  This work presents a novel posterior inference method for models with
intractable evidence and likelihood functions. Error-guided likelihood-free
MCMC, or EG-LF-MCMC in short, has been developed for scientific applications,
where a researcher is interested in obtaining approximate posterior densities
over model parameters, while avoiding the need for expensive training of
component estimators on full observational data or the tedious design of
expressive summary statistics, as in related approaches. Our technique is based
on two phases. In the first phase, we draw samples from the prior, simulate
respective observations and record their errors $\epsilon$ in relation to the
true observation. We train a classifier to distinguish between corresponding
and non-corresponding $(\epsilon, \boldsymbol{\theta})$-tuples. In the second
stage the said classifier is conditioned on the smallest recorded $\epsilon$
value from the training set and employed for the calculation of transition
probabilities in a Markov Chain Monte Carlo sampling procedure. By conditioning
the MCMC on specific $\epsilon$ values, our method may also be used in an
amortized fashion to infer posterior densities for observations, which are
located a given distance away from the observed data. We evaluate the proposed
method on benchmark problems with semantically and structurally different data
and compare its performance against the state of the art approximate Bayesian
computation (ABC).
