  The question of how best to estimate a continuous probability density from
finite data is an intriguing open problem at the interface of statistics and
physics. Previous work has argued that this problem can be addressed in a
natural way using methods from statistical field theory. Here I describe new
results that allow this field-theoretic approach to be rapidly and
deterministically computed in low dimensions, making it practical for use in
day-to-day data analysis. Importantly, this approach does not impose a
privileged length scale for smoothness of the inferred probability density, but
rather learns a natural length scale from the data due to the tradeoff between
goodness-of-fit and an Occam factor. Open source software implementing this
method in one and two dimensions is provided.
