The ADETON method

Abstract

A problem encountered in many contexts is the estimation of matrices or tables from aggregate, heterogeneous, incomplete and contradictory information. In this paper the Adeton method is presented which can be used for this estimation task under quite general conditions. The Adeton method was originally developed to estimate flow matrices of regional labour markets in the Multi-Accounting System (MAS). However, it is applicable for many purposes, e.g. to estimate contingency tables or input-output and other flow matrices. Adeton is based on a Bayesian inference model: Given a prior probability distribution on the set of possible matrices and information about the actual matrix consisting of a set of linear equality and inequality constraints, the complete matrix with highest posterior probability is calculated. The advantage of the Adeton approach is that it is possible to specify soft constraints which are obeyed only up to a certain degree. It is shown that Adeton is an estimation method of entropy optimization type and in this respect is a generalization of the well known Iterative Proportional Fitting Algorithm (used in log-linear models) or of the equivalent RAS method (used in input-output analysis).