.13.2 Exponential Growth Model.13.3 Simple Linear Regression Assumptions.13.4 Bayes' Theorem for the Regression Model.13.5 Predictive Distribution for Future Observation.Exercises.14.  Robust Bayesian Methods.14.1 Effect of Misspecified Prior.14.2 Bayes' Theorem with Mixture Priors.Exercises.A.  Introduction to Calculus.B.  Use of Statistical Tables.C.  Using the Included Minitab Macros.D.  Using the Included R Functions.E.  Answers to Selected Exercises.References.Index.
Synopsis
Traditionally, introductory statistics courses have been taught from a frequentist perspective. The recent upsurge in the use of Bayesian methods in applied statistical analysis highlights the need to expose students early on to the Bayes theorem, its advantages, and its applications. Based on the author's successful courses, Introduction to Bayesian Statistics introduces statistics from a Bayesian perspective in a way that is understandable to readers with a reasonable mathematics background. Covering most of the same ground found in a typical statistics book-but from a Bayesian perspective-Introduction to Bayesian Statistics offers thorough, clearly-explained discussions of: Scientific data gathering, including the use of random sampling methods and randomized experiments to make inferences on cause-effect relationships The rules of probability, including joint, marginal, and conditional probability Discrete and continuous random variables Bayesian inferences for means and proportions compared with the corresponding frequentist ones The simple linear regression model analyzed in a Bayesian manner To assist in the understanding of Bayesian statistics, this introduction provides readers with exercises (with selected answers); summaries of main points from each chapter; a calculus refresher, and a summary on the use of statistical tables; and R functions and Minitab macros for Bayesian analysis and Monte Carlo simulations (downloadable from the associated Web site), There is a strong upsurge in the use of Bayesian methods in applied statistical analysis, yet most introductory statistics texts only present frequentist methods. In Bayesian statistics the rules of probability are used to make inferences about the parameter.
LC Classification Number
QA279.5.B65 2004

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