Aalborg University - Departments of Mathematics & Computer Science
Both graphical models and Markov chain Monte Carlo methods enable fitting models of virtually unlimited complexity. If the amount of data is sufficient you will always get sensible conclusions, but if data is sparse compared to the complexity of the model then all the parameters will not be identifyable. Based on some observed data we want to draw conclusions about the parameters of the model, but how can we identify whether a model is too complex?
Information properties of the datamaterial can be examined using the observed Fisher information. In missing data problems we may not in general be able to calculate the observed Fisher information directly and therefore we need a method to find an approximation. Markov chain Monte Carlo methods can be used to calculate an approximation of the likelihood function in any missing data problem, (Geyer & Thompson 92) and (Gelfand & Carlin 93), and moreover we can also calculate other usefull objects such as the observed Fisher information.
I will discuss how to calculate the Monte Carlo observed Fisher information in graphical models with incomplete data and furthermore I will present results obtained in a very simple example.