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Increasingly complex applications involve large datasets in combination withnon-linear and high dimensional mathematical models. In this context,statistical inference is a challenging issue that calls for pragmaticapproaches that take advantage of both Bayesian and frequentist methods. Theelegance of Bayesian methodology is founded in the propagation of informationcontent provided by experimental data and prior assumptions to the posteriorprobability distribution of model predictions. However, for complexapplications experimental data and prior assumptions potentially constrain theposterior probability distribution insufficiently. In these situations BayesianMarkov chain Monte Carlo sampling can be infeasible. From a frequentist pointof view insufficient experimental data and prior assumptions can be interpretedas non-identifiability. The profile likelihood approach offers to detect and toresolve non-identifiability by experimental design iteratively. Therefore, itallows one to better constrain the posterior probability distribution untilMarkov chain Monte Carlo sampling can be used securely. Using an applicationfrom cell biology we compare both methods and show that a successiveapplication of both methods facilitates a realistic assessment of uncertaintyin model predictions.

philosophical transactions - royal society. mathematical, physical and engineering sciences/philosophical transactions - royal society. mathematical, physical and engineering sciences

Joining Forces of Bayesian and Frequentist Methodology: A Study for Inference in the Presence of Non-Identifiability