Ambiguous model learning made unambiguous with 1/f priors

What happens to the optimal interpretation of noisy data when there exists more than one equally plausible interpretation of the data? In a Bayesian model-learning framework the answer depends on the prior expectations of the dynamics of the model parameter that is to be inferred from the data. Local time constraints on the priors are insufficient to pick one interpretation over another. On the other hand, nonlocal time constraints, induced by a $1/f$ noise spectrum of the priors, is shown to permit learning of a specific model parameter even when there are infinitely many equally plausible interpretations of the data. This transition is inferred by a remarkable mapping of the model estimation problem to a dissipative physical system, allowing the use of powerful statistical mechanical methods to uncover the transition from indeterminate to determinate model learning.