Learning Bayesian networks probabilities from longitudinal data

Many real applications of Bayesian networks (BN's) concern problems in which several observations are collected over time on a certain number of similar plants. This situation is typical of the contest of medical monitoring, in which several measurements of the relevant physiological quantities are available over time on a population of patients under treatment, and the conditional probabilities that describe the model are usually obtained from the available data through a suitable learning algorithm. In situations with small data sets for each plant, it is useful to reinforce the parameter estimation process of the BN by taking into account the observations obtained from other similar plants. On the other hand, a desirable feature to be preserved is the ability to learn individualized conditional probability tables, rather than pooling together all the available data. In this work we apply a Bayesian hierarchical model able to preserve individual parameterization, and, at the same time, to allow the conditionals of each plant to borrow strength from all the experience contained in the data-base. A testing example and an application in the context of diabetes monitoring will be shown.