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The best of both worlds?

SAMSI: Mar 2006. The best of both worlds?. Towards combining design-based and parametric approaches to analysing galaxy surveys. Martin Hendry, Dept of Physics and Astronomy University of Glasgow, UK. SAMSI: Mar 2006. Previous session: introduction to Malmquist bias and how it

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The best of both worlds?

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  1. SAMSI: Mar 2006 The best of both worlds? Towards combining design-based and parametric approaches to analysing galaxy surveys Martin Hendry, Dept of Physics and Astronomy University of Glasgow, UK

  2. SAMSI: Mar 2006 • Previous session: introduction to Malmquist bias and how it • affects estimating galaxy distances • ‘Malmquist Correction’ methods (very) parametric • Optimal approach depends on what we are using galaxy distances • for(there may be other systematic biases besides Malmquist anyhow). • Example: using galaxy distances to estimate peculiar velocity field, • and constrain the mean density of dark matter on large scales. • Peculiar velocity = motion of a galaxy over and above the • Hubble expansion, due to the gravitational influence of its • surroundings. i.e. galaxy peculiar velocities trace the local • density field of all matter – not just the luminous matter. How are the galaxy and mass distribution related?…

  3. SAMSI: Mar 2006 Simplest model: linear biasing b= linear bias parameter, related to peculiar velocities via So galaxy distances  peculiar velocities  to constrain Underlying density field of all matter Density field of luminous matter, (smoothed version of galaxy distribution) Dimensionless mean matter density of the Universe

  4. SAMSI: Mar 2006 Problem: Through the late 90s – early 00s: dichotomy of inferred values of and . Could discrepancy be down to problems with correcting for Malmquist bias?… Could a ‘design-based’ approach (c.f. Efron & Petrosian) help? Rauzy & Hendry (2000) - ROBUST method for fitting peculiar velocity field models

  5. SAMSI: Mar 2006 Robust Method Assumption: luminosity function is Universal Spatial distribution Selection effects Luminosity function Null hypothesis (Rauzy 2001) Angular and radial Selection function Step function

  6. Robust Method: Completeness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Distance modulus m . . . . . . . . . . . . . . . Mlim(mi ) . . . . . . . . . . . . . . . . (Mi, mi) . . . . . . . . . . mlim . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Absolute magnitude M SAMSI: Mar 2006

  7. Robust Method: Completeness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Distance modulus m . . . . . . . . . . . . . . . Mlim(mi ) . . . . . . . . . . . . . . . . (Mi, mi) . . . . . . . . . . mlim . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . S1 S2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Absolute magnitude M SAMSI: Mar 2006

  8. Robust Method: Completeness m* > mlim SAMSI: Mar 2006

  9. Robust Method: Completeness Define:- where Can show:- P1: P2: uncorrelated SAMSI: Mar 2006

  10. Robust Method: Completeness Also:- but only for SAMSI: Mar 2006

  11. Robust Method: Completeness Also:- but only for SAMSI: Mar 2006

  12. Robust Method: Velocity Field Model Assuming define Can show:- P3: uncorrelated Estimate b via SAMSI: Mar 2006

  13. Robust Method Strength: Robust support for VELMOD analysis: validity of inhomogeneous Malmquist corrections Weakness: Completeness requirement may restricts sample size and depth From Rauzy & Hendry 2000 SAMSI: Mar 2006

  14. SAMSI: Mar 2006 Rauzy, Hendry & D’Mellow (2001) P1: P2: and are independent • If we have the wrong LF model, P1 and P2 are not satisfied

  15. e.g. Schechter model, For each use K-S statistic to test P1: use sample correlation coefficient to test P2: Define

  16. e.g. Schechter model, For each use K-S statistic to test P1: use sample correlation coefficient to test P2: Define

  17. SAMSI: Mar 2006 c.f ML approach: If the LF model is a good descriptor of the true distribution, 2[Lmax – L(a,M*)] ~ c2

  18. SAMSI: Mar 2006 c.f ML approach: If the LF model is a good descriptor of the true distribution, 2[Lmax – L(a,M*)] ~ c2 ‘Toy’ evolution model: Gaussian LF,

  19. SAMSI: Mar 2006 c.f ML approach: If the LF model is a good descriptor of the true distribution, 2[Lmax – L(a,M*)] ~ c2 ‘Toy’ evolution model: Gaussian LF, Model rejected

  20. SAMSI: Mar 2006 Questions / Issues • How sensitive are robust methods to measurement errors? • How to extend to ‘fuzzy’ selection / truncation? • How to extend to multi-dimensional cases? • (e.g. bivariate distribution of luminosity, surface brightness) • How to extend the K-S test to >1d? • Can ROBUST be useful as a diagnostic of systematic errors? • (e.g. where separability assumption breaks down) • (What’s wrong with 2dF?)

  21. Millennium galaxy catalog of Driver et al. (2003) Volume-limited subset of data

  22. SAMSI: Mar 2006

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