(Ebook) Introduction to Bayesian Statistics 3rd Edition by William M Bolstad, James M Curran ISBN 1118091566 9781118091562

(Ebook) Introduction to Bayesian Statistics 3rd Edition by William M Bolstad, James M Curran ISBN 1118091566 9781118091562

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ISBN 10: 1118091566 
ISBN 13: 9781118091562
Author: William M Bolstad, James M Curran

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 staistics. The author continues to provide a Bayesian treatment of introductory statistical topics, such as scientific data gathering, discrete random variables, robust Bayesian methods, and Bayesian approaches to inferenfe cfor discrete random variables, bionomial proprotion, Poisson, normal mean, and simple linear regression.

In addition, newly-developing topics in the field are presented in four new chapters: Bayesian inference  with unknown mean and variance;  Bayesian inference for Multivariate Normal mean vector; Bayesian inference for Multiple Linear RegressionModel; and Computational Bayesian Statistics including Markov Chain Monte Carlo methods.

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. WinBUGS is discussed briefly in the coverage of Markov Chain Monte Carlo methods, and MiniTab macros and R functions are available on the book's related Web site to assist with chapter exercises.

(Ebook) Introduction to Bayesian Statistics 3rd Table of contents:

Chapter 1 Introduction to Statistical Science
1.1 The Scientific Method:honey 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
Chapter 2 Scientific Data Gathering
2.1 Sampling from a Real Population
2.2 Observational Studies and Designed Experiments
Chapter 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
Chapter 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 Events
4.5 Conditional Probability
4.6 Bayes’ Theorem
4.7 Assigning Probabilities
4.8 Odds and Bayes Factor
4.9 Beat the Dealer
Exercises
Chapter 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 Poisson Distribution
5.6 Joint Random Variables
5.7 Conditional Probability for Joint Random Variables
Exercises
Chapter 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
6.4 Bayes’ Theorem for Poisson with Discrete Prior
Exercises
Computer Exercises
Chapter 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
Chapter 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
Chapter 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 One-Sided Hypothesis
9.7 Testing a Two-Sided Hypothesis
Exercises
Monte Carlo Exercises
Chapter 10 Bayesian Inference for Poisson
10.1 Some Prior Distributions for Poisson
10.2 Inference for Poisson Parameter
Exercises
Computer Exercises
Chapter 11 Bayesian Inference for Normal Mean
11.1 Bayes’ Theorem for Normal Mean with a Discrete Prior
11.2 Bayes’ Theorem for Normal Mean with a Continuous Prior
11.3 Choosing Your Normal Prior
11.4 Bayesian Credible Interval for Normal Mean
11.5 Predictive Density for Next Observation
Exercises
Computer Exercises
Chapter 12 Comparing Bayesian and Frequentist Inferences for Mean
12.1 Comparing Frequentist and Bayesian Point Estimators
12.2 Comparing Confidence and Credible Intervals for Mean
12.3 Testing a One-Sided Hypothesis about a Normal Mean
12.4 Testing a Two-Sided Hypothesis about a Normal Mean
Exercises
Chapter 13 Bayesian Inference for Difference Between Means
13.1 Independent Random Samples from Two Normal Distributions
13.2 Case 1:honey Equal Variances
13.3 Case 2:honey Unequal Variances
13.4 Bayesian Inference for Difference Between Two Proportions Using Normal Approximation
13.5 Normal Random Samples from Paired Experiments
Exercises
Chapter 14 Bayesian Inference for Simple Linear Regression
14.1 Least Squares Regression
14.2 Exponential Growth Model
14.3 Simple Linear Regression Assumptions
14.4 Bayes’ Theorem for the Regression Model
14.5 Predictive Distribution for Future Observation
Exercises
Computer Exercises
Chapter 15 Bayesian Inference for Standard Deviation
15.1 Bayes’ Theorem for Normal Variance with a Continuous Prior
15.2 Some Specific Prior Distributions and the Resulting Posteriors
15.3 Bayesian Inference for Normal Standard Deviation
Exercises
Computer Exercises
Chapter 16 Robust Bayesian Methods
16.1 Effect of Misspecified Prior
16.2 Bayes’ Theorem with Mixture Priors
Exercises
Computer Exercises
Chapter 17 Bayesian Inference for Normal with Unknown Mean and Variance
17.1 The Joint Likelihood Function
17.2 Finding the Posterior when Independent Jeffreys’ Priors for μ and σ2 Are Used
17.3 Finding the Posterior when a Joint Conjugate Prior for μ and σ2 Is Used
17.4 Difference Between Normal Means with Equal Unknown Variance
17.5 Difference Between Normal Means with Unequal Unknown Variances
Computer Exercises
Appendix:honey Proof that the Exact Marginal Posterior Distribution of μ Is Student’s t
Chapter 18 Bayesian Inference for Multivariate Normal Mean Vector
18.1 Bivariate Normal Density
18.2 Multivariate Normal Distribution
18.3 The Posterior Distribution of the Multivariate Normal Mean Vector when Covariance Matrix Is Known
18.4 Credible Region for Multivariate Normal Mean Vector when Covariance Matrix Is Known
18.5 Multivariate Normal Distribution with Unknown Covariance Matrix
Computer Exercises
Chapter 19 Bayesian Inference for the Multiple Linear Regression Model
19.1 Least Squares Regression for Multiple Linear Regression Model
19.2 Assumptions of Normal Multiple Linear Regression Model
19.3 Bayes’ Theorem for Normal Multiple Linear Regression Model
19.4 Inference in the Multivariate Normal Linear Regression Model
19.5 The Predictive Distribution for a Future Observation
Computer Exercises
Chapter 20 Computational Bayesian Statistics Including Markov Chain Monte Carlo
20.1 Direct Methods for Sampling from the Posterior
20.2 Sampling Importance Resampling
20.3 Markov Chain Monte Carlo Methods
20.4 Slice Sampling
20.5 Inference from a Posterior Random Sample
20.6 Where to Next?

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Tags: William M Bolstad, James M Curran, Bayesian, Statistics