Computational models are increasingly being used to study complex biological systems. Many modeling formalisms have been successfully applied to gene networks and other processes, but the two that have gained the most popularity are certainly ordinary differential equations (ODEs) and stochastic chemical reaction networks (SCRNs). While such models are relatively easy to construct once the structure of the system under study is known, before they can be productively used to reproduce experimental data and make predictions, one critical challenge must be overcome: the determination of the many unknown parameters that will inevitably appear in them. These are numbers such as reaction rates, production and degradation coefficients and so forth, which are often difficult to measure directly. The most common approach is, therefore, to measure other quantities involved in the models, such as concentrations or number of molecules of RNA and proteins, and to use these measurements to infer the parameters indirectly. For these reasons, the problem of parameter estimation represents a central issue in computational biology.

In this work, we present a collection of new methods that we developed to tackle this important problem. The key feature behind them is the idea of distribution matching, in which the estimation is achieved by matching pairs of suitably defined probability distributions. Specifically, distributions generated by the models are matched to distributions obtained from the experimental observations in order to obtain the unknown parameters.

We additionally show how the same theoretical tools we introduced for parameter estimation can also address the problem of model selection , in which one has to choose to best model for a given process from a list of candidates. This is a very common concern in biological applications, since the interactions among the different component of a system may be not fully known.

The use of our proposed methods is demonstrated through several examples, including one in which actual experimental data was collected. Our techniques are found to perform better than existing approaches in terms of accuracy, computational efficiency, or both, and they are readily applicable to realistic estimation problems in computational biology.