Family Studies Arena

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• Price: $49.95 $44.96
• Paperback: 320 pages
• Published: October 2012
• ISBN: 978-1-58488-849-9
• Publisher: Chapman and Hall/CRC
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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, 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, a wide range of applications from various disciplines, and numerous detailed exercises in every chapter.

Table of Contents

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

8.10 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