Simulation-based parameter inference methods based on data-conditional simulation of stochastic dynamical systems

Doctoral thesis, 2025

Statistical inference for stochastic dynamical systems is a central problem in many scientific domains, yet is complicated by intractable likelihood functions, as well as partial and noisy observations. Simulation-based methods such as Approximate Bayesian Computation (ABC) offer a general route to Bayesian inference in this setting, but standard algorithms rely on myopic simulation methods that are unconditional on the data, and consequently suffer from low acceptance rates. In Paper I we introduce a data-conditional simulator for discretely observed stochastic differential equations (SDEs). The method leverages lookahead strategies and smoothing via backward simulation to accelerate ABC-Sequential Monte Carlo. By guiding the simulated trajectories toward the data, it substantially increases acceptance rates and accelerates convergence to the posterior distribution. In Paper II we target chemical reaction networks described by the chemical Langevin equation, a nonlinear SDE with multiplicative, non-commutative noise that poses challenges for simulation and inference. We extend the data-conditional simulator to partially observed systems with measurement noise, allowing trajectories to be guided toward the data in this more realistic setting. Moreover, we design a novel splitting scheme for the numerical solution of SDEs that preserves state space, densities, and oscillatory behavior, and enables robust inference even with large integration steps where Euler–Maruyama fails. In Paper III, we improve chain mixing and reduce the rejection rate in ABC-Markov Chain Monte Carlo. Because chains are typically initialized without knowledge of the posterior’s shape, we introduce a data-conditional extension of ABC–MCMC that eases initialization and increases acceptance rates.