  We introduce the sequential neural posterior and likelihood approximation
(SNPLA) algorithm. SNPLA is a normalizing flows-based algorithm for inference
in implicit models. Thus, SNPLA is a simulation-based inference method that
only requires simulations from a generative model. Compared to similar methods,
the main advantage of SNPLA is that our method jointly learns both the
posterior and the likelihood. SNPLA completely avoid Markov chain Monte Carlo
sampling and correction-steps of the parameter proposal function that are
introduced in similar methods, but that can be numerically unstable or
restrictive. Over four experiments, we show that SNPLA performs competitively
when utilizing the same number of model simulations as used in other methods,
even though the inference problem for SNPLA is more complex due to the joint
learning of posterior and likelihood function.
