Bayesian statistical models can be represented by a joint probability function. This joint probability is a function of the data and the model parameters. Each parameter is estimated by integrating the joint probability function over all the other parameters in the model.
The Graphical Model is a powerful way of specifying the joint probability distribution. It allows complex models to be assembled from simple building blocks. We present a simple graphics editor (DoodleBUGS) which allows complex models to be drawn online.
The Graphical Model also provides a factorisation of the joint probability model. This factorisation of the joint probability distribution allows the use of simple efective Markov Chain Monte Carlo (MCMC) techniques to make inference.
The WinBUGS sofware takes the description of a model in graphical form (Doodle) or in a text form (BUGS language) and builds an object-based graph which allows the conditional distributions needed by MCMC to be easily calculated. A list of updater objects sits above the graph generating new values for the parameters of the model. Monitor objects can be created for storing and displaying summaries of parameters of interest.
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