Importance nested sampling with normalising flows

Williams, M. J. , Veitch, J. and Messenger, C. (2023) Importance nested sampling with normalising flows. Machine Learning: Science and Technology, 4, 035011. (doi: 10.1088/2632-2153/acd5aa)

Abstract

We present an improved version of the nested sampling algorithm nessai in which the core algorithm is modified to use importance weights. In the modified algorithm, samples are drawn from a mixture of normalising flows and the requirement for samples to be independently and identically distributed (i.i.d.) according to the prior is relaxed. Furthermore, it allows for samples to be added in any order, independently of a likelihood constraint, and for the evidence to be updated with batches of samples. We call the modified algorithm i-nessai. We first validate i-nessai using analytic likelihoods with known Bayesian evidences and show that the evidence estimates are unbiased in up to 32 dimensions. We compare i-nessai to standard nessai for the analytic likelihoods and the Rosenbrock likelihood, the results show that i-nessai is consistent with nessai whilst producing more precise evidence estimates. We then test i-nessai on 64 simulated gravitational-wave signals from binary black hole coalescence and show that it produces unbiased estimates of the parameters. We compare our results to those obtained using standard nessai and dynesty and find that i-nessai requires 2.68 and 13.3 times fewer likelihood evaluations to converge, respectively. We also test i-nessai of an 80-second simulated binary neutron star signal using a Reduced-Order-Quadrature (ROQ) basis and find that, on average, it converges in 24 minutes, whilst only requiring 1.01 × 106 likelihood evaluations compared to 1.42 × 106 for nessai and 4.30 × 107 for dynesty. These results demonstrate the i-nessai is consistent with nessai and dynesty whilst also being more efficient.

• Item Type: Articles
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Messenger, Dr Christopher and Williams, Michael and Veitch, Dr John
• Authors: Williams, M. J., Veitch, J., and Messenger, C.
• College/School: College of Science and Engineering > School of Physics and Astronomy
• Research Centre: College of Science and Engineering > School of Physics and Astronomy > Institute for Gravitational Research
• Journal Name: Machine Learning: Science and Technology
• Publisher: IOP Publishing
• ISSN: 2632-2153
• ISSN (Online): 2632-2153
• Published Online: 15 May 2023
• Copyright Holders: Copyright © 2023 The Authors
• First Published: First published in Machine Learning: Science and Technology 4:035011
• Publisher Policy: Reproduced under a Creative Commons License

Project Code	Award No	Project Name	Principal Investigator	Funder's Name	Funder Ref	Lead Dept
312546		Investigations in Gravitational Radiation	Sheila Rowan	Science and Technology Facilities Council (STFC)	ST/V005634/1	ENG - Electronics & Nanoscale Engineering