Uncovering stochastic reaction networks from data is central to single-cell biology. Simulation-based inference has evolved into a flexible paradigm for this purpose, circumventing the computational intractability of the likelihood. Notably, approximate Bayesian computation performs this inference by carrying out extensive Gillespie simulations, usually at a high computational cost. Here, we propose a simulation-free approximate Bayesian computation (SFABC) framework that avoids both simulation and explicit likelihood solutions of the network dynamics. Instead, SFABC exploits the Chemical Master Equation to formulate a tractable convex optimization with ensuing constraints, which are then used to accept sampled parameters consistent with the observed data. The resulting posterior approximation comes with theoretical guarantees: it can be tightened systematically, and it provably converges to the exact Bayesian posterior distributions. Using synthetic benchmarks, we show that SFABC matches the accuracy of standard simulation-based algorithms at a substantially reduced computational cost. We then showcase the applicability of SFABC to experimental systems biology by analyzing gene transcription bursting kinetics from snapshot, time-resolved, and cell-cycle-resolved single-cell data.

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