Accelerated Bayesian inference using deep learning. Issue 1 (28th May 2020) - Moss, Adam
ABSTRACT: We present a novel Bayesian inference tool that uses a neural network (NN) to parametrize efficient Markov Chain Monte Carlo (MCMC) proposals. The target distribution is first transformed into a diagonal, unit variance Gaussian by a series of non-linear, invertible, and non-volume preserving flows. NNs are extremely expressive, and can transform complex targets to a simple latent representation. Efficient proposals can then be made in this space, and we demonstrate a high degree of mixing on several challenging distributions. Parameter space can naturally be split into a block diagonal speed hierarchy, allowing for fast exploration of subspaces where it is inexpensive to evaluate the likelihood. Using this method, we develop a nested MCMC sampler to perform Bayesian inference and model comparison, finding excellent performance on highly curved and multimodal analytic likelihoods. We also test it on Planck 2015 data, showing accurate parameter constraints, and calculate the evidence for simple one-parameter extensions to the standard cosmological model in ∼20D parameter space. Our method has wide applicability to a range of problems in astronomy and cosmology and is available for download from https://github.com/adammoss/nnest .