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This work proposes ``jointly amortized neural approximation'' (JANA) ofintractable likelihood functions and posterior densities arising in Bayesiansurrogate modeling and simulation-based inference. We train three complementarynetworks in an end-to-end fashion: 1) a summary network to compress individualdata points, sets, or time series into informative embedding vectors; 2) aposterior network to learn an amortized approximate posterior; and 3) alikelihood network to learn an amortized approximate likelihood. Theirinteraction opens a new route to amortized marginal likelihood and posteriorpredictive estimation -- two important ingredients of Bayesian workflows thatare often too expensive for standard methods. We benchmark the fidelity of JANAon a variety of simulation models against state-of-the-art Bayesian methods andpropose a powerful and interpretable diagnostic for joint calibration. Inaddition, we investigate the ability of recurrent likelihood networks toemulate complex time series models without resorting to hand-crafted summarystatistics.

JANA: Jointly Amortized Neural Approximation of Complex Bayesian Models