Minimum Message Length Estimation Using EM Methods : A Case Study

The Minimum Message Length approach to inference has been expounded at length (Wallace and Freeman, 1987, 1992) but it has yet to be adopted with any great enthusiasm by the statistical community. A possible reason may be the complexity of the symbolic determinant calculations required to implement the method. Another reason may be the unusual approach taken to nuisance parameters by MML authors.In this paper we consider a modified MML approach based on the EM algorithm and using only ‘complete data' quantities which considerably simplify the computation of the determinant. In the context of the ‘Single Factor Analysis' or ‘Comparative Calibration' example of Wallace and Freeman (1992) we study our modified estimator and compare it with that of Wallace and Freeman and other alternatives