How can I update a Bayesian network model given new data on only a subset of the variables in the original model?

There are several methods for inferring network structure in Bayesian networks, given data.

In my case I have a Bayesian network model built from old data, and I have a new source of data that I want to use to update the model, both in terms of structure and parameters. This new data source has a number of observations, much higher than the past data, making it ideal for structure inference. The problem is that the new data covers only a subset of the variables in the original model. Has anyone heard of a way to update BN model network structure (and parameters) given only a subset of the variables in the model?