Title: Hierarchical Inference with Bayesian Neural Networks: An Application to Strong Gravitational Lensing

Abstract

In the past few years, approximate Bayesian Neural Networks (BNNs) have demonstrated the ability to produce statistically consistent posteriors on a wide range of inference problems at unprecedented speed and scale. However, any disconnect between training sets and the distribution of real-world objects can introduce bias when BNNs are applied to data. This is a common challenge in astrophysics and cosmology, where the unknown distribution of objects in our universe is often the science goal. In this work, we incorporate BNNs with flexible posterior parameterizations into a hierarchical inference framework that allows for the reconstruction of population hyperparameters and removes the bias introduced by the training distribution. We focus on the challenge of producing posterior PDFs for strong gravitational lens mass model parameters given Hubble Space Telescope–quality single-filter, lens-subtracted, synthetic imaging data. We show that the posterior PDFs are sufficiently accurate (statistically consistent with the truth) across a wide variety of power-law elliptical lens mass distributions. We then apply our approach to test data sets whose lens parameters are drawn from distributions that are drastically different from the training set. We show that our hierarchical inference framework mitigates the bias introduced by an unrepresentative training set's interim prior. Simultaneously, wemore » can precisely reconstruct the population hyperparameters governing our test distributions. Our full pipeline, from training to hierarchical inference on thousands of lenses, can be run in a day. The framework presented here will allow us to efficiently exploit the full constraining power of future ground- and space-based surveys (https://github.com/swagnercarena/ovejero).« less

Authors:

Wagner-Carena, Sebastian  ^[1];

• Search DOE PAGES for author "Wagner-Carena, Sebastian"
• Search DOE PAGES for ORCID "0000-0001-5039-1685"

Park, Ji Won  ^[1];

• Search DOE PAGES for author "Park, Ji Won"
• Search DOE PAGES for ORCID "0000-0002-0692-1092"

Birrer, Simon  ^[1];

• Search DOE PAGES for author "Birrer, Simon"
• Search DOE PAGES for ORCID "0000-0003-3195-5507"

Marshall, Philip J. ^[1]; Roodman, Aaron  ^[1];

• Search DOE PAGES for author "Roodman, Aaron"
• Search DOE PAGES for ORCID "0000-0001-5326-3486"

Wechsler, Risa H.  ^[1]

• Search DOE PAGES for author "Wechsler, Risa H."
• Search DOE PAGES for ORCID "0000-0003-2229-011X"

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+ Show Author Affiliations

1. Stanford Univ., CA (United States); SLAC National Accelerator Lab., Menlo Park, CA (United States)

Publication Date:

Wed Mar 17 00:00:00 EDT 2021

Research Org.:

SLAC National Accelerator Lab., Menlo Park, CA (United States)

Sponsoring Org.:

USDOE Office of Science (SC); National Science Foundation (NSF)

Contributing Org.:

LSST Dark Energy Science Collaboration

OSTI Identifier:

1772052

Alternate Identifier(s):

OSTI ID: 1772050

Report Number(s):

SLAC-PUB-17592
Journal ID: ISSN 0004-637X; TRN: US2206944

Grant/Contract Number:  

AC02-76SF00515; AC02-05CH11231; AST-1716527

Resource Type:

Accepted Manuscript

Journal Name:

The Astrophysical Journal

Additional Journal Information:

Journal Volume: 909; Journal Issue: 2; Journal ID: ISSN 0004-637X

Publisher:

Institute of Physics (IOP)

Country of Publication:

United States

Language:

English

Subject:

79 ASTRONOMY AND ASTROPHYSICS; Strong gravitational lensing; Cosmology; Computational methods; Convolutional neural networks; Hierarchical models