I’ll talk about ongoing work in collaboration with the Ding lab of Biomedical Engineering at UCI. There are unresolved mysteries about the dynamics of RNA splicing, an important molecular process in the genetic machinery. These mysteries remain because the obtainable data for this process are not time series, but rather static spatial images of cells with stochastic particles.  From a modeling perspective, this creates a challenge of finding the right mathematical description that respects the stochasticity of individual particles but remains computationally tractable. I’ll share our approach of constructing a spatial Cox process with intensity governed by a reaction-diffusion PDE. We can do inference on this process with experimental images by employing variational Bayesian inference. Several outstanding issues remain about how to combine classical and modern statistical/data-science approaches with more exotic mechanistic models in biology.