Stochastic simulation algorithms provide a powerful means to understand complex biochemical processes as well as to solve the inverse problem of reconstructing hidden states and parameters from experimental single-cell data. At presence, a repertoire of efficient algorithms for simulating and calibrating stochastic reaction networks is available. However, most of these approaches do not account for the fact that each cell of a clonal population is exposed to a random extrinsic environment, i.e., the agglomerate of so-called extrinsic factors such as cell size, shape or cell cycle stage. We recently proposed a dynamic description of stochastic chemical kinetics in random but unknown extrinsic environments, reflected by a stochastic process where uncertain parameters are marginalized out. In this work we further investigate that process and provide additional analytical results. We demonstrate the marginalization using several biologically relevant parameter distributions and derive exact waiting-time distributions. We further show that the marginalized process model can achieve a variance reduction in the context of parameter inference.
