Record Linkage - Mathematical Model

Mathematical Model

In an application with two files, A and B, denote the rows (records) by in file A and in file B. Assign characteristics to each record. The set of records that represent identical entities is defined by

and the complement of set, namely set representing different entities is defined as

A vector, is defined, that contains the coded agreements and disagreements on each characteristic:

where is a subscript for the characteristics (sex, age, marital status, etc.) in the files. The conditional probabilities of observing a specific vector given, are defined as

$m(\gamma) = P \left\{ \gamma \left | (a,b) \in M \right\} = \sum_{(a, b) \in M} P \left\{\gamma\left \right\} \cdot P \left$

and

$u(\gamma) = P \left\{ \gamma \left | (a,b) \in U \right\} = \sum_{(a, b) \in U} P \left\{\gamma\left \right\} \cdot P \left,$ respectively.

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