# Real-Time Likelihood-free Inference of Roman Binary Microlensing Events with Amortized Neural Posterior Estimation. (arXiv:2102.05673v1 [astro-ph.IM])

Fast and automated inference of binary-lens, single-source (2L1S)
microlensing events with sampling-based Bayesian algorithms (e.g., Markov Chain
Monte Carlo; MCMC) is challenged on two fronts: high computational cost of
likelihood evaluations with microlensing simulation codes, and a pathological
parameter space where the negative-log-likelihood surface can contain a
multitude of local minima that are narrow and deep. Analysis of 2L1S events
usually involves grid searches over some parameters to locate approximate
solutions as a prerequisite to posterior sampling, an expensive process that
often requires human-in-the-loop and domain expertise. As the next-generation,
space-based microlensing survey with the Roman Space Telescope is expected to
yield thousands of binary microlensing events, a new fast and automated method
is desirable. Here, we present a likelihood-free inference (LFI) approach named
amortized neural posterior estimation, where a neural density estimator (NDE)
learns a surrogate posterior $hat{p}(theta|x)$ as an observation-parametrized
conditional probability distribution, from pre-computed simulations over the
full prior space. Trained on 291,012 simulated Roman-like 2L1S simulations, the
NDE produces accurate and precise posteriors within seconds for any observation
within the prior support without requiring a domain expert in the loop, thus
allowing for real-time and automated inference. We show that the NDE also
captures expected posterior degeneracies. The NDE posterior could then be
refined into the exact posterior with a downstream MCMC sampler with minimal
burn-in steps.