  We present Monte Carlo reconstruction, a new method for ``inverting''
observational data to constrain the form of the scalar field potential
responsible for inflation. This stochastic technique is based on the flow
equation formalism and has distinct advantages over reconstruction methods
based on a Taylor expansion of the potential. The primary ansatz required for
Monte Carlo reconstruction is simply that inflation is driven by a single
scalar field. We also require a very mild slow roll constraint, which can be
made arbitrarily weak since Monte Carlo reconstruction is implemented at
arbitrary order in the slow roll expansion. While our method cannot evade
fundamental limits on the accuracy of reconstruction, it can be simply and
consistently applied to poor data sets, and it takes advantage of the attractor
properties of single-field inflation models to constrain the potential outside
the small region directly probed by observations. We show examples of Monte
Carlo reconstruction for data sets similar to that expected from the Planck
satellite, and for a hypothetical measurement with a factor of five better
parameter discrimination than Planck.
