Many statistical models can be simulated forwards but have intractable
likelihoods. Approximate Bayesian Computation (ABC) methods are used to infer
properties of these models from data...
Traditionally these methods approximate
the posterior over parameters by conditioning on data being inside an
$\epsilon$-ball around the observed data, which is only correct in the limit
$\epsilon\!\rightarrow\!0$. Monte Carlo methods can then draw samples from the
approximate posterior to approximate predictions or error bars on parameters. These algorithms critically slow down as $\epsilon\!\rightarrow\!0$, and in
practice draw samples from a broader distribution than the posterior. We
propose a new approach to likelihood-free inference based on Bayesian
conditional density estimation. Preliminary inferences based on limited
simulation data are used to guide later simulations. In some cases, learning an
accurate parametric representation of the entire true posterior distribution
requires fewer model simulations than Monte Carlo ABC methods need to produce a
single sample from an approximate posterior.