2.1 PEITH(Θ) for inference of model parameters and for prediction

In a Bayesian framework model parameters are treated as random variables for which we can define a prior probability distribution and the aim is often to infer the posterior probability distribution after having observed some data. The reduction in uncertainty of the model parameters arising from gathering data during an experiment can be measured by the mutual information between model parameters and the possible experimental outcomes, which is equal to the difference in entropy between the prior and the posterior probability distributions. In order to determine the optimal experiment to infer the model parameters one can maximize this mutual information. To compute the latter we derive the integrals in (Liepe et al., 2013). This gives, for each experiment a measure of the average reduction in uncertainty for the model parameters, thus providing an approach to quantitatively capture those experiments that provide substantial and relevant information (Liepe et al., 2013).

We extend this concept to reduce the uncertainty in the estimation of a subset of parameters. This is particular relevant, because the experiment that is optimal to estimate all systems parameters is often not the best to estimate a specific parameter with high certainty. Related to this, one often wants to predict an experiment that cannot feasibly be carried out. In this case the experiment that is most suited to infer all model parameters is not always the most informative to obtain predictions with high certainty since some specific parameters might drive the model behaviour.

PEITH(Θ) implements algorithms for all three described scenarios: reducing the uncertainty of the model parameters, a subset of the parameters, or the prediction of the outcome on an intervention. More often than not the resulting integrals are not analytically tractable and require numerical estimation, which we do here using Monte Carlo estimates (Liepe et al., 2013). This in turn is computationally extremely expensive and for most systems of biological relevance prohibits the calculation on CPUs. We therefore implemented and optimized both numerical model simulations [using CUDA-sim (Zhou et al., 2011)] and all Monte Carlo estimations on GPUs.