  A major challenge facing existing sequential Monte-Carlo methods for
parameter estimation in physics stems from the inability of existing approaches
to robustly deal with experiments that have different mechanisms that yield the
results with equivalent probability. We address this problem here by proposing
a form of particle filtering that clusters the particles that comprise the
sequential Monte-Carlo approximation to the posterior before applying a
resampler. Through a new graphical approach to thinking about such models, we
are able to devise an artificial-intelligence based strategy that automatically
learns the shape and number of the clusters in the support of the posterior. We
demonstrate the power of our approach by applying it to randomized gap
estimation and a form of low circuit-depth phase estimation where existing
methods from the physics literature either exhibit much worse performance or
even fail completely.
