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Variational inference as an alternative to MCMC for parameter estimation and model selection

Published online by Cambridge University Press:  25 January 2022

Geetakrishnasai Gunapati ,
Anirudh Jain ,
P. K. Srijith  and
Shantanu Desai Open the ORCID record for Shantanu Desai [Opens in a new window]
Geetakrishnasai Gunapati
Affiliation:
Department of Computer Science and Engineering, IIT Hyderabad, Kandi, Telangana 502285, India
Anirudh Jain
Affiliation:
Department of Computer Science, Aalto University, Espoo 02150, Finland
P. K. Srijith
Affiliation:
Department of Computer Science and Engineering, IIT Hyderabad, Kandi, Telangana 502285, India
Shantanu Desai*
Affiliation:
Department of Physics, IIT Hyderabad, Kandi, Telangana 502285, India
*
Author for correspondence: Shantanu Desai, e-mail: shntn05@gmail.com
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Abstract

Most applications of Bayesian Inference for parameter estimation and model selection in astrophysics involve the use of Monte Carlo techniques such as Markov Chain Monte Carlo (MCMC) and nested sampling. However, these techniques are time-consuming and their convergence to the posterior could be difficult to determine. In this study, we advocate variational inference as an alternative to solve the above problems, and demonstrate its usefulness for parameter estimation and model selection in astrophysics. Variational inference converts the inference problem into an optimisation problem by approximating the posterior from a known family of distributions and using Kullback–Leibler divergence to characterise the difference. It takes advantage of fast optimisation techniques, which make it ideal to deal with large datasets and makes it trivial to parallelise on a multicore platform. We also derive a new approximate evidence estimation based on variational posterior, and importance sampling technique called posterior-weighted importance sampling for the calculation of evidence, which is useful to perform Bayesian model selection. As a proof of principle, we apply variational inference to five different problems in astrophysics, where Monte Carlo techniques were previously used. These include assessment of significance of annual modulation in the COSINE-100 dark matter experiment, 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 and nested sampling techniques for most of these problems while providing competitive results. All our analysis codes have been made publicly available.

Keywords

astronomy data analysisBayesian model comparison
Type
Research Article
Information
Publications of the Astronomical Society of Australia , Volume 39 , 2022 , e001
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Copyright
© The Author(s), 2022. Published by Cambridge University Press on behalf of the Astronomical Society of Australia

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