
Introduction to Bayesian Statistics
by Bolstad, William M.Buy New
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Summary
Author Biography
Table of Contents
Preface | |
Preface to First Edition | |
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 OneSided Hypothesis | |
Testing a TwoSided Hypothesis | |
Exercises | |
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 OneSided Hypothesis about a Normal Mean | |
Testing a TwoSided Hypothesis about a Normal Mean | |
Exercises | |
Bayesian Infer | |
Table of Contents provided by Publisher. All Rights Reserved. |
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