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 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.

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

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

Example: SDSS data (ugriz; r < 17.77) ANNz (5:10:10:1) HYPERZ Collister & Lahav 2004

MegaZ-LRG. Training on ~13,000 2SLAQ MegaZ-LRG *Training on ~13,000 2SLAQ *Generating with ANNz Photo-z for ~1,000,000 LR over 5,000 sq deg z = 0.046 Collister, Lahav, Blake et al.

Photo-z for SDSS: comparison

Cosmology in 1986 Galaxy redshift surveys of thousands of galaxies (CfA1, IRAS) CMB fluctuations not detected yet Peculiar velocities popular (S7) “Standard Cold Dark Matter” m = 1, =0 H0 = 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? Baryons b Matter m Dark Energy  Hubble parameter H0 Amplitude A Initial shape of perturbations n ¼ 1 Or More?

Variations and extensions… Isocurvature perturbations Non-Gaussian initial conditions Non-power-law initial spectrum Full ionization history Hot DM, Warm DM, … Dark energy EoS 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)

Cosmic Probes CMB Galaxy clustering Cluster abundance Cluster baryon fraction Cepheids SN Ia IGM Lyman- Gravitational lensing Peculiar velocities ISW 21cm …

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

From 2dF+CMB (6 parameter fit): m=0.23 §0.02 Cole et al. 2005

The SDSS LRG correlation function Eisenstein et al 2005

WMAP3 m = 0.24 +-0.04 8 = 0.74 +-0.06 n = 0.95 +-0.02  = 0.09 +-0.03

Statistical measure of shear pattern, ~1% distortion Background sources Dark matter halos Observer Cosmic Web – bottom up scenario – clusters then filaments then walls (membranes). Note that filaments not well traced by galaxies & too ephemeral to emit x-rays, so lensing only way to detect. 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: > > | | > | = a00 + a01 +… < > | aij = 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 Jarvis & Jain, astro-ph/0502243

Surveys to measure Dark Energy 2010 2015 2005 Imaging CFHTLS SUBARU DES LSST SKA SDSS ATLAS KIDS VISTA JDEM/ SNAP Pan-STARRS Spectroscopy ATLAS SKA FMOS KAOS SDSS Supernovae Pan-STARRS DES LSST JDEM/ SNAP CFHTLS CSP Clusters AMI SZA APEX AMIBA SPT ACT DES CMB WMAP 2/3 WMAP 6 yr Planck Planck 4yr 2005 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) BAO: lmax=300 WL: lmax=1000 (no bispectrum) Statistical+photo-z systematic errors only Spatial curvature, galaxy bias marginalized Planck CMB prior w(z) =w0+wa(1–a) 68% CL geometric+ growth Clusters if 8=0.9 geometric Frieman, Ma, Weller, Tang, Huterer, etal

Mock Universes: Models vs. Epoch

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

Wiener reconstruction- Big Supercluster Erdogdu, OL, Zroubi et al. 2004

PCA for data compression (by a factor ~1000) h = 0.5 pc1 – pc2 Madgwick, OL et al.

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

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