  Markovian population models are suitable abstractions to describe well-mixed
interacting particle systems in situation where stochastic fluctuations are
significant due to the involvement of low copy particles. In molecular biology,
measurements on the single-cell level attest to this stochasticity and one is
tempted to interpret such measurements across an isogenic cell population as
different sample paths of one and the same Markov model. Over recent years
evidence built up against this interpretation due to the presence of
cell-to-cell variability stemming from factors other than intrinsic
fluctuations. To account for this extrinsic variability, Markovian models in
random environments need to be considered and a key emerging question is how to
perform inference for such models. We model extrinsic variability by a random
parametrization of all propensity functions. To detect which of those
propensities have significant variability, we lay out a sparse learning
procedure captured by a hierarchical Bayesian model whose evidence function is
iteratively maximized using a variational Bayesian expectation-maximization
algorithm.
