Bolstad W.M. Introduction to Bayesian Statistics

2nd ed. — Wiley, 2007. — 463 p.The use of Bayesian methods in applied statistical analysis has become increasingly popular, yet most introductory statistics texts continue to only present the subject using frequentist methods. Introduction to Bayesian Statistics, Second Edition focuses on Bayesian methods that can be used for inference, and it also addresses how these methods compare favorably with frequentist alternatives. Teaching statistics from the Bayesian perspective allows for direct probability statements about parameters, and this approach is now more relevant than ever due to computer programs that allow practitioners to work on problems that contain many parameters.
This book uniquely covers the topics typically found in an introductory statistics book-but from a Bayesian perspective-giving readers an advantage as they enter fields where statistics is used.Introduction to Statistical Science
The Scientific Method: A Process for Learning
The Role of Statistics in the Scientific Method
Main Approaches to Statistics
Purpose and Organization of This Text
Scientific Data Gathering
Sampling from a Real Population
Observational Studies and Designed Experiments Monte Carlo Exercises
Displaying and Summarizing Data
Graphically Displaying a Single Variable
Graphically Comparing Two Samples
Measures of Location
Measures of Spread
Displaying Relationships Between Two or More Variables
Measures of Association for Two or More Variables Exercises
Logic, Probability, and Uncertainty
Deductive Logic and Plausible Reasoning
Probability
Axioms of Probability
Joint Probability and Independent Events
Conditional Probability
Bayes' Theorem
Assigning Probabilities
Odds Ratios and Bayes Factor
Beat the Dealer Exercises
Discrete Random Variables
Discrete Random Variables
Probability Distribution of a Discrete Random Variable
Binomial Distribution
Hypergeometric Distribution
Poisson Distribution
Joint Random Variables
Conditional Probability for Joint Random Variables Exercises
Bayesian Inference for Discrete Random Variables
Two Equivalent Ways of Using Bayes' Theorem
Bayes' Theorem for Binomial with Discrete Prior
Important Consequences of Bayes' Theorem
Bayes' Theorem for Poisson with Discrete Prior
Exercises
Computer Exercises
Continuous Random Variables
Probability Density Function
Some Continuous Distributions
Joint Continuous Random Variables
Joint Continuous and Discrete Random Variables Exercises
Bayesian Inference for Binomial Proportion
Using a Uniform Prior
Using a Beta Prior
Choosing Your Prior
Summarizing the Posterior Distribution
Estimating the Proportion
Bayesian Credible Interval Exercises
Computer Exercises
Comparing Bayesian and Frequentist Inferences for Proportion
Frequentist Interpretation of Probability and Parameters
Point Estimation
Comparing Estimators for Proportion
Interval Estimation
Hypothesis Testing
Testing a One-Sided Hypothesis
Testing a Two-Sided Hypothesis Exercises
Monte Carlo Exercises
Bayesian Inference for Poisson
Some Prior Distributions for Poisson
Inference for Poisson Parameter Exercises
Computer Exercises
Bayesian Inference for Normal Mean
Bayes' Theorem for Normal Mean with a Discrete Prior
Bayes' Theorem for Normal Mean with a Continuous Prior
Choosing Your Normal Prior
Bayesian Credible Interval for Normal Mean
Predictive Density for Next Observation Exercises
Computer Exercises
Comparing Bayesian and Frequentist Inferences for Mean
Comparing Frequentist and Bayesian Point Estimators
Comparing Confidence and Credible Intervals for Mean
Testing a One-Sided Hypothesis about a Normal Mean
Testing a Two-Sided Hypothesis about a Normal Mean Exercises
Bayesian Inference for Difference Between Means
Independent Random Samples from Two Normal Distributions
Case 1: Equal Variances
Case 2: Unequal Variances
Bayesian Inference for Difference Between Two Proportions Using Normal Approximation
Normal Random Samples from Paired Experiments Exercises
Bayesian Inference for Simple Linear Regression
Least Squares Regression
Exponential Growth Model
Simple Linear Regression Assumptions
Bayes' Theorem for the Regression Model
Predictive Distribution for Future Observation Exercises
Computer Exercises
Bayesian Inference for Standard Deviation
Bayes' Theorem for Normal Variance with a Continuous Prior
Some Specific Prior Distributions and the Resulting Posteriors
Bayesian Inference for Normal Standard Deviation Exercises
Computer Exercises
Robust Bayesian Methods
Effect of Misspecified Prior
Bayes' Theorem with Mixture Priors Exercises
Computer Exercises
Introduction to Calculus
Use of Statistical Tables
Using the Included Minitab Macros
Using the Included R Functions
Answers to Selected Exercises