Puza B. Bayesian Methods for Statistical Analysis

ANU Press, 2017. — 697 p. — ISBN: 9781921934254.Bayesian methods for statistical analysis is a book on statistical methods for analysing a wide variety of data. The book consists of 12 chapters, starting with basic concepts and covering numerous topics, including Bayesian estimation, decision theory, prediction, hypothesis testing, hierarchical models, Markov chain Monte Carlo methods, finite population inference, biased sampling and nonignorable nonresponse. The book contains many exercises, all with worked solutions, including complete computer code. It is suitable for self-study or a semester-long course, with three hours of lectures and one tutorial per week for 13 weeks.Bayesian Basics Part 1Bayes’ rule
Bayes factors
Bayesian models
The posterior distribution
The proportionality formula
Continuous parameters
Finite and infinite population inference
Continuous data
Conjugacy
Bayesian point estimation
Bayesian interval estimation
Inference on functions of the model parameter
Credibility estimates
Bayesian Basics Part 2
Frequentist characteristics of Bayesian estimators
Mixture prior distributions
Dealing with a priori ignorance
The Jeffreys prior
Bayesian decision theory
The posterior expected loss
The Bayes estimate
Bayesian Basics Part 3
Inference given functions of the data
Bayesian predictive inference
Posterior predictive p-values
Bayesian models with multiple parameters
Computational Tools
Solving equations
The Newton-Raphson algorithm
The multivariate Newton-Raphson algorithm
The Expectation-Maximisation (EM) algorithm
Variants of the NR and EM algorithms
Integration techniques
The optim() function
Monte Carlo BasicsThe method of Monte Carlo integration for estimating means
Other uses of the MC sample
Importance sampling
C estimation involving two or more random variables
The method of composition
Monte Carlo estimation of a binomial parameter
Random number generation
Sampling from an arbitrary discrete distribution
The inversion technique
Random number generation via compositions
Rejection sampling
Methods based on the rejection algorithm
Monte Carlo methods in Bayesian inference
MC predictive inference via the method of composition
Rao-Blackwell methods for estimation and prediction
MC estimation of posterior predictive p-values
MCMC Methods Part 1The Metropolis algorithm
The batch means method
Computational issues
Non-symmetric drivers and the general Metropolis algorithm
The Metropolis-Hastings algorithm
Independence drivers and block sampling
Gibbs steps and the Gibbs sampler
MCMC Methods Part 2Data augmentation
Inference via WinBUGS
Introduction to BUGS
A first tutorial in BUGS
Tutorial on calling BUGS in R
Bayesian Finite Population TheoryFinite population notation and terminology
Bayesian finite population models
Two types of sampling mechanism
Two types of inference
Analytic inference
Descriptive inference
Normal Finite Population Models
The basic normal-normal finite population model
The general normal-normal finite population model
Derivation of the predictive distribution of the nonsample vector
Alternative formulae for the predictive distribution of the nonsample vector
Prediction of the finite population mean and other linear combinations
Special cases including ratio estimation
The normal-normal-gamma finite population model
Special cases of the normal-normal-gamma finite population model
The case of an informative prior on the regression parameter
Transformations and Other Topics
Inference on complicated quantities
Data transformations
Frequentist properties of Bayesian finite population estimators
Biased Sampling and Nonresponse
Review of sampling mechanisms
Nonresponse mechanisms
Selection bias in volunteer surveys
A classical model for self-selection bias
Uncertainty regarding the sampling mechanism
Finite population inference under selection bias in volunteer surveys
Appendix A: Additional Exercises
Practice with the Metropolis algorithm
Practice with the MH algorithm
Practice with a Bayesian finite population regression model
Case study in Bayesian finite population models with biased sampling
Appendix B: Distributions and Notation
The normal distribution
The gamma distribution
The exponential distribution
The chi-squared distribution
The inverse gamma distribution
The t distribution
The F distribution
The (continuous) uniform distribution
The discrete uniform distribution
The binomial distribution
The Bernoulli distribution
The geometric distribution
Appendix C: Abbreviations and Acronyms