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Jens Jasche La Thuile, 11 March 2012. Bayesian Large Scale Structure inference. Motivation. Goal: 3D cosmography homogeneous evolution Cosmological parameters Dark Energy Power-spectrum / BAO non-linear structure formation Galaxy properties Initial conditions - PowerPoint PPT Presentation
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J. Jasche, Bayesian LSS Inference
Jens Jasche
La Thuile, 11 March 2012
Bayesian Large Scale Structureinference
J. Jasche, Bayesian LSS Inference
Goal: 3D cosmography• homogeneous evolution
• Cosmological parameters• Dark Energy• Power-spectrum / BAO
• non-linear structure formation• Galaxy properties• Initial conditions• Large scale flows
Motivation
Tegmark et al. (2004)
Jasche et al. (2010)
J. Jasche, Bayesian LSS Inference
Motivation
No ideal Observations in reality
J. Jasche, Bayesian LSS Inference
Motivation
No ideal Observations in reality• Statistical uncertainties
Noise, cosmic variance etc.
J. Jasche, Bayesian LSS Inference
Motivation
No ideal Observations in reality• Statistical uncertainties • Systematics
Noise, cosmic variance etc.
Kitaura et al. (2009)
Survey geometry, selection effects,biases
J. Jasche, Bayesian LSS Inference
Motivation
No ideal Observations in reality• Statistical uncertainties • Systematics
Noise, cosmic variance etc.
Kitaura et al. (2009)
Survey geometry, selection effects,biases
No unique recovery possible!!!
J. Jasche, Bayesian LSS Inference
Bayesian Approach
“Which are the possible signals compatible with the observations?”
J. Jasche, Bayesian LSS Inference
Object of interest: Signal posterior distribution
“Which are the possible signals compatible with the observations?”
Bayesian Approach
J. Jasche, Bayesian LSS Inference
Object of interest: Signal posterior distribution
“Which are the possible signals compatible with the observations?”
Prior
Bayesian Approach
J. Jasche, Bayesian LSS Inference
Object of interest: Signal posterior distribution
“Which are the possible signals compatible with the observations?”
Likelihood
Bayesian Approach
J. Jasche, Bayesian LSS Inference
Object of interest: Signal posterior distribution
“Which are the possible signals compatible with the observations?”
Evidence
Bayesian Approach
J. Jasche, Bayesian LSS Inference
Object of interest: Signal posterior distribution
“Which are the possible signals compatible with the observations?”
We can do science!• Model comparison• Parameter studies• Report statistical summaries• Non-linear, Non-Gaussian error propagation
Bayesian Approach
J. Jasche, Bayesian LSS Inference
LSS Posterior Aim: inference of non-linear density fields
• non-linear density field lognormal
See e.g. Coles & Jones (1991), Kayo et al. (2001)
J. Jasche, Bayesian LSS Inference
LSS Posterior Aim: inference of non-linear density fields
• non-linear density field lognormal
• “correct” noise treatment full Poissonian distribution
See e.g. Coles & Jones (1991), Kayo et al. (2001)
Credit: M. Blanton and the
Sloan Digital Sky Survey
J. Jasche, Bayesian LSS Inference
LSS Posterior
Problem: Non-Gaussian sampling in high dimensions • direct sampling not possible• usual Metropolis-Hastings algorithm inefficient
Aim: inference of non-linear density fields• non-linear density field
lognormal
• “correct” noise treatment full Poissonian distribution
See e.g. Coles & Jones (1991), Kayo et al. (2001)
Credit: M. Blanton and the
Sloan Digital Sky Survey
J. Jasche, Bayesian LSS Inference
LSS Posterior
Problem: Non-Gaussian sampling in high dimensions • direct sampling not possible• usual Metropolis-Hastings algorithm inefficient
Aim: inference of non-linear density fields• non-linear density field
lognormal
• “correct” noise treatment full Poissonian distribution
See e.g. Coles & Jones (1991), Kayo et al. (2001)
HADES (HAmiltonian Density Estimation and Sampling)
Jasche, Kitaura (2010)
Credit: M. Blanton and the
Sloan Digital Sky Survey
J. Jasche, Bayesian LSS Inference
LSS inference with the SDSS
Application of HADES to SDSS DR7• cubic, equidistant box with sidelength 750 Mpc• ~ 3 Mpc grid resolution• ~ 10^7 volume elements / parameters
Jasche, Kitaura, Li, Enßlin (2010)
J. Jasche, Bayesian LSS Inference
Application of HADES to SDSS DR7• cubic, equidistant box with sidelength 750 Mpc• ~ 3 Mpc grid resolution• ~ 10^7 volume elements / parameters
Goal: provide a representation of the SDSS density posterior• to provide 3D cosmographic descriptions• to quantify uncertainties of the density distribution
LSS inference with the SDSS
Jasche, Kitaura, Li, Enßlin (2010)
J. Jasche, Bayesian LSS Inference
Application of HADES to SDSS DR7• cubic, equidistant box with sidelength 750 Mpc• ~ 3 Mpc grid resolution• ~ 10^7 volume elements / parameters
Goal: provide a representation of the SDSS density posterior• to provide 3D cosmographic descriptions• to quantify uncertainties of the density distribution
3 TB, 40,000 density samples
LSS inference with the SDSS
Jasche, Kitaura, Li, Enßlin (2010)
J. Jasche, Bayesian LSS Inference
What are the possible density fields compatible with the data ?
