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Title: Exploring the posterior surface of the large scale structure reconstruction

Abstract

The large scale structure (LSS) of the universe is generated by the linear density gaussian modes, which are evolved into the observed nonlinear LSS. Given a set of data the posterior surface of the modes is convex in the linear regime, leading to a unique global maximum (MAP), but this is no longer guaranteed in the nonlinear regime. In this paper we investigate the nature of posterior surface using the recently developed MAP reconstruction method, with a simplified but realistic N-body simulation as the forward model. The reconstruction method uses optimization with analytic gradients from back-propagation through the simulation. For low noise cases we recover the initial conditions well into the nonlinear regime (k~ 1 h/Mpc) nearly perfectly. We show that the large scale modes can be recovered more precisely than the linear expectation, which we argue is a consequence of nonlinear mode coupling. For noise levels achievable with current and planned LSS surveys the reconstruction cannot recover very small scales due to noise. We see some evidence of non-convexity, specially for smaller scales where the non-injective nature of the mappings: several very different initial conditions leading to the same near perfect final data reconstruction. We investigate the nature ofmore » these phenomena further using a 1-d toy gravity model, where many well separated local maximas are found to have identical data likelihood but differ in the prior. We also show that in 1-d the prior favors some solutions over the true solution, though no clear evidence of these in 3-d. Our main conclusion is that on very small scales and for a very low noise the posterior surface is multi-modal and the global maximum may be unreachable with standard methods, while for realistic noise levels in the context of the current and next generation LSS surveys MAP optimization method is likely to be nearly optimal.« less

Authors:
; ;
Publication Date:
Research Org.:
Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States). National Energy Research Scientific Computing Center (NERSC)
Sponsoring Org.:
USDOE
OSTI Identifier:
1543936
Resource Type:
Accepted Manuscript
Journal Name:
Journal of Cosmology and Astroparticle Physics
Additional Journal Information:
Journal Volume: 2018; Journal Issue: 07; Journal ID: ISSN 1475-7516
Publisher:
Institute of Physics (IOP)
Country of Publication:
United States
Language:
English
Subject:
79 ASTRONOMY AND ASTROPHYSICS; Astronomy & Astrophysics; Physics; cosmological simulations; power spectrum

Citation Formats

Feng, Yu, Seljak, Uroš, and Zaldarriaga, Matias. Exploring the posterior surface of the large scale structure reconstruction. United States: N. p., 2018. Web. doi:10.1088/1475-7516/2018/07/043.
Feng, Yu, Seljak, Uroš, & Zaldarriaga, Matias. Exploring the posterior surface of the large scale structure reconstruction. United States. doi:10.1088/1475-7516/2018/07/043.
Feng, Yu, Seljak, Uroš, and Zaldarriaga, Matias. Fri . "Exploring the posterior surface of the large scale structure reconstruction". United States. doi:10.1088/1475-7516/2018/07/043. https://www.osti.gov/servlets/purl/1543936.
@article{osti_1543936,
title = {Exploring the posterior surface of the large scale structure reconstruction},
author = {Feng, Yu and Seljak, Uroš and Zaldarriaga, Matias},
abstractNote = {The large scale structure (LSS) of the universe is generated by the linear density gaussian modes, which are evolved into the observed nonlinear LSS. Given a set of data the posterior surface of the modes is convex in the linear regime, leading to a unique global maximum (MAP), but this is no longer guaranteed in the nonlinear regime. In this paper we investigate the nature of posterior surface using the recently developed MAP reconstruction method, with a simplified but realistic N-body simulation as the forward model. The reconstruction method uses optimization with analytic gradients from back-propagation through the simulation. For low noise cases we recover the initial conditions well into the nonlinear regime (k~ 1 h/Mpc) nearly perfectly. We show that the large scale modes can be recovered more precisely than the linear expectation, which we argue is a consequence of nonlinear mode coupling. For noise levels achievable with current and planned LSS surveys the reconstruction cannot recover very small scales due to noise. We see some evidence of non-convexity, specially for smaller scales where the non-injective nature of the mappings: several very different initial conditions leading to the same near perfect final data reconstruction. We investigate the nature of these phenomena further using a 1-d toy gravity model, where many well separated local maximas are found to have identical data likelihood but differ in the prior. We also show that in 1-d the prior favors some solutions over the true solution, though no clear evidence of these in 3-d. Our main conclusion is that on very small scales and for a very low noise the posterior surface is multi-modal and the global maximum may be unreachable with standard methods, while for realistic noise levels in the context of the current and next generation LSS surveys MAP optimization method is likely to be nearly optimal.},
doi = {10.1088/1475-7516/2018/07/043},
journal = {Journal of Cosmology and Astroparticle Physics},
number = 07,
volume = 2018,
place = {United States},
year = {2018},
month = {7}
}

