Bayesian Inference with physical models of the cosmic ... fileBayesian Inference with physical...
Transcript of Bayesian Inference with physical models of the cosmic ... fileBayesian Inference with physical...
![Page 1: Bayesian Inference with physical models of the cosmic ... fileBayesian Inference with physical models of the cosmic Large Scale Structure Jens Jasche Guilhem Lavaux, Florent Leclercq,](https://reader030.fdocuments.us/reader030/viewer/2022041217/5e05c99879084d19a804567b/html5/thumbnails/1.jpg)
Bayesian Inferencewith
physical models of the cosmic Large Scale Structure
Jens JascheGuilhem Lavaux, Florent Leclercq, Alexander Merson,
Benjamin Wandelt
Lightcone Workshop, Garching, 19 October 2016
![Page 2: Bayesian Inference with physical models of the cosmic ... fileBayesian Inference with physical models of the cosmic Large Scale Structure Jens Jasche Guilhem Lavaux, Florent Leclercq,](https://reader030.fdocuments.us/reader030/viewer/2022041217/5e05c99879084d19a804567b/html5/thumbnails/2.jpg)
The cosmic large scale structure...
... A source of knowledge!
- Cosmological parameter
- Geometry of the Universe
- Constituents of the Universe
- Tests of Gravity
- Galaxy formation
- fundamental physics
Image credit: Volker Springel for the Millenium Simulation, MPA Garching
![Page 3: Bayesian Inference with physical models of the cosmic ... fileBayesian Inference with physical models of the cosmic Large Scale Structure Jens Jasche Guilhem Lavaux, Florent Leclercq,](https://reader030.fdocuments.us/reader030/viewer/2022041217/5e05c99879084d19a804567b/html5/thumbnails/3.jpg)
The need for statistics
“If your experiment needs statistics, you ought to do a better experiment.”Lord Ernest Rutherford
No unique recovery! We need statistics!
Inference of signals = Ill-posed problem
Cosmic varianceNoise
Survey geometrySelection effectsForegroundsGalaxy bias
Finite resolution of telescopeRedshift distortionsPhotometric uncertainties
![Page 4: Bayesian Inference with physical models of the cosmic ... fileBayesian Inference with physical models of the cosmic Large Scale Structure Jens Jasche Guilhem Lavaux, Florent Leclercq,](https://reader030.fdocuments.us/reader030/viewer/2022041217/5e05c99879084d19a804567b/html5/thumbnails/4.jpg)
4D Bayesian Inference
Gravity
Initial State Final State
Bayesian physical inference
Statistically complex final state
Statistically simple initial state
Solve inverse Problem via forward modeling
![Page 5: Bayesian Inference with physical models of the cosmic ... fileBayesian Inference with physical models of the cosmic Large Scale Structure Jens Jasche Guilhem Lavaux, Florent Leclercq,](https://reader030.fdocuments.us/reader030/viewer/2022041217/5e05c99879084d19a804567b/html5/thumbnails/5.jpg)
4D Bayesian Inference
Gravity
Initial State Final State
Bayesian physical inference
Statistically complex final state
Statistically simple initial state
Solve inverse Problem via forward modeling
Requires to handle >10 million parameters
![Page 6: Bayesian Inference with physical models of the cosmic ... fileBayesian Inference with physical models of the cosmic Large Scale Structure Jens Jasche Guilhem Lavaux, Florent Leclercq,](https://reader030.fdocuments.us/reader030/viewer/2022041217/5e05c99879084d19a804567b/html5/thumbnails/6.jpg)
( Parameter ) space: The final Frontier
“The Curse of dimensionality” Bellman, 1961
High dimensional parameter spaces are sparse!!!
![Page 7: Bayesian Inference with physical models of the cosmic ... fileBayesian Inference with physical models of the cosmic Large Scale Structure Jens Jasche Guilhem Lavaux, Florent Leclercq,](https://reader030.fdocuments.us/reader030/viewer/2022041217/5e05c99879084d19a804567b/html5/thumbnails/7.jpg)
( Parameter ) space: The final Frontier
“The Curse of dimensionality” Bellman, 1961
High dimensional parameter spaces are sparse!!!
![Page 8: Bayesian Inference with physical models of the cosmic ... fileBayesian Inference with physical models of the cosmic Large Scale Structure Jens Jasche Guilhem Lavaux, Florent Leclercq,](https://reader030.fdocuments.us/reader030/viewer/2022041217/5e05c99879084d19a804567b/html5/thumbnails/8.jpg)
( Parameter ) space: The final Frontier
“The Curse of dimensionality” Bellman, 1961
High dimensional parameter spaces are sparse!!!
