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Raue, A.* ; Kreutz, C.* ; Theis, F.J. ; Timmer, J.

Joining forces of Bayesian and frequentist methodology: A study for inference in the presence of non-identiability.

Philos. Trans. R. Soc. A - Math. Phys. Eng. Sci. 371:20110544 (2013)

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Increasingly complex applications involve large datasets in combination with nonlinear and high dimensional mathematical models. In this context, statistical inference is a challenging issue that calls for pragmatic approaches that take advantage of both Bayesian and frequentist methods. The elegance of Bayesian methodology is founded in the propagation of information content provided by experimental data and prior assumptions to the posterior probability distribution of model predictions. However, for complex applications experimental data and prior assumptions potentially constrain the posterior probability distribution insuciently. In these situations Bayesian Markov chain Monte Carlo sampling can be infeasible. From a frequentist point of view insucient experimental data and prior assumptions can be interpreted as non-identiability. The prole likelihood approach oers to detect and to resolve non-identiability by experimental design iteratively. Therefore, it allows one to better constrain the posterior probability distribution until Markov chain Monte Carlo sampling can be used securely. Using an application from cell biology we compare both methods and show that a successive application of both methods facilitates a realistic assessment of uncertainty in model predictions.

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