By definition, the maximum likelihood estimator of $\theta$ maximizes Here, we consider a model that includes observations $\by=(y_i, 1\leq i \leq N)$, unobserved individual parameters $\bpsi=(\psi_i, 1\leq i \leq N)$ and a vector of parameters $\theta$. It has also been implemented in NONMEM, the R package saemix and the Matlab statistics toolbox as the function nlmefitsa.m. SAEM was first implemented in the $\monolix$ software. In fact, it converges to the MLE under very general hypotheses. SAEM has been shown to be a very powerful NLMEM tool, known to accurately estimate population parameters as well as having good theoretical properties. The SAEM (Stochastic Approximation of EM) algorithm is a stochastic algorithm for calculating the maximum likelihood estimator (MLE) in the quite general setting of incomplete data models. 6 A simulated annealing version of SAEM.5 A simple example to understand why SAEM converges in practice.4.1 SAEM for general hierarchical models.
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