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CosmoCoffee
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CosmoMC: test run with no data input
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Xin Wang
Joined: 11 Jan 2012
Posts: 29
Affiliation: NAOC/NJU
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 Posted: May 17 2012 |
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Hi, Antony,
Out of curiosity, I run cosmomc with no datasets specified, i.e.
| Code: |
use_CMB = F
use_HST = F
use_mpk = F
use_BAO = F
use_clusters = F
use_BBN = F
use_Age_Tophat_Prior = F
use_SN = F
use_lya = F
use_min_zre = 0
use_OHD = F
bbn_consistency= F
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A reasonable expectation would be that the output likelihood is entirely flat, since no observational evidences are supplied. And the marginalized posterior probability for each parameter may be screwed from being totally even, due to the biased prior information involved in this marginalization.
Later on, the program leaves me with below results, which worry me a little.
emptyrun.ps
emptyrun_2D.ps
The likelihood curves (dotted) are all flat as expected. However the marg curves are all totally non-trivial, which means that either the results given by cosmomc (even with obs data) are strongly biased by the parameters' prior information, or an additional prior information (which is very similar to the results from CMB; see the solid contour between Ωm and ΩΛ) is already coded in cosmomc by design.
I sincerely hope it's not the former case. But for the latter case, due to the fact that this additional prior resemble the parameter degeneracy given by CMB, it will give incorrect results when we run cosmomc without CMB data. If we use SNe (or BAO) as the only input dataset, which according to the frequentist results shows nearly perpendicular degeneracy direction with CMB's in the Ωm vs. ΩΛ plot, this additional prior information should be commented out. Could you tell me where this additional prior is and is it safe and sound to do that?
I would very much appreciate any explanation and further discussion on this issue. Please correct any misunderstandings here.
Thanks! |
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Antony Lewis
Joined: 23 Sep 2004
Posts: 673
Affiliation: University of Sussex
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Xin Wang
Joined: 11 Jan 2012
Posts: 29
Affiliation: NAOC/NJU
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| Posted: May 17 2012 |
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Thanks, Antony. And I'm sorry I didn't notice that piece of topic before.
That's a vivid illustration and I've got a hint of that it's the "Disallowed" region in your plots that gives marg curves non-trivial results. Then I still want to know how do you obtain this "Disallowed" region, in other words, the additional prior information, in the first place?
Please compare the plot of Ωm vs ΩΛ in the following two figures, one from Amanullah et al. 2010 using frequentist method, and the other calculated by myself using only SNe data and cosmomc.
colorOm-Ol_BAO_CMB_sysinterp.epsi
w1_tau0_SN21_2D.ps
From the cosmomc plot, we see the color contour (likelihood) resembles what we obtain from the frequentist method, whereas the solid line contour (marg. PDF for Ωm and ΩΛ) is somehow screwed. I believe the aforementioned additional prior information (or in your words, "Disallowed" region) has something to do with this result, doesn't it?
Thanks! |
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Antony Lewis
Joined: 23 Sep 2004
Posts: 673
Affiliation: University of Sussex
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| Posted: May 18 2012 |
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| There's a constaint on H0 in the code that you'd have to change. But anyway you wouldn't expect it to be flat, since CosmoMC uses theta and physical densities as the main parameters with the flat prior; other parameters are derived and will not have flat priors. It doesn't make any difference when you do constraints with good data (posterior much smaller than prior). |
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