Interpretation of the WMAP data

Christopher Gordon
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Affiliation: University of Canterbury
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Re: Interpretation of the WMAP data

Post by Christopher Gordon » July 27 2005

Anze Slosar wrote:
Christopher Gordon wrote: Slosar and Seljak find the probability of the data, given the Lambda CDM prediction, to be lower than observed to be between 3 and 4%, see table 2. They find the probability of the true value being higher than the Lambda CDM prediction given the data to be between 5 and 10%. But, this second measure is very sensitive to the prior chosen for the data.
Well, there is no such thing as priorless claim... And the frequentist approach does seem to change data while fixing the , which definitelly sounds much more wrong than fixing the data and changing the ..., but I do not want to start yet another pointless freq/bayes war... My personal perference is the 5-10% from Bayesian approach... Anyway, this is discussed very nicely in [astro-ph/0306431]
In working out the Bayesian P(theory|data) \propto P(data|theory) P(theory)
you need to specify a distribution for P(theory). I don’t think there is any good way of doing this. For example if you take a uniform distribution, your probability is inversely proportional to the upper limit of the distribution. So you can make P(theory|data) as small as you like by making the upper limit of P(theory) large.

In my opinion, asking the question: "How improbable is the observed data if I assume the theory to be true?" makes just as much sense as asking: "Giving this data, how probable is the theory to be true?", but requires less arbitrary assumptions.

Garth Antony Barber
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Interpretation of the WMAP data

Post by Garth Antony Barber » July 27 2005

In my opinion, asking the question: "How improbable is the observed data if I assume the theory to be true?" makes just as much sense as asking: "Giving this data, how probable is the theory to be true?", but requires less arbitrary assumptions.
My other question was:
If the low mode morphology is aligned to Magueijo's 'axis of evil', might the CMB power spectrum be contaminated with a local signal?
in which case the question would be: "How improbable is the observed data set, cleansed from local contamination, if I assume the (standard) theory to be true?"
It seems to me that before any assessment is given as to whether the data is consistent with the standard model the question of the remaining peculiar low mode alignments has to be resolved.

Christopher Gordon
Posts: 14
Joined: September 27 2004
Affiliation: University of Canterbury
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Re: Interpretation of the WMAP data

Post by Christopher Gordon » July 27 2005

Christopher Gordon wrote: In working out the Bayesian P(theory|data) \propto P(data|theory) P(theory)
you need to specify a distribution for P(theory). I don’t think there is any good way of doing this. For example if you take a uniform distribution, your probability is inversely proportional to the upper limit of the distribution. So you can make P(theory|data) as small as you like by making the upper limit of P(theory) large.
I wrote my last post a bit quickly. Of course P(theory|data) becomes arbitrary large as one makes the limits of the prior smaller, as \int P(theory|data)= 1. But my main point was that judging whether the quadrupole is a problem or not by looking at P(C_2^{theory}|C_2^{data}) is problematical because the answer is so sensitive to the prior. For example Seljak and Slosar would get a probability of 5% rather than 9%, for the ILC map, if they took the uniform prior upper limit of P(C_2^{theory}) to be about 1500 rather than 2000.

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