Lunn / Jackson / Best The BUGS Book

A Practical Introduction to Bayesian Analysis
1. Auflage 2013
ISBN: 978-1-4665-8666-6
Verlag: Taylor & Francis
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 399 Seiten

Reihe: Chapman & Hall/CRC Texts in Statistical Science

Bayesian statistical methods have become widely used for data analysis and modelling in recent years, and the BUGS software has become the most popular software for Bayesian analysis worldwide. Authored by the team that originally developed this software, The BUGS Book 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 and a wide range of applications from various disciplines.

The book introduces regression models, techniques for criticism and comparison, and a wide range of modelling issues before going into the vital area of hierarchical models, one of the most common applications of Bayesian methods. It deals with essentials of modelling without getting bogged down in complexity. The book emphasises model criticism, model comparison, sensitivity analysis to alternative priors, and thoughtful choice of prior distributions—all those aspects of the "art" of modelling that are easily overlooked in more theoretical expositions.

More pragmatic than ideological, the authors systematically work through the large range of "tricks" that reveal the real power of the BUGS software, for example, dealing with missing data, censoring, grouped data, prediction, ranking, parameter constraints, and so on. Many of the examples are biostatistical, but they do not require domain knowledge and are generalisable to a wide range of other application areas.

Full code and data for examples, exercises, and some solutions can be found on the book’s website.

Zielgruppe

Advanced undergraduate and graduate students of statistics and quantitative sciences.

Autoren/Hrsg.

Lunn, David

Jackson, Chris

Best, Nicky

Thomas, Andrew

Spiegelhalter, David

Fachgebiete

• Mathematik | Informatik EDV | Informatik Business Application Mathematische & Statistische Software
• Mathematik | Informatik Mathematik Stochastik Mathematische Statistik

Inhaltsverzeichnis

Introduction: Probability and Parameters
Probability
Probability distributions
Calculating properties of probability distributions
Monte Carlo integration

Monte Carlo Simulations Using BUGS
Introduction to BUGS
DoodleBUGS
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
Posterior predictive distributions
Conjugate Bayesian inference
Inference about a discrete parameter
Combinations of conjugate analyses
Bayesian and classical methods

Introduction to Markov Chain Monte Carlo Methods
Bayesian computation
Initial values
Convergence
Efficiency and accuracy
Beyond MCMC

Prior Distributions
Different purposes of priors
Vague, ‘objective’ and ‘reference’ priors
Representation of informative priors
Mixture of prior distributions
Sensitivity analysis

Regression Models
Linear regression with normal errors
Linear regression with non-normal errors
Nonlinear regression with normal errors
Multivariate responses
Generalised linear regression models
Inference on functions of parameters
Further reading

Categorical Data
2 × 2 tables
Multinomial models
Ordinal regression
Further reading

Model Checking and Comparison
Introduction
Deviance
Residuals
Predictive checks and Bayesian p-values
Model assessment by embedding in larger models
Model comparison using deviances
Bayes factors
Model uncertainty
Discussion on model comparison
Prior-data conflict

Issues in Modelling
Missing data
Prediction
Measurement error
Cutting feedback
New distributions
Censored, truncated and grouped observations
Constrained parameters
Bootstrapping
Ranking

Hierarchical Models
Exchangeability
Priors
Hierarchical regression models
Hierarchical models for variances
Redundant parameterisations
More general formulations
Checking of hierarchical models
Comparison of hierarchical models
Further resources

Specialised Models
Time-to-event data
Time series models
Spatial models
Evidence synthesis
Differential equation and pharmacokinetic models
Finite mixture and latent class models
Piecewise parametric models
Bayesian nonparametric models

Different Implementations of BUGS
Introduction BUGS engines and interfaces
Expert systems and MCMC methods
Classic BUGS
WinBUGS
OpenBUGS
JAGS

A Appendix: BUGS Language Syntax
Introduction
Distributions
Deterministic functions
Repetition
Multivariate quantities
Indexing
Data transformations
Commenting

B Appendix: Functions in BUGS
Standard functions
Trigonometric functions
Matrix algebra
Distribution utilities and model checking
Functionals and differential equations
Miscellaneous

C Appendix: 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

Bibliography

Index