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

Benitez 2000 (BPZ)Redshift z

likelihood

prior

ANNz - Artificial Neural Network

Output:redshift

Input:magnitudes

Collister & Lahav 2004http://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*Generating with ANNz Photo-z for ~1,000,000 LR over 5,000 sq deg

z = 0.046

Collister, Lahav, Blake et al.

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 …

CMB

Cluster counts

Supernovae

Baryon Wiggles

Cosmic Shear

Probes of Dark Matter and Dark Energy

Angular diameter distanceGrowth rate of structure

Evolution of dark matter perturbations

Standard rulerAngular diameter distance

Standard candleLuminosity distance

Evolution of dark matter perturbationsAngular diameter distanceGrowth rate of structure

Snapshot of Universe at ~400,000 yrAngular diameter distance to z~1000Growth rate of structure (from ISW)

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 al2005

WMAP3

m = 0.24 +-0.04 8 = 0.74 +-0.06 n = 0.95 +-0.02 = 0.09 +-0.03

Observer

Dark matter halos

Background sources

Statistical measure of shear pattern, ~1% distortion Radial distances depend on geometry of Universe Foreground mass distribution depends on growth of structure

Weak Lensing: Cosmic Shear

A. Taylor

Shapelets

= a00 + a01 +…

aij = <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.

Refregier 2003|| > | >

Decompose a galaxy into a set of shapelets:

| >>

Recent w from the CTIO

Jarvis & Jain, astro-ph/0502243

W=-0.894+0.156 -0.208W=P/

Einstein told usW = -1

2015

CMB WMAP 2/3 WMAP 6 yr

Planck Planck 4yr

Clusters AMI

SZA

APEX

AMIBA

SPT

ACT

DES

Supernovae

Pan-STARRS

DES LSST

JDEM/SNAP

CFHTLS

CSP

Spectroscopy

ATLAS

SKAFMOS KAOS

SDSS

Imaging CFHTLS

ATLAS KIDS

DES

VISTA JDEM/SNAP

LSST SKA

Pan-STARRSSDSS

SUBARU

Surveys to measure Dark Energy

2005

20152005 2010

2010

Dark EnergyDark EnergyTask ForceTask Force

Dark EnergyDark EnergyTask ForceTask Force

Multi-parameter Estimation

• Fisher matrix

Rocha et al. (2004)Fisher (1935) Tegmark, Taylor & Heavens(1997)

P5 – April 20, 2006

DES Forecasts: Power of Multiple Techniques

Frieman, Ma, Weller, Tang, Huterer, etal

Assumptions:Clusters: 8=0.75, zmax=1.5,WL mass calibration(no clustering)

BAO: lmax=300WL: lmax=1000(no bispectrum)

Statistical+photo-z systematic errors only

Spatial curvature, galaxy biasmarginalized

Planck CMB prior

w(z) =w0+wa(1–a) 68% CL

geometric

geometric+growth

Clustersif 8=0.9

Mock Universes:Models vs. Epoch

Wiener Reconstruction of density and velocity fields

Erdogdu, OL, Huchra et al

Gravitational Waves (LIGO, LISA…)

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

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