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Estimating the generator of a continuous-time Markov jump process based on incomplete data is a problem which arises in various applications ranging from machine learning to molecular dynamics. Several methods have been devised for this purpose: a quadratic programming approach (cf. . Some of these methods, however, seem to be known only in a particular research community, and have later been reinvented in a different context. The purpose of this paper is to compile a catalogue of existing approaches, to compare the strengths and weaknesses, and to test their performance in a series of numerical examples. These examples include carefully chosen model problems and an application to a time series from molecular dynamics.

Single-dose nevirapine (sd-NVP) and extended NVP prophylaxis are widely used in resource-constrained settings to prevent vertical HIV-1 transmission. We assessed the pharmacokinetics of sd-NVP in 62 HIV-1-positive pregnant Ugandan woman and their newborns who were receiving sd-NVP prophylaxis to prevent mother-to-child HIV-1 transmission. Based on these data, we developed a mathematical model system to quantify the impact of different sd-NVP regimens at delivery and of extended infant NVP prophylaxis (

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