Dresden 2017 – wissenschaftliches Programm
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BP: Fachverband Biologische Physik
BP 4: Systems Biology & Gene Expression and Signalling
BP 4.6: Vortrag
Montag, 20. März 2017, 16:30–16:45, ZEU 250
Local Riemannian geometry of model manifolds and its implications for practical parameter identifiability — •Daniel Kaschek1, Daniel Lill2, and Jens Timmer1 — 1Physikalisches Institut, Universität Freiburg — 2Systems Biology Ireland, University College Dublin
When dynamic models are fitted to time-resolved experimental data, parameter estimates can be poorly constrained albeit being identifiable in principle. This means that along certain paths in parameter space, the negative log-likelihood does not exceed a given threshold but remains bounded.
This situation, denoted as practical non-identifiability, can only be detected by Monte Carlo sampling or systematic scanning by the profile likelihood method. In contrast, the Fisher information matrix which is based on second-order model sensitivities in the optimum reveals no information about the boundedness at all.
Here, we show that for some dynamic models the information about the bounds is already contained in the Christoffel symbols, which are also computed from model sensitivities up to order two at the optimum. Assuming constant Christoffel symbols in the geodesic equation, approximate Riemannian normal coordinates are constructed. The new coordinates give rise to an approximative log-likelihood, featuring flat directions and bounds similar to that of the original log-likelihood.