  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.
