Parameter estimation of stochastic models based on limited data

Abstract

Progress in experimental techniques enables a more accurate quantification of genes, mRNA, and proteins at the single cell level. Provided with limited time series data from single-cell measurements, this note proposes a new quasi-Newton optimization algorithm (QNSTOP) for parameter estimation of stochastic models. To capture the stochasticity inside models and data, the random objective function is constructed based on the maximum log-likelihood of transition probabilities rather than summary statistics, which relies heavily on stochastic simulations. Simple to use and efficient, QNSTOP can find the "best" parameter vector from far away starting points in just a few iterations. Results on a bistable model match well the bistable dynamics that can only be obtained from stochastic models.