J. Jasche, Bayesian LSS Inference Jens Jasche La Thuile, 11 March 2012 Bayesian Large Scale Structure inference

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

 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 ~ 2 x 10^7 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 ~ 2 x 10^7 radial galaxy positions / parameters (~100 Mpc) ~ 3 x 10^7 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 ~ 2 x 10^7 radial galaxy positions / parameters (~100 Mpc) ~ 3 x 10^7 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) BeforeAfter

J. Jasche, Bayesian LSS Inference Deviation from the truth Jasche, Wandelt (2011) Raw dataDensity 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)

J. Jasche, Bayesian LSS Inference HADES vs. ARES HADES Variance Mean

J. Jasche, Bayesian LSS Inference ARES HADES 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