LSS inference with the SDSS
J. Jasche, Bayesian LSS Inference
What are the possible density fields compatible with the data ?
LSS inference with the SDSS
J. Jasche, Bayesian LSS Inference
J. Jasche, Bayesian LSS Inference
ISW-templates
LSS inference with the SDSS
J. Jasche, Bayesian LSS Inference
Redshift uncertainties Photometric surveys
• deep volumes• millions of galaxies• low redshift accuracy
J. Jasche, Bayesian LSS Inference
Redshift uncertainties
Galaxy positions
Matter density
Photometric surveys• deep volumes• millions of galaxies• low redshift accuracy
J. Jasche, Bayesian LSS Inference
Redshift uncertainties
Galaxy positions
Matter density
We know that:• Galaxies trace the matter distribution• Matter distribution is homogeneous and isotropic
Jasche et al. (2010)
Photometric surveys• deep volumes• millions of galaxies• low redshift accuracy
J. Jasche, Bayesian LSS Inference
Redshift uncertainties
Galaxy positions
Matter density
We know that:• Galaxies trace the matter distribution• Matter distribution is homogeneous and isotropic
Jasche et al. (2010)
Photometric surveys• deep volumes• millions of galaxies• low redshift accuracy
J. Jasche, Bayesian LSS Inference
Redshift uncertainties
Galaxy positions
Matter density
We know that:• Galaxies trace the matter distribution• Matter distribution is homogeneous and isotropic
Jasche et al. (2010)
Joint inference
Photometric surveys• deep volumes• millions of galaxies• low redshift accuracy
J. Jasche, Bayesian LSS Inference
Joint sampling
J. Jasche, Bayesian LSS Inference
Joint sampling
Metropolis Block sampling:
J. Jasche, Bayesian LSS Inference
Application of HADES to artificial photometric data • cubic, equidistant box with sidelength 1200 Mpc• ~ 5 Mpc grid resolution• ~ 10^7 volume elements / parameters
Photometric redshift inference
J. Jasche, Bayesian LSS Inference
Application of HADES to artificial photometric data • cubic, equidistant box with sidelength 1200 Mpc• ~ 5 Mpc grid resolution• ~ 10^7 volume elements / parameters• ~ 2x10^7 radial galaxy positions / parameters
• (~100 Mpc)
Photometric redshift inference
J. Jasche, Bayesian LSS Inference
Application of HADES to artificial photometric data • cubic, equidistant box with sidelength 1200 Mpc• ~ 5 Mpc grid resolution• ~ 10^7 volume elements / parameters• ~ 2x10^7 radial galaxy positions / parameters
• (~100 Mpc)• ~ 3x10^7 parameters in total
Photometric redshift inference
J. Jasche, Bayesian LSS Inference
Application of HADES to artificial photometric data • cubic, equidistant box with sidelength 1200 Mpc• ~ 5 Mpc grid resolution• ~ 10^7 volume elements / parameters• ~ 2x10^7 radial galaxy positions / parameters
• (~100 Mpc)• ~ 3x10^7 parameters in total
Photometric redshift inference
J. Jasche, Bayesian LSS Inference
Photometric redshift sampling
Jasche, Wandelt (2011)
J. Jasche, Bayesian LSS Inference
Deviation from the truth
Jasche, Wandelt (2011)
Before After
J. Jasche, Bayesian LSS Inference
Deviation from the truth
Jasche, Wandelt (2011)
Raw data Density estimate
J. Jasche, Bayesian LSS Inference
Summary & Conclusion
LSS 3D density inference Correction of systematic effects, survey geometry, selection effects Accurate treatment of Poissonian shot noise Precision non-linear density inference Non-linear, non-Gaussian error propagation
Joint redshift & 3D density inference Positive influence on mutual inference Improved redshift accuracy Treatment of joint uncertainties
Also note: methods are general complementary data sets
• 21 cm, X-ray, etc
J. Jasche, Bayesian LSS Inference
The End …
Thank you
J. Jasche, Bayesian LSS Inference
Resimulating the SGW
Building initial conditions for the Sloan Volume• resimulate the Sloan Great Wall (SGW)
Preliminary Work
J. Jasche, Bayesian LSS Inference
Marginalized redshift posterior
Jasche, Wandelt (2011)
J. Jasche, Bayesian LSS Inference
IDEA: Follow Hamiltonian dynamics
Conservation of energy Metropolis acceptance probability is unity
All samples are accepted
Persistent motion
Hamiltonian Sampling
= 1
HADES (Hamiltonian Density Estimation and Sampling)HADES (Hamiltonian Density Estimation and Sampling)
J. Jasche, Bayesian LSS Inference
HADES vs. ARES
HADES
Variance
Mean
J. Jasche, Bayesian LSS Inference
ARESHADES
HADES vs. ARES
J. Jasche, Bayesian LSS Inference
Lensing templates
LSS inference with the SDSS
J. Jasche, Bayesian LSS Inference
Extensions of the sampler Multiple block Metropolis Hastings sampling
Example redshift sampling
