BUGS Book A Practical Introduction to Bayesian Analysis

ISBN-10: 1584888490

ISBN-13: 9781584888499

Edition: 2013

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In recent years, Bayesian methods have become the most widely used statistical methods for data analysis and modeling. The BUGS software has become the most popular software for Bayesian analysis worldwide. Authored by the team that originally developed this software, Bayesian Analysis using BUGS provides a practical introduction to this program and its use. The text presents complete coverage of all the functionalities of BUGS, including prediction, missing data, model criticism, and prior sensitivity. It also features a large number of worked examples, a wide range of applications from various disciplines, and numerous detailed exercises in every chapter.
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Book details

List price: $59.95
Copyright year: 2013
Publisher: CRC Press LLC
Publication date: 10/2/2012
Binding: Paperback
Pages: 399
Size: 6.00" wide x 9.00" long x 0.75" tall
Weight: 1.100
Language: English

Introduction: Probability and parameters
Probability distributions
Calculating properties of probability distributions
Monte Carlo integration
Monte Carlo simulations using BUGS
Introduction to BUGS
Directed graphical models
The BUGS language
Running BUGS models
Running WinBUGS for a simple example
Using BUGS to simulate from distributions
Transformations of random variables
Complex calculations using Monte Carlo
Multivariate Monte Carlo analysis
Predictions with unknown parameters
Introduction to Bayesian inference
Bayesian learning
Bayes' theorem for observable quantities
Bayesian inference for parameters
Posterior predictive distributions
Conjugate Bayesian inference
Binomial data
Normal data with unknown mean, known variance
Inference about a discrete parameter
Combinations of conjugate analyses
Bayesian and classical methods
Likelihood-based inference
Long-run properties of Bayesian methods
Model-based vs procedural methods
The "likelihood principle"
Introduction to Markov chain Monte Carlo methods
Bayesian computation
Single-parameter models
Multi-parameter models
Monte Carlo integration for evaluating posterior integrals
Markov chain Monte Carlo methods
Gibbs sampling
Gibbs sampling and directed graphical models
Derivation of full conditional distributions in BUGS
Other MCMC methods
Initial values
Detecting convergence/stationarity by eye
Formal detection of convergence/stationarity
Efficiency and accuracy
Monte Carlo standard error of the posterior mean
Accuracy of the whole posterior
Beyond MCMC
Prior distributions
Different purpose of priors
Vague, "objective," and "reference" priors
Discrete uniform distributions
Continuous uniform distributions and Jeffreys prior
Location parameters
Counts and rates
Scale parameters
Distributions on the positive integers
More complex situations
Representation of informative priors
Elicitation of pure judgement
Discounting previous data
Mixture of prior distributions
Sensitivity analysis
Regression models
Linear regression with normal errors
Linear regression with non-normal errors
Non-linear regression with normal errors
Multivariate responses
Generalised linear regression models
Inference on functions of parameters
Further reading
Categorical data
2 X 2 tables
Tables with one margin fixed
Case-control studies
Tables with both margins fixed
Multinomial models
Conjugate analysis
Non-conjugate analysis-parameter constraints
Categorical data with covariates
Multinomial and Poisson regression equivalence
Contingency tables
Ordinal regression
Further reading
Model checking and comparison
Standardised Pearson residuals
Multivariate residuals
Observed p-values for distributional shape
Deviance residuals and tests of fit
Predictive checks and Bayesian p-values
Interpreting discrepancy statistics - how big is big?
Out-of-sample prediction
Checking functions based on data alone
Checking functions based on data and parameters
Goodness of fit for grouped data
Model assessment by embedding in larger models
Model comparison using deviances
pD: The effective number of parameters
Issues with pD
Alternative measures of the effective number of parameters
DIC for model comparison
How and why does WinBUGS partition DIC and pD?
Alternatives to DIC
Bayes factors
Lindley-Bartlett paradox in model selection
Computing marginal likelihoods
Model uncertainty
Bayesian model averaging
MCMC sampling over a space of models
Model averaging when all models are wrong
Model expansion
Discussion on model comparison
Prior-data conflict
Identification of prior-data conflict
Accommodation of prior-data conflict
Issues in Modelling
Missing data
Missing response data
Missing covariate data
Measurement error
Cutting feedback
New distributions
Specifying a new sampling distribution
Specifying a new prior distribution
Censored, truncated, and grouped observations
Censored observations
Truncated sampling distributions
Grouped, rounded, or interval-censored data
Constrained parameters
Univariate fully specified prior distributions
Multivariate fully specified prior distributions
Prior distributions with unknown parameters
Hierarchical models
Unit-specific parameters
Parameter constraints
Priors for variance components
Hierarchical regression models
Data formatting
Hierarchical models for variances
Redundant parameterisations
More general formulations
Checking of hierarchical models
Comparison of hierarchical models
"Focus": The crucial element of model comparison in hierarchical models
Further resources
Specialised models
Time-to-event data
Parametric survival regression
Time series models
Spatial models
Intrinsic conditionally autoregressive (CAR) models
Supplying map polygon data to WinBUGS and creating adjacency matrices
Multivariate CAR models
Proper CAR model
Poisson-gamma moving average models
Geostatistical models
Evidence synthesis
Generalised evidence synthesis
Differential equation and pharmacokinetic models
Finite mixture and latent class models
Mixture models using an explicit likelihood
Piecewise parametric models
Change-point models
Semiparametric survival models
Bayesian nonparametric models
Dirichlet process mixtures
Stick-breaking implementation
Different implementations of BUGS
Introduction-BUGS engines and interfaces
Expert systems and MCMC methods
Classic BUGS
Using WinBUGS: compound documents
Formatting data
Using the WinBUGS graphical interface
Interfaces with other software
Differences from WinBUGs
OpenBUGS on Linux
Parallel computation
Extensibility: modules
Language differences
Other differences from WinBUGS
Running JAGS from the command line
Running JAGS from R
BUGS language syntax
Standard distributions
Censoring and truncation
Non-standard distributions
Deterministic functions
Standard functions
Special functions
Add-on functions
Multivariate quantities
Functions as indices
Implicit indexing
Nested indexing
Data transformations
Functions in BUGS
Standard functions
Trigonometric functions
Matrix algebra
Distribution utilities and model checking
Functionals and differential equations
Distributions in BUGS
Continuous univariate, unrestricted range
Continuous univariate, restricted to be positive
Continuous univariate, restricted to a finite interval
Continuous multivariate distributions
Discrete univariate distributions
Discrete multivariate distributions
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