An Efficient Probabilistic Merging Procedure Applied to Statistical Matching

We propose to use a recently introduced merging procedure for jointly inconsistent probabilistic assessments to the statistical matching problem. The merging procedure is based on an efficient L1 distance minimization through mixed-integer linear programming that results not only feasible but also meaningful for imprecise (lower-upper) probability evaluations elicitation. Significance of the method can be appreciated whenever among quantities (events) there are logical (structural) constraints and there are different sources of information. Statistical matching problem has these features and is characterized by a set of random (discrete) variables that cannot be jointly observed. Separate observations share some common variable and this, together with structural constraints, make sometimes inconsistent the estimates of probability occurrences. Even though estimates on statistical matching are mainly conditional probabilities, inconsistencies appear only on events with the same conditioning, hence the correction procedure can be easily reduced to unconditional cases and the aforementioned procedure applied.