Building unbiased estimators from non-gaussian likelihoods with application to shear estimation
Abstract
We develop a general framework for generating estimators of a given quantity which are unbiased to a given order in the difference between the true value of the underlying quantity and the fiducial position in theory space around which we expand the likelihood. We apply this formalism to rederive the optimal quadratic estimator and show how the replacement of the second derivative matrix with the Fisher matrix is a generic way of creating an unbiased estimator (assuming choice of the fiducial model is independent of data). Next we apply the approach to estimation of shear lensing, closely following the work of Bernstein and Armstrong (2014). Our first order estimator reduces to their estimator in the limit of zero shear, but it also naturally allows for the case of non-constant shear and the easy calculation of correlation functions or power spectra using standard methods. Both our first-order estimator and Bernstein and Armstrong’s estimator exhibit a bias which is quadratic in true shear. Our third-order estimator is, at least in the realm of the toy problem of Bernstein and Armstrong, unbiased to 0.1% in relative shear errors Δg/g for shears up to |g| = 0.2.
- Authors:
-
- Stony Brook Univ., NY (United States)
- Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
- Brookhaven National Lab. (BNL), Upton, NY (United States)
- Publication Date:
- Research Org.:
- Brookhaven National Lab. (BNL), Upton, NY (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC), High Energy Physics (HEP)
- OSTI Identifier:
- 1183831
- Report Number(s):
- BNL-107853-2015-JA
Journal ID: ISSN 1475-7516; KA2301020; TRN: US1500515
- Grant/Contract Number:
- SC00112704
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Journal of Cosmology and Astroparticle Physics
- Additional Journal Information:
- Journal Volume: 2015; Journal Issue: 1; Journal ID: ISSN 1475-7516
- Publisher:
- Institute of Physics (IOP)
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 79 ASTRONOMY AND ASTROPHYSICS
Citation Formats
Madhavacheril, Mathew S., McDonald, Patrick, Sehgal, Neelima, and Slosar, Anze. Building unbiased estimators from non-gaussian likelihoods with application to shear estimation. United States: N. p., 2015.
Web. doi:10.1088/1475-7516/2015/01/022.
Madhavacheril, Mathew S., McDonald, Patrick, Sehgal, Neelima, & Slosar, Anze. Building unbiased estimators from non-gaussian likelihoods with application to shear estimation. United States. https://doi.org/10.1088/1475-7516/2015/01/022
Madhavacheril, Mathew S., McDonald, Patrick, Sehgal, Neelima, and Slosar, Anze. Thu .
"Building unbiased estimators from non-gaussian likelihoods with application to shear estimation". United States. https://doi.org/10.1088/1475-7516/2015/01/022. https://www.osti.gov/servlets/purl/1183831.
@article{osti_1183831,
title = {Building unbiased estimators from non-gaussian likelihoods with application to shear estimation},
author = {Madhavacheril, Mathew S. and McDonald, Patrick and Sehgal, Neelima and Slosar, Anze},
abstractNote = {We develop a general framework for generating estimators of a given quantity which are unbiased to a given order in the difference between the true value of the underlying quantity and the fiducial position in theory space around which we expand the likelihood. We apply this formalism to rederive the optimal quadratic estimator and show how the replacement of the second derivative matrix with the Fisher matrix is a generic way of creating an unbiased estimator (assuming choice of the fiducial model is independent of data). Next we apply the approach to estimation of shear lensing, closely following the work of Bernstein and Armstrong (2014). Our first order estimator reduces to their estimator in the limit of zero shear, but it also naturally allows for the case of non-constant shear and the easy calculation of correlation functions or power spectra using standard methods. Both our first-order estimator and Bernstein and Armstrong’s estimator exhibit a bias which is quadratic in true shear. Our third-order estimator is, at least in the realm of the toy problem of Bernstein and Armstrong, unbiased to 0.1% in relative shear errors Δg/g for shears up to |g| = 0.2.},
doi = {10.1088/1475-7516/2015/01/022},
journal = {Journal of Cosmology and Astroparticle Physics},
number = 1,
volume = 2015,
place = {United States},
year = {Thu Jan 15 00:00:00 EST 2015},
month = {Thu Jan 15 00:00:00 EST 2015}
}
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Works referenced in this record:
Bayesian lensing shear measurement
journal, January 2014
- Bernstein, Gary M.; Armstrong, Robert
- Monthly Notices of the Royal Astronomical Society, Vol. 438, Issue 2
An implementation of Bayesian lensing shear measurement
journal, July 2014
- Sheldon, Erin S.
- Monthly Notices of the Royal Astronomical Society: Letters, Vol. 444, Issue 1
Estimating the power spectrum of the cosmic microwave background
journal, February 1998
- Bond, J. R.; Jaffe, A. H.; Knox, L.
- Physical Review D, Vol. 57, Issue 4
Cosmography and Power Spectrum Estimation: A Unified Approach
journal, August 1998
- Seljak, Uroš
- The Astrophysical Journal, Vol. 503, Issue 2
Radical Compression of Cosmic Microwave Background Data
journal, April 2000
- Bond, J. R.; Jaffe, A. H.; Knox, L.
- The Astrophysical Journal, Vol. 533, Issue 1
Galaxy‐Galaxy Flexion: Weak Lensing to Second Order
journal, February 2005
- Goldberg, David M.; Bacon, David J.
- The Astrophysical Journal, Vol. 619, Issue 2
Bayesian galaxy shape measurement for weak lensing surveys - I. Methodology and a fast-fitting algorithm
journal, November 2007
- Miller, L.; Kitching, T. D.; Heymans, C.
- Monthly Notices of the Royal Astronomical Society, Vol. 382, Issue 1
A way forward for Cosmic Shear: Monte-Carlo Control Loops
journal, April 2014
- Refregier, Alexandre; Amara, Adam
- Physics of the Dark Universe, Vol. 3
Works referencing / citing this record:
An accurate and practical method for inference of weak gravitational lensing from galaxy images
journal, April 2016
- Bernstein, Gary M.; Armstrong, Robert; Krawiec, Christina
- Monthly Notices of the Royal Astronomical Society, Vol. 459, Issue 4
An accurate and practical method for inference of weak gravitational lensing from galaxy images
text, January 2015
- Bernstein, Gary M.; Armstrong, Robert; Krawiec, Christina
- arXiv