Dealing with Stochasticity in Biological ODE Models
This addresses uncertainty handling in biological modeling for researchers, but it is incremental as it applies existing methods to new data.
The paper tackled the problem of stochasticity and uncertainty in biological ODE models by converting them to Dynamic Bayesian Networks (DBNs) and applying Particle Filtering for parameter re-estimation, achieving high accuracy in inferring model variables with missing, incomplete, sparse, and irregular data.
Mathematical modeling with Ordinary Differential Equations (ODEs) has proven to be extremely successful in a variety of fields, including biology. However, these models are completely deterministic given a certain set of initial conditions. We convert mathematical ODE models of three benchmark biological systems to Dynamic Bayesian Networks (DBNs). The DBN model can handle model uncertainty and data uncertainty in a principled manner. They can be used for temporal data mining for noisy and missing variables. We apply Particle Filtering algorithm to infer the model variables by re-estimating the models parameters of various biological ODE models. The model parameters are automatically re-estimated using temporal evidence in the form of data streams. The results show that DBNs are capable of inferring the model variables of the ODE model with high accuracy in situations where data is missing, incomplete, sparse and irregular and true values of model parameters are not known.