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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.

Stochasticity is a fundamental feature of biology at the single cell level. Quantitative experimental data ranging from microscopy to single-cell transcriptomic is continually expanding our understanding of the role of stochasticity in gene expression and other cellular processes.

The estimation of micromechanical parameters of discrete element method (DEM) models is a nonlinear history-dependent inverse problem. In order to reproduce the experimental measurements with high accuracy, this work aims to develop a machine learning-based calibration toolbox named “Grain learning”, which can extract grains from X-ray computed tomography (CT) images and perform Bayesian parameter estimation for DEM models of dry granular materials.