Download Astronomy perspective

Astronomy Perspective
Ofer Lahav
University College London
SCMA IV
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Cosmology (I, II)
Small-N problems (incl. HEP)
Astronomical surveys
Planetary systems
Periodic variability
Developments in statistics
Cross-disciplinary perspectives
Astro-Statistics
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Data Compression
Classification
Reconstruction
Feature extraction
Parameter estimation
Model selection
Astro-Statistics Books
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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
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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
Input:
magnitudes
Collister & Lahav 2004
http://www.star.ucl.ac.uk/~lahav/annz.html
Output:
redshift
Example: SDSS data (ugriz;
r < 17.77)
ANNz (5:10:10:1)
Collister & Lahav 2004
HYPERZ
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…
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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)
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
Background sources
Dark matter halos
Observer
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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 =
<
= a00
|
|
>
>
+ a01
|
>
+…
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
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 4yr
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) =w0+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
P5 – 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
LISA
Further input much needed from statistics
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Model selection methodology
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MCMC machinery and extensions
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Detection of non-Gaussianity and shape finders
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Blind de-convolution (eg. PSF)
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Object classification
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Comparing simulations with data
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Visualisation
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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
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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