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