Generator estimation of Markov jump processes

Philipp Metzner, Evelyn Dittmer, Tobias Jahnke, Christof Schütte Institute of Mathematics II, Free University Berlin, Arnimallee 2-6, D-14195 Berlin, Germany (Dated: March 5, 2007) Abstract Recently, two new methods have been presented for the estimation of an infinitesimal generator of a Markov jump process from an incomplete observation. The first approach, introduced by Crommelin and Vanden-Eijnden, determines an infinitesimal generator via the approximation of the eigenstructure of the transition matrix whereas the MLE-method developed by Bladt and Sørensen finds a generator via the EM-algorithm which maximizes the likelihood of the given incomplete observation. The purpose of this paper is to compare both methods and, moreover, to present an enhanced version of the MLE-method which overcomes numerical difficulties in the original approach. Finally, we apply the enhanced MLE-method to data from molecular dynamics.