Hi,
COSMOMC takes theta as a fitting parameter and gives prior for that. I have the following questions:
(1) theta is a complicated function of H_0,omge_b,omega_gamma,omega_lambda, omega_m.. and a_dec (Verde et al. 2003). My question is how to set priors for theta ?
Basically how to relate constraints on theta to that on H_0 or h.
(2) Now for example we have found the best fit value for theta using COSMOMC or some other method, how to get best fit for h from that ?
(3) CAMB does not take theta (it is not there in CAMB's parameter file) so how we create H (h in actual practice) from theta ?
(4) what are the modules/function in cosmomc which do theta <-> h conversion ?
Please help me ..
Prior on theta but constraints on H !
-
jayanti prasad
- Posts: 14
- Joined: October 21 2010
- Affiliation: Inter-University Centre for Astronomy and Astrophysics (IUCAA)
- Contact:
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jayanti prasad
- Posts: 14
- Joined: October 21 2010
- Affiliation: Inter-University Centre for Astronomy and Astrophysics (IUCAA)
- Contact:
Prior on theta but constraints on H !
Finally I have written two programs (basically segments of cosmomc with some changes ) :
1. H02theta:
theta=H02theta(omegab,omegac,omegav,H0)
and
2. theta2H0:
H0=theta2H0(omegab,omegac,omegav,H0,theta)
note that it needs H0 also so I am not sure what H0 I should use.
The reason for this is that theta depends on omegab, omegac etc., and what we have are omegabh2, omegach2 etc., (the fitting parameters).
I have another problem also : for H0 [40,100], I am having theta from [.9,1.1] roughly c., so that is the range I can have. However, in cosmomc default parameter file (as well as Verde's paper (WMAP I) it is [0.5,10], which is too big).
> I also want to know how the range for parameters is set in cosmomc. I have observed that the chains never visit any of the extreme values.
For example :
omegabh2 never goes outside of [.0205,.0245] however, priors on it are [.005, 0.1]
the same is true is for other parameters also.
my question is :
> why the chains never visit any points close to the end points ?
> are not chains suppose to start from any point in the search space ?
It seems chains already know in advance the best fit values so they start walking from points which are very close to the best fit values. I want to know how that is possible.
regards
jayanti
1. H02theta:
theta=H02theta(omegab,omegac,omegav,H0)
and
2. theta2H0:
H0=theta2H0(omegab,omegac,omegav,H0,theta)
note that it needs H0 also so I am not sure what H0 I should use.
The reason for this is that theta depends on omegab, omegac etc., and what we have are omegabh2, omegach2 etc., (the fitting parameters).
I have another problem also : for H0 [40,100], I am having theta from [.9,1.1] roughly c., so that is the range I can have. However, in cosmomc default parameter file (as well as Verde's paper (WMAP I) it is [0.5,10], which is too big).
> I also want to know how the range for parameters is set in cosmomc. I have observed that the chains never visit any of the extreme values.
For example :
omegabh2 never goes outside of [.0205,.0245] however, priors on it are [.005, 0.1]
the same is true is for other parameters also.
my question is :
> why the chains never visit any points close to the end points ?
> are not chains suppose to start from any point in the search space ?
It seems chains already know in advance the best fit values so they start walking from points which are very close to the best fit values. I want to know how that is possible.
regards
jayanti
-
Antony Lewis
- Posts: 1944
- Joined: September 23 2004
- Affiliation: University of Sussex
- Contact:
Re: Prior on theta but constraints on H !
Chain starting point and dispersions are set in the params.ini file. Saves time to start somewhere roughly in the right region.
Output chains (and .margestats etc) include a column with H_0 in, which you can use for CAMB.
The transformation between flat prior on theta and H is indeed not obvious, so mostly people just define it to be flat on theta (flat on H would be almost as abitrary). It makes very little difference except for poorly constrained parameters.
The best-fit is independent of the space on which you put flat priors (it's just hte maximum likelihood). There's no automated way to adjust the posterior means etc between different parameter spaces, though you can use AdjustPriors in GetDist to multiply by the appropriate Jacobian if you can work it out.
Output chains (and .margestats etc) include a column with H_0 in, which you can use for CAMB.
The transformation between flat prior on theta and H is indeed not obvious, so mostly people just define it to be flat on theta (flat on H would be almost as abitrary). It makes very little difference except for poorly constrained parameters.
The best-fit is independent of the space on which you put flat priors (it's just hte maximum likelihood). There's no automated way to adjust the posterior means etc between different parameter spaces, though you can use AdjustPriors in GetDist to multiply by the appropriate Jacobian if you can work it out.
-
jayanti prasad
- Posts: 14
- Joined: October 21 2010
- Affiliation: Inter-University Centre for Astronomy and Astrophysics (IUCAA)
- Contact:
Prior on theta but constraints on H !
Thank you sir ..that was quite useful.
Regards
jayanti
Regards
jayanti