![Page 9: Bayesian Inference with physical models of the cosmic ... fileBayesian Inference with physical models of the cosmic Large Scale Structure Jens Jasche Guilhem Lavaux, Florent Leclercq,](https://reader030.fdocuments.us/reader030/viewer/2022041217/5e05c99879084d19a804567b/html5/thumbnails/9.jpg)
( Parameter ) space: The final Frontier
“The Curse of dimensionality” Bellman, 1961
High dimensional parameter spaces are sparse!!!
Bona fide PDFs:
![Page 10: Bayesian Inference with physical models of the cosmic ... fileBayesian Inference with physical models of the cosmic Large Scale Structure Jens Jasche Guilhem Lavaux, Florent Leclercq,](https://reader030.fdocuments.us/reader030/viewer/2022041217/5e05c99879084d19a804567b/html5/thumbnails/10.jpg)
( Parameter ) space: The final Frontier
“The Curse of dimensionality” Bellman, 1961
High dimensional parameter spaces are sparse!!!
Bona fide PDFs:
Space filling and random sampling methods will fail!!!
![Page 11: Bayesian Inference with physical models of the cosmic ... fileBayesian Inference with physical models of the cosmic Large Scale Structure Jens Jasche Guilhem Lavaux, Florent Leclercq,](https://reader030.fdocuments.us/reader030/viewer/2022041217/5e05c99879084d19a804567b/html5/thumbnails/11.jpg)
( Parameter ) space: The final Frontier
“The Curse of dimensionality” Bellman, 1961
High dimensional parameter spaces are sparse!!!
Bona fide PDFs:
Space filling and random sampling methods will fail!!!
But gradients are very valuable!!!
![Page 12: Bayesian Inference with physical models of the cosmic ... fileBayesian Inference with physical models of the cosmic Large Scale Structure Jens Jasche Guilhem Lavaux, Florent Leclercq,](https://reader030.fdocuments.us/reader030/viewer/2022041217/5e05c99879084d19a804567b/html5/thumbnails/12.jpg)
MCMC in high dimensions
HMC: Use Classical mechanics to solve statistical problems!
The potential :
see e.g. Duane et al. (1987)
![Page 13: Bayesian Inference with physical models of the cosmic ... fileBayesian Inference with physical models of the cosmic Large Scale Structure Jens Jasche Guilhem Lavaux, Florent Leclercq,](https://reader030.fdocuments.us/reader030/viewer/2022041217/5e05c99879084d19a804567b/html5/thumbnails/13.jpg)
MCMC in high dimensions
HMC: Use Classical mechanics to solve statistical problems!
The potential :
The Hamiltonian :
see e.g. Duane et al. (1987)
![Page 14: Bayesian Inference with physical models of the cosmic ... fileBayesian Inference with physical models of the cosmic Large Scale Structure Jens Jasche Guilhem Lavaux, Florent Leclercq,](https://reader030.fdocuments.us/reader030/viewer/2022041217/5e05c99879084d19a804567b/html5/thumbnails/14.jpg)
MCMC in high dimensions
HMC: Use Classical mechanics to solve statistical problems!
The potential :
The Hamiltonian :
see e.g. Duane et al. (1987)
Nuisance parameter!!!
![Page 15: Bayesian Inference with physical models of the cosmic ... fileBayesian Inference with physical models of the cosmic Large Scale Structure Jens Jasche Guilhem Lavaux, Florent Leclercq,](https://reader030.fdocuments.us/reader030/viewer/2022041217/5e05c99879084d19a804567b/html5/thumbnails/15.jpg)
MCMC in high dimensions
HMC: Use Classical mechanics to solve statistical problems!
The potential :
The Hamiltonian :
see e.g. Duane et al. (1987)
Nuisance parameter!!!
![Page 16: Bayesian Inference with physical models of the cosmic ... fileBayesian Inference with physical models of the cosmic Large Scale Structure Jens Jasche Guilhem Lavaux, Florent Leclercq,](https://reader030.fdocuments.us/reader030/viewer/2022041217/5e05c99879084d19a804567b/html5/thumbnails/16.jpg)
MCMC in high dimensions
HMC: Use Classical mechanics to solve statistical problems!
The potential :
The Hamiltonian :
see e.g. Duane et al. (1987)
Nuisance parameter!!!
