2001
   Basel, Switzerland

Graphical Models and Missing Data

Dave Lunn

Imperial College School of Medicine

Missing data are often 'non-ignorable', for example, assayed concentrations that fall below the limit of quantification (LOQ). In this talk I will discuss how and why the use of graphical modelling theory and MCMC techniques renders both the specification and analysis of arbitrary missing data problems easy. Graphical modelling entails the (abstract) specification of a full probability model (FPM), that is, a joint distribution for all stochastic quantities. This is the same regardless of whether any of the observable quantities have actually been observed -- thus missing data and observed data enter the model in exactly the same way. Under fairly general conditions this joint distribution can be factorized into a product of simple 'local' components, meaning that the specification of complex mechanisms can be broken down into a number of much simpler specifications. These statements about graphical models are true regardless of the modeller's preferred methodology: where maximum likelihood and MCMC approaches differ, in this respect, is in the inferential process. Likelihood-based inference would typically begin with integration of the FPM with respect to the missing data (as well as the random effects, etc.) whereas MCMC methods can exploit the form of the FPM directly (as it is proportional to the joint posterior) -- the appropriate integrals are essentially evaluated during the analysis.