A Bayesian framework for inferring heterogeneity of cellular processes using single-cell data

The advances of single-cell technologies provide un-precedented opportunities to investigate heterogeneity of cellular processes. Although population modelling is a powerful tool to describe different cellular dynamics in a number of cells, it is a challenge and computational burden to infer different sets of parameters in the mathematical models based on the observations in different cells. To address this issue, this work proposes a population Monte Carlo framework to increase the acceptance rates in the approximate Bayesian computation algorithms. We first test a prior distribution and distinct tolerance threshold sequence for the dataset of the first cell. After applying the Bayesian inference methods, we obtain the estimated model parameters of the first cell. This inferred parameter set will be used to construct the prior distribution and tolerance threshold sequence of the following cells. This adaptive approach will be repeatedly applied for the inference of the following cells. The accuracy and efficacy of the proposed algorithms is rigorously examined by using two mathematical models for genetic networks. Numerical results shows that the proposed algorithm improve the efficiency substantially and provide a powerful tool to obtain more accurate inference results for large-scale regulatory networks.