![Page 17: Bayesian Inference with physical models of the cosmic ... fileBayesian Inference with physical models of the cosmic Large Scale Structure Jens Jasche Guilhem Lavaux, Florent Leclercq,](https://reader030.fdocuments.us/reader030/viewer/2022041217/5e05c99879084d19a804567b/html5/thumbnails/17.jpg)
MCMC in high dimensions
HMC: Use Classical mechanics to solve statistical problems!
The potential :
The Hamiltonian :
see e.g. Duane et al. (1987)
Nuisance parameter!!!
HMC beats the “curse of dimensionality” by:
Exploiting gradients
Using conserved quantities
Randomize and accept :
![Page 18: Bayesian Inference with physical models of the cosmic ... fileBayesian Inference with physical models of the cosmic Large Scale Structure Jens Jasche Guilhem Lavaux, Florent Leclercq,](https://reader030.fdocuments.us/reader030/viewer/2022041217/5e05c99879084d19a804567b/html5/thumbnails/18.jpg)
4D Bayesian Inference
BORG
BORG (Bayesian Origin Reconstruction from Galaxies)
Incorporates physical model into Likelihood
Approximate LSS formation model (2LPT / PM)
Uses HMC to solve initial conditions problem
Jasche, Wandelt (2013)
![Page 19: Bayesian Inference with physical models of the cosmic ... fileBayesian Inference with physical models of the cosmic Large Scale Structure Jens Jasche Guilhem Lavaux, Florent Leclercq,](https://reader030.fdocuments.us/reader030/viewer/2022041217/5e05c99879084d19a804567b/html5/thumbnails/19.jpg)
Data application
Analyzing the SDSS DR7 main sample
750 Mpc/h box
~3 Mpc/h grid resolution
Treatment of luminosity dependent bias
Automatic noise calibration
Credit: M. Blanton and the Sloan Digital Sky Survey
![Page 20: Bayesian Inference with physical models of the cosmic ... fileBayesian Inference with physical models of the cosmic Large Scale Structure Jens Jasche Guilhem Lavaux, Florent Leclercq,](https://reader030.fdocuments.us/reader030/viewer/2022041217/5e05c99879084d19a804567b/html5/thumbnails/20.jpg)
−5
0
5 −5
0
50
0.2
0.4
4D Bayesian inference
BORG performs MCMC sampling
Explores space of physical 3D initial conditions
Cartoon! In Reality we deal with 10^7
dimensions!!
![Page 21: Bayesian Inference with physical models of the cosmic ... fileBayesian Inference with physical models of the cosmic Large Scale Structure Jens Jasche Guilhem Lavaux, Florent Leclercq,](https://reader030.fdocuments.us/reader030/viewer/2022041217/5e05c99879084d19a804567b/html5/thumbnails/21.jpg)
4D analysis of the SDSS
Initial density fieldz ~ 1000
final density fieldz=0
SDSS number counts
z=0
Jasche et al. 2015 ( arXiv:1409.6308 )
![Page 22: Bayesian Inference with physical models of the cosmic ... fileBayesian Inference with physical models of the cosmic Large Scale Structure Jens Jasche Guilhem Lavaux, Florent Leclercq,](https://reader030.fdocuments.us/reader030/viewer/2022041217/5e05c99879084d19a804567b/html5/thumbnails/22.jpg)
4D analysis of the SDSS
Dynamic Information
Plausible LSS formation history
Jasche et al. 2015 ( arXiv:1409.6308 )
![Page 23: Bayesian Inference with physical models of the cosmic ... fileBayesian Inference with physical models of the cosmic Large Scale Structure Jens Jasche Guilhem Lavaux, Florent Leclercq,](https://reader030.fdocuments.us/reader030/viewer/2022041217/5e05c99879084d19a804567b/html5/thumbnails/23.jpg)
4D analysis of the SDSS
Jasche et al. 2015 ( arXiv:1409.6308 )
Dynamic Information
Inference of 3D velocity fields
![Page 24: Bayesian Inference with physical models of the cosmic ... fileBayesian Inference with physical models of the cosmic Large Scale Structure Jens Jasche Guilhem Lavaux, Florent Leclercq,](https://reader030.fdocuments.us/reader030/viewer/2022041217/5e05c99879084d19a804567b/html5/thumbnails/24.jpg)
4D Bayesian inference
Lavaux & Jasche 2016 (arXiv:1509.05040 )
![Page 25: Bayesian Inference with physical models of the cosmic ... fileBayesian Inference with physical models of the cosmic Large Scale Structure Jens Jasche Guilhem Lavaux, Florent Leclercq,](https://reader030.fdocuments.us/reader030/viewer/2022041217/5e05c99879084d19a804567b/html5/thumbnails/25.jpg)
4D Bayesian inference
A factor 10 in S/N with respect to state-of-the-art!
