j. jasche, bayesian lss inference jens jasche la thuile, 11 march 2012 bayesian large scale...
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J. Jasche, Bayesian LSS Inference
Jens Jasche
La Thuile, 11 March 2012
Bayesian Large Scale Structureinference
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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)
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J. Jasche, Bayesian LSS Inference
Motivation
No ideal Observations in reality
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J. Jasche, Bayesian LSS Inference
Motivation
No ideal Observations in reality• Statistical uncertainties
Noise, cosmic variance etc.
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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
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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!!!
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J. Jasche, Bayesian LSS Inference
Bayesian Approach
“Which are the possible signals compatible with the observations?”
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J. Jasche, Bayesian LSS Inference
Object of interest: Signal posterior distribution
“Which are the possible signals compatible with the observations?”
Bayesian Approach
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J. Jasche, Bayesian LSS Inference
Object of interest: Signal posterior distribution
“Which are the possible signals compatible with the observations?”
Prior
Bayesian Approach
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J. Jasche, Bayesian LSS Inference
Object of interest: Signal posterior distribution
“Which are the possible signals compatible with the observations?”
Likelihood
Bayesian Approach
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J. Jasche, Bayesian LSS Inference
Object of interest: Signal posterior distribution
“Which are the possible signals compatible with the observations?”
Evidence
Bayesian Approach
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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
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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)
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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
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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
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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
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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)
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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)
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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)
![Page 20: J. Jasche, Bayesian LSS Inference Jens Jasche La Thuile, 11 March 2012 Bayesian Large Scale Structure inference](https://reader035.vdocuments.mx/reader035/viewer/2022070415/5697bff11a28abf838cbb176/html5/thumbnails/20.jpg)
J. Jasche, Bayesian LSS Inference
What are the possible density fields compatible with the data ?
LSS inference with the SDSS
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J. Jasche, Bayesian LSS Inference
What are the possible density fields compatible with the data ?
LSS inference with the SDSS
![Page 22: J. Jasche, Bayesian LSS Inference Jens Jasche La Thuile, 11 March 2012 Bayesian Large Scale Structure inference](https://reader035.vdocuments.mx/reader035/viewer/2022070415/5697bff11a28abf838cbb176/html5/thumbnails/22.jpg)
J. Jasche, Bayesian LSS Inference
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J. Jasche, Bayesian LSS Inference
ISW-templates
LSS inference with the SDSS
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J. Jasche, Bayesian LSS Inference
Redshift uncertainties Photometric surveys
• deep volumes• millions of galaxies• low redshift accuracy
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J. Jasche, Bayesian LSS Inference
Redshift uncertainties
Galaxy positions
Matter density
Photometric surveys• deep volumes• millions of galaxies• low redshift accuracy
![Page 26: J. Jasche, Bayesian LSS Inference Jens Jasche La Thuile, 11 March 2012 Bayesian Large Scale Structure inference](https://reader035.vdocuments.mx/reader035/viewer/2022070415/5697bff11a28abf838cbb176/html5/thumbnails/26.jpg)
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
![Page 27: J. Jasche, Bayesian LSS Inference Jens Jasche La Thuile, 11 March 2012 Bayesian Large Scale Structure inference](https://reader035.vdocuments.mx/reader035/viewer/2022070415/5697bff11a28abf838cbb176/html5/thumbnails/27.jpg)
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
![Page 28: J. Jasche, Bayesian LSS Inference Jens Jasche La Thuile, 11 March 2012 Bayesian Large Scale Structure inference](https://reader035.vdocuments.mx/reader035/viewer/2022070415/5697bff11a28abf838cbb176/html5/thumbnails/28.jpg)
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
![Page 29: J. Jasche, Bayesian LSS Inference Jens Jasche La Thuile, 11 March 2012 Bayesian Large Scale Structure inference](https://reader035.vdocuments.mx/reader035/viewer/2022070415/5697bff11a28abf838cbb176/html5/thumbnails/29.jpg)
J. Jasche, Bayesian LSS Inference
Joint sampling
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J. Jasche, Bayesian LSS Inference
Joint sampling
Metropolis Block sampling:
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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
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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
![Page 33: J. Jasche, Bayesian LSS Inference Jens Jasche La Thuile, 11 March 2012 Bayesian Large Scale Structure inference](https://reader035.vdocuments.mx/reader035/viewer/2022070415/5697bff11a28abf838cbb176/html5/thumbnails/33.jpg)
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
![Page 34: J. Jasche, Bayesian LSS Inference Jens Jasche La Thuile, 11 March 2012 Bayesian Large Scale Structure inference](https://reader035.vdocuments.mx/reader035/viewer/2022070415/5697bff11a28abf838cbb176/html5/thumbnails/34.jpg)
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
![Page 35: J. Jasche, Bayesian LSS Inference Jens Jasche La Thuile, 11 March 2012 Bayesian Large Scale Structure inference](https://reader035.vdocuments.mx/reader035/viewer/2022070415/5697bff11a28abf838cbb176/html5/thumbnails/35.jpg)
J. Jasche, Bayesian LSS Inference
Photometric redshift sampling
Jasche, Wandelt (2011)
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J. Jasche, Bayesian LSS Inference
Deviation from the truth
Jasche, Wandelt (2011)
Before After
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J. Jasche, Bayesian LSS Inference
Deviation from the truth
Jasche, Wandelt (2011)
Raw data Density estimate
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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
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J. Jasche, Bayesian LSS Inference
The End …
Thank you
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J. Jasche, Bayesian LSS Inference
Resimulating the SGW
Building initial conditions for the Sloan Volume• resimulate the Sloan Great Wall (SGW)
Preliminary Work
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J. Jasche, Bayesian LSS Inference
Marginalized redshift posterior
Jasche, Wandelt (2011)
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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)
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J. Jasche, Bayesian LSS Inference
HADES vs. ARES
HADES
Variance
Mean
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J. Jasche, Bayesian LSS Inference
ARESHADES
HADES vs. ARES
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J. Jasche, Bayesian LSS Inference
Lensing templates
LSS inference with the SDSS
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J. Jasche, Bayesian LSS Inference
Extensions of the sampler Multiple block Metropolis Hastings sampling
Example redshift sampling