Bayesian comparison of Langevin dynamics for cell motility from positional observation
We develop a Bayesian framework for model comparison of second-order Langevin dynamics from position-only trajectories. While approximate increment likelihoods for nonlinear position-only inference have been formulated previously, a unified evidence-based framework for comparing multiple second-order models under positional observation has remained lacking. Here we address this problem by combining exact increment likelihoods for linear Gaussian models with a previously proposed approximate likelihood for nonlinear dynamics. Synthetic-data benchmarks show reliable recovery of the generating model at fine sampling intervals and progressive loss of identifiability under coarse temporal sampling. Application to Dictyostelium discoideum trajectories demonstrates that the statistically supported model depends strongly on temporal resolution. Moreover, the selected models reproduce key statistical properties of the experimental trajectories, providing additional support for the model-comparison results. Our framework therefore offers a practical approach to evidence-based comparison of partially observed stochastic dynamics.