Likelihood-free parameter inference for spatiotemporal stochastic biological models using neural posterior estimation

Cell migration is a key biological process underlying wound healing, tissue development, and cancer metastasis, yet calibrating mathematical models of migration to experimental data remains a major challenge. Scratch and barrier assays are widely used to study collective cell spreading, and agent-based random walk models provide a natural stochastic description of these experiments. However, parameter inference for such models is hampered by intractable likelihoods, forcing researchers to rely on Approximate Bayesian Computation, which introduces biases and tuning difficulties, or surrogate models that require potentially erroneous noise model specifications. Here, we overcome these limitations using neural posterior estimation, a simulation-based inference framework that learns the full posterior distribution directly from stochastic simulations without surrogate approximations or explicit noise model specifications. We deploy this framework on four progressively complex random walk models of barrier assay experiments describing in vitro cell migration: an isotropic baseline, a model with directional bias (chemotaxis), a model with cell proliferation, and a combined model incorporating both bias and proliferation. For each model, we demonstrate inference in two settings: using one-dimensional summary statistics (column counts), and using a convolutional neural network that enables inference directly from raw two-dimensional spatial data. Neural posterior estimation performs well across all four models, recovering biologically interpretable parameters (e.g. cell motility, directional bias, proliferation rates) from cases where classical surrogate-based methods are adequate through to the combined model where the interplay of multiple mechanisms renders surrogate approximations unreliable. We validate all posteriors using simulation-based calibration diagnostics and provide an open-source implementation of our pipeline to facilitate its adoption and extension to more complex, spatially-structured biological models.