Computation of the posterior entropy in a Bayesian framework for parameter estimation in biological networks

In this paper we consider the problem of parameter estimation for intracellular network models with statistical Bayesian approaches. We use systems of nonlinear differential equations in order to describe the dynamics of those networks. In this setting, the posterior distribution has to be investigated via Markov chain Monte Carlo sampling. An estimation of summary statistics of the posterior from these samples requires appropriate density estimation methods. We focus in this study particularly on the influence of kernel density estimators on the expected information content of the posterior. A new method for the calculation of this information content is introduced that uses directly the unnormalized posterior values at the sample points. We exemplarily show its superiority to kernel estimators on a model of secretory pathway control at the trans-Golgi network in mammalian cells.