A Legacy of EM Algorithms

Nan Laird has an enormous and growing impact on computational statistics. Her paper with Dempster and Rubin on the expectation-maximisation (EM) algorithm is the second most cited paper in statistics. Her papers and book on longitudinal modelling are nearly as impressive. In this brief survey, we revisit the derivation of some of her most useful algorithms from the perspective of the minorisation-maximisation (MM) principle. The MM principle generalises the EM principle and frees it from the shackles of missing data and conditional expectations. Instead, the focus shifts to the construction of surrogate functions via standard mathematical inequalities. The MM principle can deliver a classical EM algorithm with less fuss or an entirely new algorithm with a faster rate of convergence. In any case, the MM principle enriches our understanding of the EM principle and suggests new algorithms of considerable potential in high-dimensional settings where standard algorithms such as Newton's method and Fisher scoring falter.

Automated summary

Nan Laird has made a significant impact on computational statistics, particularly in the areas of the expectation-maximisation algorithm and longitudinal modelling. This article revisits the derivation of some of her most useful algorithms, using the perspective of the minorisation-maximisation principle. The MM principle allows for a more straightforward implementation of the classical EM algorithm and suggests the potential for faster convergence in entirely new algorithms, particularly in high-dimensional settings.