Variational Inference as an alternative to MCMC for parameter estimationand model selection

Jain, Anirudh and Srijith, P K and Desai, Shantanu (2018) Variational Inference as an alternative to MCMC for parameter estimationand model selection. arXiv.org.

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Abstract

Most applications of Bayesian Inference for parameter estimation and model selection in astrophysics involve the use of Markov Chain Monte Carlo (MCMC) techniques. In this work, we introduce Variational Inference as an alternative to solve these problems, and compare how the results hold up to MCMC methods. Variational Inference converts the inference problem into an optimization problem by approximating the posterior from a known family of distributions and using Kullback-Leibler divergence to measure closeness. Variational Inference takes advantage of fast optimization techniques, which make it ideal to deal with large datasets and also makes it trivial to parallelize. As a proof of principle, we apply Variational Inference to four different problems in astrophysics, where MCMC techniques were previously used. These include measuring exoplanet orbital parameters from radial velocity data, tests of periodicities in measurements of Newton's constant G, assessing the significance of a turnover in the spectral lag data of GRB 160625B , and estimating the mass of a galaxy cluster using weak gravitational lensing. We find that Variational Inference is much faster than MCMC for these problems.

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