Berlin 2018 – wissenschaftliches Programm
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DY: Fachverband Dynamik und Statistische Physik
DY 72: Poster: Stoch. and Nonl. Dy., Modeling, Compl. Sys.
DY 72.15: Poster
Donnerstag, 15. März 2018, 15:30–18:00, Poster A
Local Riemannian geometry of model manifolds and its implications for practical parameter identifiability — •Daniel Lill1, Jens Timmer1,2, and Daniel Kaschek1 — 1Institute of Physics, Freiburg University — 2BIOSS Centre for Biological Signaling Studies, Freiburg University
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 the parameter space, the negative log-likelihood does not exceed a given threshold but remains bounded. This so-called practical non-identifiability can only be detected by Monte Carlo sampling or systematic scanning by the profile likelihood method. In contrast, any method based on a Taylor expansion of the log-likelihood around the optimum, e.g., parameter uncertainty estimation by the Fisher Information Matrix, reveals no information about the boundedness at all.
We show that for some dynamic models the information about the bounds of the log-likelihood is already contained in the Christoffel symbols, which are 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.