Abstract
The finite state projection (FSP) approach to solving the chemical master equation (CME) has enabled successful inference of discrete stochastic models to predict single-cell gene regulation dynamics. Unfortunately, the FSP approach is highly computationally intensive for all but the simplest models, an issue that is highly problematic when parameter inference and uncertainty quantification takes enormous numbers of parameter evaluations. To address this issue, we propose two new computational methods for the Bayesian inference of stochastic gene expression parameters given single-cell experiments. First, we present an adaptive scheme to improve parameter proposals for Metropolis-Hastings sampling using full FSP-based likelihood evaluations. We then formulate and verify an Adaptive Delayed Acceptance Metropolis-Hastings (ADAMH) algorithm to utilize with reduced Krylov-basis projections of the FSP. We test and compare both algorithms on three example models and simulated data to show that the ADAMH scheme achieves substantial speedup in comparison to the full FSP approach. By reducing the computational costs of parameter estimation, we expect the ADAMH approach to enable efficient data-driven estimation for more complex gene regulation models.