A Dictyostelium amoeba crawls across glass. Its path is recorded — a chain of points on a plane. But what forces are pushing it? Inside the cell, a molecular motor works: proteins pull, the membrane springs, water presses. This resembles Brownian motion of pollen in water, but more complex — here, there's memory of the previous step.

The authors built a 'judge'—a Bayesian algorithm that compares second-order models (accounting for inertia and elasticity) using only coordinates. Previously, such comparisons were inaccurate or required knowledge of velocities. Now, using exact formulas for linear cases and approximations for nonlinear ones, one can compute the 'weight' of each hypothesis.

On living cells, it turned out that the choice of the best model depends on the measurement frequency. The same cell 'chooses' one description under fast imaging and another under slow imaging. But the chosen model always reproduces key features of the real motion — for example, the extent of wandering and its autocorrelation. It's like being able to tell from a blurry photo of a runner whether it's a sprint or a marathon, and not err on the basic parameters of the stride.