Intro+to+WinBUGS.ppt

Introduction to WinBUGS Olivier Gimenez University of St Andrews, Scotland A brief history 1989: project began with a Unix version called BUGS 1998: first Windows version, WinBUGS was born Initially developed by the MRC Biostatistics Unit in Cambridge and now joint work with Imperial College School of Medicine at St Marys, London. Windows Bayesian inference Using Gibbs Sampling Software for the Bayesian analysis of complex statistical models using Markov chain Monte Carlo (MCMC) methods Who? Key principle You specify the prior and build up the likelihood WinBUGS computes the posterior by running a Gibbs sampling algorithm, based on: ?(?|D) / L(D|?) ?(?) WinBUGS computes some convergence diagnostics that you have to check Bayesian Model Selection Discriminating between different models can often be of particular interest, since they represent competing biological hypotheses. How do we decide which covariates to use? – often there may be a large number of possible covariates. Example (cont) We express the survival rate as a logistic function of the covariates: logit ?t = ? + ?Txt + ?t where xt denotes the set of covariate values at time t and ?t are random effects, ?t ~ N(0,?2). However, which rainfalls explain the survival rates for the adults? Alternatively, what values of ? are non-zero? Model Selection In the classical framework, likelihood ratio tests or information criterion (e.g. AIC) are often used. There is a “similar’’ Bayesian statistic – the DIC. This is programmed within WinBUGS – however its implementation is not suitable for hierarchical models (e.g. random effect models). In addition, the DIC is known to give fallacious results in even simple problems. Within the general Bayesian framework, there is a more natural way of dealing with the issue of model discrimination. Bayesian Approach We treat the model itself as an unknown parameter to be estimated. Then, applying Bayes’ Theorem we obtain the posterior distribution over both parameter