In the natural sciences, we often face complex datasets with little prior intuition about the correct underlying model to describe them. In this talk, I will highlight how Bayesian nonparametric methods—particularly Beta-Bernoulli processes and related stochastic process priors—can be harnessed for tracking applications. This framework enables us, for the first time, to move beyond the conventional localization paradigm of tracking, where molecules are localized in each frame. Such an approach becomes especially powerful when extended to binary pixel output, for instance when tracking with single-photon detector arrays.

I will also examine the limitations of parametric modeling. Motion models beyond ordinary diffusion—frequently reported in the single-molecule literature—are notoriously difficult to disentangle from experimental noise when inferred from optical data. Our results call into question claims of anomalous diffusion and other parametric models often invoked in biophysical contexts. In the same vein, I will demonstrate how hidden Markov models can fail when applied to physical systems, as their restrictive assumptions risk producing misleading conclusions. Taken together, these examples illustrate both the strength of Bayesian nonparametric approaches and the pitfalls of over-reliance on parametric simplifications in data-rich settings.