Bayesian Modeling Using WinBUGS

Abstract

integration, and their implementation in Bayesian inference 31 2.2 Markov chain Monte Carlo methods 2.2.1 The algorithm 36 2.2.2 Terminology and implementation details 2.3 Popular MCMC algorithms 2.3.1 The Metropolis-Hastings algorithm 2.3.2 Componentwise Metropolis-Hastings 2.3.3 The Gibbs sampler 2.3.4 Metropolis within Gibbs 2.3.5 The slice Gibbs sampler 2.3.6 A simple example using the slice sampler 2.4 Summary and closing remarks Problems 81 3 WinBUGS Software: Introduction, Setup, and Basic Analysis 83 275 8.1 Models with nonstandard distributions 8.1.1 Specification of arbitrary likelihood using the zeros-ones trick 8.12 The inverse Gaussian model 8.2 Models for positive continuous response variables 8.2.1 The gamma model 8.2.2 Other models 8.2.3 An example 8.3 Additional models for count data 8.3.1 The negative binomial model 8.3.2 The generalized Poisson model 8.3.3 Zero inflated models 8.3.4 The bivariate Poisson model 8.3.5 The Poisson difference model 8.4 Further GLM-based models and extensions 8.4.1 Survival analysis models 8.4.2 Multinomial models 8.4.3 Additional models and further reading Problems 9 Bayesian Hierarchical Models 305 9.1

Bayesian hypothesis testing for psychologists: A tutorial on the Savage–Dickey method

“…More detailed information can be found in Bayesian articles and books that discuss philosophical foundations (Lindley, 2000;O'Hagan & Forster, 2004), computational innovations (Gamerman & Lopes, 2006), and practical contributions (Congdon, 2003;Ntzoufras, 2009). An indepth discussion on the advantages of Bayesian inference, especially when compared to p-value 1 For more information about the difference between the three statistical paradigms, see for instance Christensen (2005), Hubbard and Bayarri (2003) and Royall (1997).…”

“…For most interesting models, this posterior is not available in closed-form, but instead has to be approximated by MCMC techniques. Fortunately, these MCMC techniques are implemented in the popular WinBUGS program (Lunn et al, 2000;Lunn et al, 2009;Ntzoufras, 2009); when using WinBUGS, all researchers have to do is to describe their model using an intuitive scripting language, and the details of the sampling process are automatically taken care of by WinBUGS (see Appendix B for examples). 2.…”

The BUGS project: Evolution, critique and future directions

“…Numerous applications of the software can be found in the literature, in a wide array of application areas, including disease mapping [4], pharmacometrics [5], ecology [6], health-economics [7], genetics [8], archaeology [9], psychometrics [10], coastal engineering [11], educational performance [12], behavioural studies [13], econometrics [14], automated music transcription [15], sports modelling [16], fisheries stock assessment [17], and actuarial science [18]. The software is also used widely for the teaching of Bayesian modelling ideas to students and researchers the world over, and several texts use BUGS extensively for illustrating the Bayesian approach [19][20][21][22][23][24][25][26]. The importance of the software has been acknowledged in 'An International Review of U.K. Research in Mathematics' (http://www.cms.ac.uk/irm/irm.pdf).…”

Modelling African swine fever presence and reported abundance in the Russian Federation using national surveillance data from 2007 to 2014

“…Univariable analyses were then conducted and variables associated with at least one coefficient for which zero was not included in the 80% credible interval of its posterior distribution were retained for multivariable analyses. Next, all selected variables were added one by one following a stepwise forward selection procedure using the Deviance Information Criterion (DIC) as the selection criterion (Ntzoufras, 2009). The DIC is based on a trade-off between the fit of…”