ODE model of gene regulation

In determining regulatory interactions within cells, models based on ordinary differential equations (ODE) are a popular choice. Here, we present a reimplementation of one such model in Stan. The model features a spline fit where the resulting spline is a parameter of the ODE. For practical reasons, the model avoids the Stan’s ODE solver in favor of a custom solution. We also discuss why the model as traditionally formulated is not well identified and introduce reparametrizations that improve identifiability and make it easier to specify reasonable default priors.

This notebook shows first usable version of the model, but there are still several outstanding issues which we highlight. We nevertheless hope that the modelling approach we took is of interest to the Stan community and can provide inspiration for other models.

A runnable version of this Rmd file and all supporting code can be found at https://github.com/cas-bioinf/genexpi-stan/tree/stancon2018