Hybrid method for quantifying and analyzing Bayesian belief nets

Bayesian belief nets (BBNs) have become a popular tool for specifying high-dimensional probabilistic models. Commercial tools with an advanced graphical user interface that support BBNs construction and inference are available. Thus, building and working with BBNs is very efficient as long as one is not forced to quantify complex BBNs. A high assessment burden of discrete BBNs is often caused by the discretization of continuous variables. Until recently, continuous BBNs were restricted to the joint normal distribution. We present the 'copula-vine' approach to continuous BBNs. This approach is quite general and allows traceable and defendable quantification methods, but it comes at a price: these BBNs must be evaluated by Monte Carlo simulation. Updating such a BBN requires re-sampling the whole structure. The advantages of fast updating algorithms for discrete BBNs are decisive. A hybrid method advanced here samples the continuous BBN once, and then discretizes this so as to enable fast updating. This combines the reduced assessment burden and modelling flexibility of the continuous BBNs with the fast updating algorithms of discrete BBNs. Sampling large complex structures only once can still involve time consuming numerical calculations. Therefore a new sampling protocol based on normal vines is developed. Normal vines are used to realize the dependence structure specified via (conditional) rank correlations on the continuous BBN. We will emphasize the advantages of this method by means of examples. Copyright (c) 2006 John Wiley & Sons, Ltd.