Selecting nonlinear stochastic process rate models using information criteria

We demonstrate how unknown process rates within a stochastic modelling framework based on Markov processes can be approximated from time series data using polynomial basis functions. The problem of model selection is considered by adapting basis function selection methods and the minimum description length information criteria which have previously been developed for nonlinear autoregressive models of time series under Gaussian noise assumptions. We investigate the effectiveness of the methods with application to stochastic biological population models.