  Inferring the input parameters of simulators from observations is a crucial
challenge with applications from epidemiology to molecular dynamics. Here we
show a simple approach in the regime of sparse data and approximately correct
models, which is common when trying to use an existing model to infer latent
variables with observed data. This approach is based on the principle of
maximum entropy and provably makes the smallest change in the latent joint
distribution to accommodate new data. This simple method requires no likelihood
or simulator derivatives and its fit is insensitive to prior strength, removing
the need to balance observed data fit with prior belief. We demonstrate this
MaxEnt approach and compare with other likelihood-free inference methods across
three systems; a linear simulator with Gaussian noise, a point particle moving
in a gravitational field, and finally a compartmental mode of epidemic spread.
We demonstrate that our method compares favorably, and in some cases exceeds
the performance of other methods.
