Astronomy Perspective Ofer Lahav University College London SCMA

Astronomy Perspective Ofer Lahav University College London

SCMA IV • • Cosmology (I, II) Small-N problems (incl. HEP) Astronomical surveys Planetary systems Periodic variability Developments in statistics Cross-disciplinary perspectives

Astro-Statistics • • • Data Compression Classification Reconstruction Feature extraction Parameter estimation Model selection

Astro-Statistics Books • • Babu & Feigelson (1992) Lupton (1993) Martinez & Saar (2002) Wall & Jenkins (2003) Saha (2003) Gregory (2005) …

“That is the curse of statistics, that it can never prove things, only disprove them! At best, you can substantiate a hypothesis by ruling out, statistically, a whole long list of competing hypotheses, every one that has ever been proposed. After a while your adversaries and competitors will give up trying to think of alternative hypotheses, or else they will grow old and die, and then your hypothesis will become accepted. Sounds crazy, we know, but that’s how science works!“ Press et al. , Numerical Recipes

Methodology & Approaches • Frequentist Probability is interpreted as the frequency of the outcome of a repeatable experiment. • Bayesian The interpretation of probability is more general and includes ‘a degree of belief’. * “The information in the data” vs. “the information about something”

Bayes’ Theorem w w P(A|B) = P(B|A) P(A) / P(B) P(model | data)= P(data | model) P (model) / P(data) ↑ ↑ ↑ Likelihood Prior Evidence exp (- 2 /2) 1702 -1761 (paper only published in 1764)

Ed Jaynes (1984) on Bayesian Methods “communication problems… a serious disease that has afflicted probability theory for 200 years. There is a long history of confusion and controversy, leading in some cases to a paralytic inability to communicate…”

How to choose a prior? * Theoretical prejudice (e. g. “according to Inflation the universe must be flat” ) * Previous observations (e. g. “we know from WMAP the universe is flat to within 2%” ) * Parameterized ignorance ( e. g. ``a uniform prior, Jeffrey’s prior, or Entropy prior? ” )

Recent trends • Astro-Statistics is more ‘respectable’. • Bayesian approaches are more common, in co-existence with frequentist methods • More awareness of model selection methods (e. g. AIC, BIC, …) • Computer intensive methods (e. g. MCMC) are more popular. * Free packages

The Doppler detection method

Gregory 2005

P=190 days Gregory 05

P=128 days

P= 376 days

Photometric redshift • Probe strong spectral features (4000 break) • Difference in flux through filters as the galaxy is redshifted. Jan. 6, 2005 Lensing, Dark Matter, and Dark Energy

Bayesian Photo-z likelihood prior Redshift z Benitez 2000 (BPZ)

ANNz - Artificial Neural Network Input: magnitudes Collister & Lahav 2004 http: //www. star. ucl. ac. uk/~lahav/annz. html Output: redshift

Example: SDSS data (ugriz; r < 17. 77) ANNz (5: 10: 1) Collister & Lahav 2004 HYPERZ

Mega. Z-LRG *Training on ~13, 000 2 SLAQ *Generating with ANNz Photo-z for ~1, 000 LR over 5, 000 sq deg z = 0. 046 Collister, Lahav, Blake et al.

Cosmology in 1986 w Galaxy redshift surveys of thousands of galaxies (Cf. A 1, IRAS) w CMB fluctuations not detected yet w Peculiar velocities popular (S 7) w “Standard Cold Dark Matter” m = 1, =0 H 0 = 50 km/sec/Mpc = 1/(19. 6 Gyr)

The Concordance Model * Reality or ‘Epicycles’? * Sub-components? * More components?

Centre Daily Times Sunday 11 June 2006 “Scientists near end in search for Dark Matter substance thought to bond universe”

Just Six numbers? w Baryons b w Matter m w Dark Energy w Hubble parameter H 0 w Amplitude A w Initial shape of perturbations n ¼ 1 Or More?

