Abstract of Comparison Of Numerical Behavior Of The Em And Osl Agorithms For Poisson Data

Mathematics Research Report CMA-MRR71-94

Comparison Of Numerical Behavior Of The Em And Osl Agorithms For Poisson Data

Shihong Yu

Abstract: The one-step-late (OSL) algorithm for maximum penalized likelihood estimation (MPLE) problem for Poisson data is compared with the expectation maximization (EM) algorithm for the corresponding maximum likelihood estimate (MLE) problem from the same positive starting value. This comparison shows that, the OSL iterates stay in step with the EM iterates as long as the smoothing parameter is sufficiently small, and that, if the underlying system is fully or overdetermined and the unique MLE solution is positive, the OSL algorithm, with a suitable small smoothing parameter, converges to a unique positive MPLE solution which is close to the MLE solution. For the underdetermined system, it is shown that, when a positive MPLE solution exists, the OSL algorithm converges to this MPLE solution, under mild regularity, when the initial positive starting value is either sufficiently close to this solution, or is such that the convergent point of the EM algorithm, started from this value, is sufficiently close to this MPLE solution. The sensitivity of the EM and OSL iterates with respect to perturbations in the data and model matrix is also analyzed.

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