Bayesian Large Scale Structure inference

1. Jens Jasche La Thuile, 11 March 2012 Bayesian Large Scale Structureinference J. Jasche, Bayesian LSS Inference

2. J. Jasche, Bayesian LSS Inference Motivation • Goal: 3D cosmography • homogeneous evolution • Cosmological parameters • Dark Energy • Power-spectrum / BAO • non-linear structure formation • Galaxy properties • Initial conditions • Large scale flows Tegmark et al. (2004) Jasche et al. (2010)

3. J. Jasche, Bayesian LSS Inference Motivation • No ideal Observations in reality

4. J. Jasche, Bayesian LSS Inference Motivation • No ideal Observations in reality • Statistical uncertainties Noise, cosmic variance etc.

5. J. Jasche, Bayesian LSS Inference Motivation • No ideal Observations in reality • Statistical uncertainties • Systematics Kitaura et al. (2009) Survey geometry, selection effects, biases Noise, cosmic variance etc.

6. J. Jasche, Bayesian LSS Inference Motivation • No ideal Observations in reality • Statistical uncertainties • Systematics Kitaura et al. (2009) Survey geometry, selection effects, biases Noise, cosmic variance etc. No unique recovery possible!!!

7. J. Jasche, Bayesian LSS Inference Bayesian Approach “Which are the possible signals compatible with the observations?”

8. J. Jasche, Bayesian LSS Inference Bayesian Approach “Which are the possible signals compatible with the observations?” • Object of interest: Signal posterior distribution

9. J. Jasche, Bayesian LSS Inference Bayesian Approach “Which are the possible signals compatible with the observations?” • Object of interest: Signal posterior distribution Prior

10. J. Jasche, Bayesian LSS Inference Bayesian Approach “Which are the possible signals compatible with the observations?” • Object of interest: Signal posterior distribution Likelihood

11. J. Jasche, Bayesian LSS Inference Bayesian Approach “Which are the possible signals compatible with the observations?” • Object of interest: Signal posterior distribution Evidence

12. J. Jasche, Bayesian LSS Inference Bayesian Approach “Which are the possible signals compatible with the observations?” • Object of interest: Signal posterior distribution • We can do science! • Model comparison • Parameter studies • Report statistical summaries • Non-linear, Non-Gaussian error propagation

13. 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)

14. 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

15. 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 • Problem: Non-Gaussian sampling in high dimensions • direct sampling not possible • usual Metropolis-Hastings algorithm inefficient

16. 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 • Problem: Non-Gaussian sampling in high dimensions • direct sampling not possible • usual Metropolis-Hastings algorithm inefficient HADES (HAmiltonian Density Estimation and Sampling) Jasche, Kitaura (2010)

17. 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)

18. 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 • Goal: provide a representation of the SDSS density posterior • to provide 3D cosmographic descriptions • to quantify uncertainties of the density distribution Jasche, Kitaura, Li, Enßlin (2010)

19. 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 • 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 Jasche, Kitaura, Li, Enßlin (2010)

20. LSS inference with the SDSS What are the possible density fields compatible with the data ? J. Jasche, Bayesian LSS Inference

21. LSS inference with the SDSS What are the possible density fields compatible with the data ? J. Jasche, Bayesian LSS Inference

22. J. Jasche, Bayesian LSS Inference

23. J. Jasche, Bayesian LSS Inference LSS inference with the SDSS • ISW-templates

24. J. Jasche, Bayesian LSS Inference Redshift uncertainties • Photometric surveys • deep volumes • millions of galaxies • low redshift accuracy

25. J. Jasche, Bayesian LSS Inference Redshift uncertainties • Photometric surveys • deep volumes • millions of galaxies • low redshift accuracy Galaxy positions Matter density

26. J. Jasche, Bayesian LSS Inference Redshift uncertainties • Photometric surveys • deep volumes • millions of galaxies • low redshift accuracy Galaxy positions Matter density • We know that: • Galaxies trace the matter distribution • Matter distribution is homogeneous and isotropic Jasche et al. (2010)

27. J. Jasche, Bayesian LSS Inference Redshift uncertainties • Photometric surveys • deep volumes • millions of galaxies • low redshift accuracy Galaxy positions Matter density • We know that: • Galaxies trace the matter distribution • Matter distribution is homogeneous and isotropic Jasche et al. (2010)

28. J. Jasche, Bayesian LSS Inference Redshift uncertainties • Photometric surveys • deep volumes • millions of galaxies • low redshift accuracy Galaxy positions Matter density Joint inference • We know that: • Galaxies trace the matter distribution • Matter distribution is homogeneous and isotropic Jasche et al. (2010)

29. J. Jasche, Bayesian LSS Inference Joint sampling

30. J. Jasche, Bayesian LSS Inference Joint sampling • Metropolis Block sampling:

31. J. Jasche, Bayesian LSS Inference Photometric redshift inference • Application of HADES to artificial photometric data • cubic, equidistant box with sidelength 1200 Mpc • ~ 5 Mpc grid resolution • ~ 10^7 volume elements / parameters

32. J. Jasche, Bayesian LSS Inference Photometric redshift 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)

33. J. Jasche, Bayesian LSS Inference Photometric redshift 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

34. J. Jasche, Bayesian LSS Inference Photometric redshift 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

35. J. Jasche, Bayesian LSS Inference Photometric redshift sampling Jasche, Wandelt (2011)

36. J. Jasche, Bayesian LSS Inference Deviation from the truth Before After Jasche, Wandelt (2011)

37. J. Jasche, Bayesian LSS Inference Deviation from the truth Raw data Density estimate Jasche, Wandelt (2011)

38. 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

39. J. Jasche, Bayesian LSS Inference The End … Thank you

40. J. Jasche, Bayesian LSS Inference Resimulating the SGW Preliminary Work • Building initial conditions for the Sloan Volume • resimulate the Sloan Great Wall (SGW)

41. J. Jasche, Bayesian LSS Inference Marginalized redshift posterior Jasche, Wandelt (2011)

42. Hamiltonian Sampling • IDEA: Follow Hamiltonian dynamics • Conservation of energy • Metropolis acceptance probability is unity • All samples are accepted Persistent motion = 1 HADES (Hamiltonian Density Estimation and Sampling) HADES (Hamiltonian Density Estimation and Sampling) J. Jasche, Bayesian LSS Inference

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

44. J. Jasche, Bayesian LSS Inference HADES vs. ARES HADES ARES

45. J. Jasche, Bayesian LSS Inference LSS inference with the SDSS • Lensing templates

46. J. Jasche, Bayesian LSS Inference Extensions of the sampler • Multiple block Metropolis Hastings sampling Example redshift sampling