Trieste, 14 Mai 2015 J. Jasche, Bayesian LSS Inference What do we - - PowerPoint PPT Presentation

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Trieste, 14 Mai 2015 J. Jasche, Bayesian LSS Inference What do we - - PowerPoint PPT Presentation

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INFERRING PAST AND PRESENT COSMIC STRUCTURES FROM OBSERVATIONS Jens Jasche, Florent Leclercq, Guilhem Lavaux and Benjamin Wandelt Trieste, 14 Mai 2015 J. Jasche, Bayesian LSS Inference What do we want to do? homogeneous vs. inhomogeneous

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  • J. Jasche, Bayesian LSS Inference

Jens Jasche,

Florent Leclercq, Guilhem Lavaux and Benjamin Wandelt

Trieste, 14 Mai 2015

INFERRING PAST AND PRESENT COSMIC STRUCTURES FROM OBSERVATIONS

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What do we want to do?

 homogeneous vs. inhomogeneous Universe On the verge of numerical feasibility

Jasche et al. (2010)

Credit: M. Blanton and the Sloan Digital Sky Survey

Galaxy survey 3D density map

homogeneous Universe ~ 6 -10 parameter inhomogeneous Universe ~ 107 parameter

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Why Bayesian Statistics?

Noise Incompleteness Blurring  Inference of signals = ill-posed problem!

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Why Bayesian Statistics?

Noise Incompleteness Blurring

No unique recovery! Bayesian inference

 Inference of signals = ill-posed problem!

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Why Bayesian Statistics?

Noise Incompleteness Blurring

No unique recovery! Bayesian inference

 Inference of signals = ill-posed problem!

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Why Bayesian Statistics?

Noise Incompleteness Blurring

No unique recovery! Bayesian inference

Complex nonlinear statistics and extremely high dimensional!  Inference of signals = ill-posed problem!

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Why 4D inference?

 Physical motivation

  • Complex final state
  • Simple initial state

Initial state Final state Gravity

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Chrono-cosmography

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Chrono-cosmography

 The naive approach:

  • We need a very very very large computer!
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Chrono-cosmography

 The naive approach:

  • We need a very very very large computer!
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Chrono-cosmography

 The naive approach:

  • We need a very very very large computer!

Not practical! Even with approximations!!!!

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4D Bayesian inference

Jasche, Wandelt (2013)

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4D analysis of the SDSS

Credit: M. Blanton and the Sloan Digital Sky Survey

 Analyzing the SDSS DR7 main sample

  • Explore a 2LPT-Normal-Poissonian distribution
  • 750 Mpc/h box
  • ~3 Mpc/h grid resolution
  • treatment of luminosity dependent bias ( 6 luminosity bins)
  • Automatic calibration of noise levels via sampling
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4D analysis of the SDSS

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4D analysis of the SDSS

 3D ensemble mean fields from 10000 data constrained realizations

Initial density field z = 1000 Final density field z = 0 SDSS data z = 0

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4D analysis of the SDSS

 Full non-linear and non-Gaussian uncertainty quantification

  • Example: voxel-wise standard deviations

Initial density field z = 1000 Final density field z = 0 Jasche et al. 2014 ( arXiv:1409.6308 )

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4D analysis of the SDSS

Jasche et al. 2014 ( arXiv:1409.6308 )

 Inference of plausible cosmic formation histories

  • From 3D to 4D inference
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Dynamical information in the SDSS

 Inferred 3D velocity fields

Jasche et al. 2014 ( arXiv:1409.6308 )

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Dark matter void in the SDSS

Leclercq et al. 2014 (arXiv:1410.0355)

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4D analysis of the 2M++ survey

Lavaux and Jasche (in prep )

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The Supergalactic plane

?

Lavaux and Jasche (in prep )

Shapley concentration Pisces-Cetus Perseus-Pisces Coma ?

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kSZ in the 2M++ survey

Lavaux (2011)

 Applying BORG to the 2M++ survey

  • 600 Mpc/h Box (Full sky)
  • Construct kSZ Template

Lavaux and Jasche (in prep)

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Comparing Inference schemes

Jasche & Lavaux (in prep)

Gaussian Log-normal-Poisson 2LPT-Poisson

Which scheme performs best? Ask the data!

a.k.a: Wiener-filtering Zaroubi et al. 1994 Erdogdu et al. 2004 Kitaura & Ensslin 2008 Kitaura 2010 Jasche&Kitaura 2010 log-normal-filtering 2LPT-filtering Jasche&Wandelt 2012

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Summary & Conclusion

 4D Bayesian inference

  • From 3D to 4D (Spatio-Temporal inference)
  • Non-linear, non-Gaussian statistics
  • Noise, survey geometry, selection effects and biases

 4D Bayesian analyses of the SDSS and 2M++ survey

  • Characterization of initial conditions
  • Higher order statistics
  • Dynamic information, structure formation histories
  • Improved inference in noisy regimes (see Florent's Talk)
  • Predictions and test of physical effects (ISW, kSZ, weak lensing)
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The End... Thank You!

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