Lavaux & Jasche 2016 (arXiv:1509.05040 )
![Page 26: Bayesian Inference with physical models of the cosmic ... fileBayesian Inference with physical models of the cosmic Large Scale Structure Jens Jasche Guilhem Lavaux, Florent Leclercq,](https://reader030.fdocuments.us/reader030/viewer/2022041217/5e05c99879084d19a804567b/html5/thumbnails/26.jpg)
Comparing inference schemesGaussian Log-normal-Poisson 2LPT-Poisson
a.k.a: Wiener-filteringZaroubi et al. 1994Erdogdu et al. 2004Kitaura & Ensslin 2008Grannet et al. 2015
Kitaura 2010Jasche&Kitaura 2010
log-normal-filtering
Jasche&Wandelt 2012
Jasche & Lavaux (in prep)
Which scheme performs best?
Ask the data!
![Page 27: Bayesian Inference with physical models of the cosmic ... fileBayesian Inference with physical models of the cosmic Large Scale Structure Jens Jasche Guilhem Lavaux, Florent Leclercq,](https://reader030.fdocuments.us/reader030/viewer/2022041217/5e05c99879084d19a804567b/html5/thumbnails/27.jpg)
Some thoughts on light cone modeling
Physical modeling of light cone effects in Bayesian inferences
Deep surveys are statistical inhomogeneous
Not a mere scaling of density amplitudes
Speed vs. Accuracy
Are there fast and accurate light cone models?
![Page 28: Bayesian Inference with physical models of the cosmic ... fileBayesian Inference with physical models of the cosmic Large Scale Structure Jens Jasche Guilhem Lavaux, Florent Leclercq,](https://reader030.fdocuments.us/reader030/viewer/2022041217/5e05c99879084d19a804567b/html5/thumbnails/28.jpg)
Summary & Conclusion
4D Bayesian inference
From 3D to 4D (Spatio-Temporal inference)
Non-linear, non-Gaussian
Handling of noise, bias, selection effects, survey geometries
etc.
Scientific results
Physical modeling helps to make the most of data
Characterization of initial conditions
Higher order statistics
Dynamic information, Structure formation
Greatly improved reconstructions of LSS
![Page 29: Bayesian Inference with physical models of the cosmic ... fileBayesian Inference with physical models of the cosmic Large Scale Structure Jens Jasche Guilhem Lavaux, Florent Leclercq,](https://reader030.fdocuments.us/reader030/viewer/2022041217/5e05c99879084d19a804567b/html5/thumbnails/29.jpg)
The end...
Thank You!
![Page 30: Bayesian Inference with physical models of the cosmic ... fileBayesian Inference with physical models of the cosmic Large Scale Structure Jens Jasche Guilhem Lavaux, Florent Leclercq,](https://reader030.fdocuments.us/reader030/viewer/2022041217/5e05c99879084d19a804567b/html5/thumbnails/30.jpg)
−5
0
5 −5
0
50
0.2
0.4
4D Bayesian inference
BORG performs MCMC sampling
Explores space of physical 3D initial conditions
Cartoon! In Reality we deal with 10^7
dimensions!!
![Page 31: Bayesian Inference with physical models of the cosmic ... fileBayesian Inference with physical models of the cosmic Large Scale Structure Jens Jasche Guilhem Lavaux, Florent Leclercq,](https://reader030.fdocuments.us/reader030/viewer/2022041217/5e05c99879084d19a804567b/html5/thumbnails/31.jpg)
−5
0
5 −5
0
50
0.2
0.4
4D Bayesian inference
BORG performs MCMC sampling
Explores space of physical 3D initial conditions
Cartoon! In Reality we deal with 10^7
dimensions!!
![Page 32: Bayesian Inference with physical models of the cosmic ... fileBayesian Inference with physical models of the cosmic Large Scale Structure Jens Jasche Guilhem Lavaux, Florent Leclercq,](https://reader030.fdocuments.us/reader030/viewer/2022041217/5e05c99879084d19a804567b/html5/thumbnails/32.jpg)
Dark matter voids in the SDSS
Leclercq et al. 2015 (arXiv:1410.0355)
Cumulative void number functions