Towards Confident Bayesian Parameter Estimation in Stochastic Chemical Kinetics

We investigate the feasibility of Bayesian parameter inference for chemical reaction networks described in the low copy number regime. Here stochastic models are often favorable implying that the Bayesian approach becomes natural. Our discussion circles around a concrete oscillating system describing a circadian rhythm, and we ask if its parameters can be inferred from observational data. The main challenge is the lack of analytic likelihood and we circumvent this through the use of a synthetic likelihood based on summarizing statistics. We are particularly interested in the robustness and confidence of the inference procedure and therefore estimates a priori as well as a posteriori the information content available in the data. Our all-synthetic experiments are successful but also point out several challenges when it comes to real data sets.