Statistical matching of multiple sources: A look through coherence

In several applications there is the need to consider different data sources and to integrate information: a specific case is the so-called statistical matching, where data sources have just a set of common variables and inference is required on the other variables. The traditional way to cope with such situations is to combine the available data with assumptions strong enough to identify pointwise the joint probability. Such assumptions cannot always be justified and inference should take into account all the set of compatible probabilities. In this paper, we show how statistical matching problems can be managed by means of coherent conditional probability: coherence allows us to combine the knowledge coming from different multiple sources, included those given from field experts, without necessarily assuming further hypothesis. Moreover, inferences and decisions can be dealt with by taking in consideration also logical constraints among the variables, which arise naturally in the applications. An example showing advantages and drawbacks of the proposed method is given.