Improved renormalization group computation of likelihood functions for cosmological data sets
Abstract
Evaluation of likelihood functions for cosmological large scale structure data sets (including CMB, galaxy redshift surveys, etc.) naturally involves marginalization, i.e., integration, over an unknown underlying random signal field. Recently, I showed how a renormalization group method can be used to carry out this integration efficiently by first integrating out the smallest scale structure, i.e., localized structure on the scale of differences between nearby data cells, then combining adjacent cells in a coarse graining step, then repeating this process over and over until all scales have been integrated. Here I extend the formulation in several ways in order to reduce the prefactor on the method's linear scaling with data set size. The key improvement is showing how to integrate out the difference between specific adjacent cells before summing them in the coarse graining step, compared to the original formulation in which small-scale fluctuations were integrated more generally. I suggest some other improvements in details of the scheme, including showing how to perform the integration around a maximum likelihood estimate for the underlying random field. In the end, an accurate likelihood computation for a million-cell Gaussian test data set runs in two minutes on my laptop, with room for further optimizationmore »
- Publication Date:
- Research Org.:
- Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC), High Energy Physics (HEP)
- OSTI Identifier:
- 1564070
- Alternate Identifier(s):
- OSTI ID: 1547984
- Grant/Contract Number:
- AC02-05CH11231; AC02-05-CH11231
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Physical Review D
- Additional Journal Information:
- Journal Volume: 100; Journal Issue: 4; Journal ID: ISSN 2470-0010
- Publisher:
- American Physical Society (APS)
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 79 ASTRONOMY AND ASTROPHYSICS
Citation Formats
McDonald, Patrick. Improved renormalization group computation of likelihood functions for cosmological data sets. United States: N. p., 2019.
Web. doi:10.1103/physrevd.100.043511.
McDonald, Patrick. Improved renormalization group computation of likelihood functions for cosmological data sets. United States. https://doi.org/10.1103/physrevd.100.043511
McDonald, Patrick. Tue .
"Improved renormalization group computation of likelihood functions for cosmological data sets". United States. https://doi.org/10.1103/physrevd.100.043511. https://www.osti.gov/servlets/purl/1564070.
@article{osti_1564070,
title = {Improved renormalization group computation of likelihood functions for cosmological data sets},
author = {McDonald, Patrick},
abstractNote = {Evaluation of likelihood functions for cosmological large scale structure data sets (including CMB, galaxy redshift surveys, etc.) naturally involves marginalization, i.e., integration, over an unknown underlying random signal field. Recently, I showed how a renormalization group method can be used to carry out this integration efficiently by first integrating out the smallest scale structure, i.e., localized structure on the scale of differences between nearby data cells, then combining adjacent cells in a coarse graining step, then repeating this process over and over until all scales have been integrated. Here I extend the formulation in several ways in order to reduce the prefactor on the method's linear scaling with data set size. The key improvement is showing how to integrate out the difference between specific adjacent cells before summing them in the coarse graining step, compared to the original formulation in which small-scale fluctuations were integrated more generally. I suggest some other improvements in details of the scheme, including showing how to perform the integration around a maximum likelihood estimate for the underlying random field. In the end, an accurate likelihood computation for a million-cell Gaussian test data set runs in two minutes on my laptop, with room for further optimization and straightforward parallelization.},
doi = {10.1103/physrevd.100.043511},
journal = {Physical Review D},
number = 4,
volume = 100,
place = {United States},
year = {2019},
month = {8}
}
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FIG. 1: N = 16384 test. The exact likelihood is computed by brute force linear algebra at five representative values of A. To guide the eye, I fit a quadratic polynomial to the points, using this to define the maximum. I use the RG method to compute the likelihood atmore »
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Figures/Tables have been extracted from DOE-funded journal article accepted manuscripts.