Variations and extensions… w w w Isocurvature perturbations Non-Gaussian initial conditions Non-power-law initial spectrum Full ionization history Hot DM, Warm DM, … Dark energy Eo. S w(z) Modified Friedmann eq Relativistic MOND Varying ‘constants’ Cosmic Topology …

Probes of Dark Matter and Dark Energy Cosmic Shear Evolution of dark matter perturbations Angular diameter distance Growth rate of structure Baryon Wiggles Standard ruler Angular diameter distance Supernovae Standard candle Luminosity distance Cluster counts Evolution of dark matter perturbations Angular diameter distance Growth rate of structure CMB Snapshot of Universe at ~400, 000 yr Angular diameter distance to z~1000 Growth rate of structure (from ISW)

Sources of uncertainties • Cosmological (parameters and priors) • Astrophysical (e. g. cluster M-T, biasing) • Instrumental (e. g. PSF)

From 2 d. F+CMB (6 parameter fit): m=0. 23 § 0. 02 Cole et al. 2005

The SDSS LRG correlation function Eisenstein et al 2005

WMAP 3 m = 0. 24 +-0. 04 8 = 0. 74 +-0. 06 n = 0. 95 +-0. 02 = 0. 09 +-0. 03

Weak Lensing: Cosmic Shear Background sources Dark matter halos Observer n n n Statistical measure of shear pattern, ~1% distortion Radial distances depend on geometry of Universe Foreground mass distribution depends on growth of structure A. Taylor

Shapelets Decompose a galaxy into a set of shapelets: | aij = < > = a 00 | | > > + a 01 | > +… Refregier 2003 where the basis states are based on orthogonal polynomials (SHO eigenstates). This can generate useful methods for measuring lensing (eg Bernstein & Jarvis 2002, Refregier & Bacon 2003, Goldberg & Bacon 2005) by forming estimators for shear or flexion from aij.

Recent w from the CTIO W=P/ W=-0. 894+0. 156 -0. 208 Einstein told us W = -1 Jarvis & Jain, astro-ph/0502243

Surveys to measure Dark Energy Imaging CFHTLS SUBARU SDSS ATLAS KIDS Spectroscopy 2015 2010 2005 DES LSST VISTA Pan-STARRS JDEM/ SNAP FMOS KAOS SKA SDSS ATLAS Supernovae CSP CFHTLS Clusters AMI DES LSST Pan-STARRS JDEM/ SNAP APEX SPT DES SZA AMIBA ACT CMB WMAP 2/3 WMAP 6 yr Planck 2005 Planck 4 yr 2010 2015

Dark Energy Task Force

Multi-parameter Estimation • Fisher matrix Fisher (1935) Tegmark, Taylor & Heavens(1997) Rocha et al. (2004)

DES Forecasts: Power of Multiple Techniques Assumptions: Clusters: 8=0. 75, zmax=1. 5, WL mass calibration (no clustering) w(z) =w 0+wa(1–a) 68% CL BAO: lmax=300 WL: lmax=1000 (no bispectrum) Statistical+photo-z systematic errors only Spatial curvature, galaxy bias marginalized geometric+ growth Clusters if 8=0. 9 geometric Planck CMB prior Frieman, Ma, Weller, Tang, Huterer, etal P 5 – April 20, 2006

Mock Universes: Models vs. Epoch

Wiener Reconstruction of density and velocity fields Erdogdu, OL, Huchra et al

Gravitational Waves (LIGO, LISA…) LISA

Further input much needed from statistics ● Model selection methodology ● MCMC machinery and extensions ● Detection of non-Gaussianity and shape finders ● Blind de-convolution (eg. PSF) ● Object classification ● Comparing simulations with data ● Visualisation ● VO technology

Globalisation and the New Astronomy w One definition of globalisation: “A decoupling of space and time emphasising that with instantaneous communications, knowledge and culture can be shared around the world simultaneously. ”

Globalisation and the New Astronomy w How is the New Astronomy affected by globalisation? Free information (WWW), big international projects, numerous conferences, telecons… w Recall the Cold War era: Hot Dark Matter/top-down (Russia) vs. Cold Dark Matter/bottom-up (West) w Is the agreement on the `concordance model’ a product of globalisation?

Globalisation and the New Astronomy w Independent communities are beneficial, but eventually they should talk to each other!

Conclusions ● ● ● Fundamental issues in statistics will not go away! Real Data vs. Mock data: the Virtual Observatories Great need for interaction of astronomers with experts in other fields

Thanks! w Co-organisers: Jogesh Babu, Eric Feigelson w SOC: JB, EF, Jim Berger, Kris Gorski, Thomas Laredo, Vicent Martinez, Larry Wasserman, Michael Woodroofe w Grad Students: Hyunsook Lee, Derek Young w Conference Planner: John Farris w Sponsors: SAMSI, NSF, NASA, IMS, PSU