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Works referenced in this record:

Improving Cosmological Distance Measurements by Reconstruction of the Baryon Acoustic Peak
journal, August 2007

  • Eisenstein, Daniel J.; Seo, Hee‐Jong; Sirko, Edwin
  • The Astrophysical Journal, Vol. 664, Issue 2
  • DOI: 10.1086/518712

Minimizing the stochasticity of halos in large-scale structure surveys
journal, August 2010


The cosmological simulation code gadget-2
journal, December 2005


Bayesian reconstruction of the cosmological large-scale structure: methodology, inverse algorithms and numerical optimization
journal, September 2008


Bayesian physical reconstruction of initial conditions from large-scale structure surveys
journal, April 2013

  • Jasche, Jens; Wandelt, Benjamin D.
  • Monthly Notices of the Royal Astronomical Society, Vol. 432, Issue 2
  • DOI: 10.1093/mnras/stt449

Planck 2015 results : XIII. Cosmological parameters
journal, September 2016


Primordial fluctuations and non-linear structure
journal, November 1991

  • Little, Blane; Weinberg, David H.; Park, Changbom
  • Monthly Notices of the Royal Astronomical Society, Vol. 253, Issue 2
  • DOI: 10.1093/mnras/253.2.295

Iterative initial condition reconstruction
journal, July 2017


Past and present cosmic structure in the SDSS DR7 main sample
journal, January 2015

  • Jasche, J.; Leclercq, F.; Wandelt, B. D.
  • Journal of Cosmology and Astroparticle Physics, Vol. 2015, Issue 01
  • DOI: 10.1088/1475-7516/2015/01/036

Transfer of power in non-linear gravitational clustering
journal, April 1997

  • Bagla, J. S.; Padmanabhan, T.
  • Monthly Notices of the Royal Astronomical Society, Vol. 286, Issue 4
  • DOI: 10.1093/mnras/286.4.1023

Methods for Bayesian Power Spectrum Inference with Galaxy Surveys
journal, November 2013


Towards optimal extraction of cosmological information from nonlinear data
journal, December 2017

  • Seljak, Uroš; Aslanyan, Grigor; Feng, Yu
  • Journal of Cosmology and Astroparticle Physics, Vol. 2017, Issue 12
  • DOI: 10.1088/1475-7516/2017/12/009

Nonlinear reconstruction
journal, December 2017


Bayesian non-linear large-scale structure inference of the Sloan Digital Sky Survey Data Release 7: Bayesian non-linear LSS inference of the SDSS DR 7
journal, October 2010


Reconstructing the Initial Density Field of the Local Universe: Methods and Tests with mock Catalogs
journal, July 2013


FastPM: a new scheme for fast simulations of dark matter and haloes
journal, August 2016

  • Feng, Yu; Chu, Man-Yat; Seljak, Uroš
  • Monthly Notices of the Royal Astronomical Society, Vol. 463, Issue 3
  • DOI: 10.1093/mnras/stw2123

Planck 2015 results : XXIII. The thermal Sunyaev-Zeldovich effect-cosmic infrared background correlation
journal, September 2016


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    journal, June 2019

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