  Scientific modeling applications often require estimating a distribution of
parameters consistent with a dataset of observations - an inference task also
known as source distribution estimation. This problem can be ill-posed,
however, since many different source distributions might produce the same
distribution of data-consistent simulations. To make a principled choice among
many equally valid sources, we propose an approach which targets the maximum
entropy distribution, i.e., prioritizes retaining as much uncertainty as
possible. Our method is purely sample-based - leveraging the Sliced-Wasserstein
distance to measure the discrepancy between the dataset and simulations - and
thus suitable for simulators with intractable likelihoods. We benchmark our
method on several tasks, and show that it can recover source distributions with
substantially higher entropy than recent source estimation methods, without
sacrificing the fidelity of the simulations. Finally, to demonstrate the
utility of our approach, we infer source distributions for parameters of the
Hodgkin-Huxley model from experimental datasets with thousands of single-neuron
measurements. In summary, we propose a principled method for inferring source
distributions of scientific simulator parameters while retaining as much
uncertainty as possible.
