[astro-ph/0409569] Polarization Observations with the Cosmic Background Imager

Authors:  A. C. S. Readhead, S. T. Myers, T. J. Pearson, J. L. Sievers, B. S. Mason, C. R. Contaldi, J. R. Bond, R. Bustos, P. Altamirano, C. Achermann, L. Bronfman, J. E. Carlstrom, J. K. Cartwright, S. Casassus, C. Dickinson, W. L. Holzapfel, J. M
Abstract:  Polarization observations of the cosmic microwave background with the Cosmic Background Imager over the period September 2002 - May 2004 provide a highly significant detection of the E-mode polarization and reveal an angular power spectrum of polarized emission showing peaks and valleys that are shifted in phase by half a cycle relative to those of the total intensity spectrum, as predicted by theory. This key agreement between the phase of the observed polarization spectrum and that predicted based on the total intensity spectrum provides new support for the standard model of cosmology, in which dark matter and dark energy are the dominant constituents, the geometry is close to flat, and primordial density fluctuations are predominantly adiabatic with a matter power spectrum commensurate with inflationary cosmological models.
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Anze Slosar
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[astro-ph/0409569] Polarization Observations with the Cosmic

Post by Anze Slosar » September 24 2004

A few observations:

a) Physical prior that power is always >0 is not used. Contaldi prefers not to use it, alhotugh it would improve error-bars to some extend. Any opinions on induced bias? (i don't think there is)

b) I like the EE mode phase fitting... Any ideas on how this could be incorporated usefully into model constraints? Can you invent a model that shifts only EE PS? (and thus constrain it?)

Antony Lewis
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Re: astro-ph/0409569 Polarization Observations with the Cosm

Post by Antony Lewis » September 24 2004

I think it's very hard to change only the EE power spectrum, though it's certainly possible that the pol will constrain some isocurvature models better now. Nothing like the significance with which they measure the free shift though which is a totally physics-free parameterization.

I guess they don't use a EE>0 prior so that people don't think they have a spurious detection (ie. assumed the result before adding any data).

Anze Slosar
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Re: astro-ph/0409569 Polarization Observations with the Cosm

Post by Anze Slosar » September 24 2004

Antony Lewis wrote: I guess they don't use a EE>0 prior so that people don't think they have a spurious detection (ie. assumed the result before adding any data).
Well, that is not true, if your full likelihood maximises below zero, you can still say you constrain it to be below <x uk, which is fair enough... Or if it peaks below 1 sigma you say can say it's x-x+y uk.... So even if you put a prior on positivity of power you can have a non-detection (e.g. last by one bin in VSA 2002 data)

Benjamin Wandelt
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Re: astro-ph/0409569 Polarization Observations with the Cosm

Post by Benjamin Wandelt » September 24 2004

Anze Slosar wrote:
Antony Lewis wrote: I guess they don't use a EE>0 prior so that people don't think they have a spurious detection (ie. assumed the result before adding any data).
Well, that is not true, if your full likelihood maximises below zero, you can still say you constrain it to be below <x uk, which is fair enough... Or if it peaks below 1 sigma you say can say it's x-x+y uk.... So even if you put a prior on positivity of power you can have a non-detection (e.g. last by one bin in VSA 2002 data)
Since the EE Cl is positive definite by definition, the maximum likelihood estimator cannot be negative. So I am non-plussed, since the paper does claim that a maximum likelihood estimator was computed.

For a non-detection of power the maximum likelihood is driven to zero and the likelihood decays to high Cl.

Cheers,

Ben

Antony Lewis
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Re: astro-ph/0409569 Polarization Observations with CBI

Post by Antony Lewis » September 25 2004

Benjamin Wandelt wrote: Since the EE Cl is positive definite by definition, the maximum likelihood estimator cannot be negative. So I am non-plussed, since the paper does claim that a maximum likelihood estimator was computed.
With noise I think the maximum likelihood can be negative (on fully isotropic sky goes singular at [tex]C_l=-N_l[/tex] not at [tex]C_l=0[/tex]), though certainly the maximum posterior shouldn't be negative for a sensible prior. Is this all the debate is about, or this there something else?
Last edited by Antony Lewis on September 27 2004, edited 1 time in total.

dick bond
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to be positive or not to be that is the question

Post by dick bond » September 25 2004

could not resist joining the forum at its inauguration. so greetings all.

we have thought long about this issue, maybe even hard: should one enforce positivity of bandpowers. in various treatments we have enforced it and not. indeed in some of the codes it is a switch - to be + or not to be.

it is of course possible that noise may be misdiagnosed and negative bandpowers appear. it is also possible to get it by statistical fluctuation. spirit of linear multipliers times the bandpower templates. nothing wrong with it except that it cannot be. (simplest way to think about this, as usual, is signal-to-noise eigenmodes and how the power is estimated for them in the low signal limit, especially if there were only a few modes that were being used in the band.)

when positivity constraints are applied, it does no distortion at all that we have noticed to positively (but fisher-connected) values. still it is an issue and if we have a big negative crash rest assured we do investigate it.



without modification of the iterative proc

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