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.
Yusuke Kato, Jan Albrecht, T. Moldenhawer et al.· 0 citations
Anticipating the onset of collective synchronization is important in many networked systems, yet observing every oscillator is often impractical. We investigate whether synchronization transitions can be detected from a small set of monitored, or sentinel, nodes. Using a stochastic Kuramoto model on networks, we numerically compare three early warning signals: the local order parameter, its temporal variance, and the variance of individual oscillator phases after removing their mean rotational trends. We also compare sentinel-selection strategies based on node dynamics, degree, and random sampling. We show that, under partial observation, the local order parameter and the variance of detrended phases provide substantially stronger warning signals than the variance of the local order parameter. Selecting nodes according to their dynamical behavior near the transition consistently improves performance over other sentinel-selection methods. With only $\lfloor\ln N\rfloor$ dynamically selected sentinels, two success indicators approach the performance obtained by observing all $N$ nodes. These results demonstrate that synchronization transitions can be anticipated from sparse observations when the warning signal and monitored nodes are chosen appropriately.
Yusuke Kato, Naoki Masuda· 0 citations
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