Field Level Inference of Cosmological Large Scale Structure with Neural Quantile Estimation

While upcoming cosmological surveys promise to map the universe with unprecedented precision, the challenge remains on how to optimally extract information from this wealth of data. We introduce Neural Quantile Estimation (NQE), a novel Simulation-Based Inference method based on conditional quantile regression, and its application to the field level inference of cosmological large scale structure. NQE autoregressively learns one-dimensional quantiles for each posterior dimension, conditioned on both the observation data and previous posterior dimensions. Our studies indicate that, when provided with sufficient training data, NQE converges to the Bayesian optimal posterior, yielding constraints that are considerably tighter than traditional approaches. In scenarios with limited training data, a post-processing step can be employed to ensure the posterior remains unbiased, with minimal computational overhead. Moreover, this post-processing correction can mitigate biases stemming from model misspecification, notably those associated with the intricate aspects of small-scale baryonic physics.