Parameter estimation in ordinary differential equations, although applied andrefined in various fields of the quantitative sciences, is still confrontedwith a variety of difficulties. One major challenge is finding the globaloptimum of a log-likelihood function that has several local optima, e.g. inoscillatory systems. In this publication, we introduce a formulation based oncontinuation of the log-likelihood function that allows to restate theparameter estimation problem as a boundary value problem. By construction, theordinary differential equations are solved and the parameters are estimatedboth in one step. The formulation as a boundary value problem enables anoptimal transfer of information given by the measurement time courses to thesolution of the estimation problem, thus favoring convergence to the globaloptimum. This is demonstrated explicitly for the fully as well as the partiallyobserved Lotka-Volterra system.
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