Multilevel Monte Carlo for likelihood-free Bayesian inference of rate parameters for stochastic models of biochemical reactions

Stochastic models of biochemical reaction networks are often more realistic descriptions of cellular processes over deterministic counterparts when small populations of certain chemical species are considered. The statistical inference of reaction rate parameters, however, is a computationally intensive task that often relies upon likelihood-free methods, also called approximate Bayesian computation (ABC). We investigate a modified ABC approach that is based on multilevel Monte Carlo; a stochastic variant of multigrid methods. Our method constructs an approximation of the posterior distribution function through a telescoping summation of biased estimators. We demonstrate the effectiveness of our method using several stochastic models of biochemical reaction networks and compare performance with Markov chain Monte Carlo and sequential Monte Carlo.