Problem: H0 marginalization in the supernovae_Union2.f90

 Posts: 3
 Joined: October 19 2015
 Affiliation: Beijing Normal University
Problem: H0 marginalization in the supernovae_Union2.f90
Dear Prof. Antony Lewis,
I have some questions about the H0 marginalization in the supernovae_Union2.f90.
In the old version of cosmomc, such as the Oct. 2012, the chisq = ATBT**2/sn_sumninv. This form is what we usually used formula: chi^2 = AB^2/C, where the distance moduli mu=5 log10(dL) is independent of the nuisance parameter H0. However, in the latest version, the chisq = dot_product(diffs,matmul(this%sn_ninv,diffs)). I don't konw whether the formula: diffs=5 log10(dL)+25 is independent of H0. I don't know how to deal with it.
(1 ) diffs = 5 log10(dL) %independent of H0
chisq = dot_product(diffs,matmul(this%sn_ninv,diffs))
(2) diffs = 5 log10(dL) + \mu0 (H0) %depend on H0
chisq = dot_product(diffs,matmul(this%sn_ninv,diffs))
(3) diffs = 5 log10(dL) %independent of H0
AT = dot_product(diffs,matmul(sn_ninv,diffs))
BT = SUM(matmul(sn_ninv,diffs))
chisq = ATBT**2/sn_sumninv
I want to know which is right for the above three formula when we use the Union2.1 data.
Thanks very much for your help.
Best wishes,
mingjian
I have some questions about the H0 marginalization in the supernovae_Union2.f90.
In the old version of cosmomc, such as the Oct. 2012, the chisq = ATBT**2/sn_sumninv. This form is what we usually used formula: chi^2 = AB^2/C, where the distance moduli mu=5 log10(dL) is independent of the nuisance parameter H0. However, in the latest version, the chisq = dot_product(diffs,matmul(this%sn_ninv,diffs)). I don't konw whether the formula: diffs=5 log10(dL)+25 is independent of H0. I don't know how to deal with it.
(1 ) diffs = 5 log10(dL) %independent of H0
chisq = dot_product(diffs,matmul(this%sn_ninv,diffs))
(2) diffs = 5 log10(dL) + \mu0 (H0) %depend on H0
chisq = dot_product(diffs,matmul(this%sn_ninv,diffs))
(3) diffs = 5 log10(dL) %independent of H0
AT = dot_product(diffs,matmul(sn_ninv,diffs))
BT = SUM(matmul(sn_ninv,diffs))
chisq = ATBT**2/sn_sumninv
I want to know which is right for the above three formula when we use the Union2.1 data.
Thanks very much for your help.
Best wishes,
mingjian

 Posts: 1636
 Joined: September 23 2004
 Affiliation: University of Sussex
 Contact:
Re: Problem: H0 marginalization in the supernovae_Union2.f90
This may be a question for Nao Suzuki who I think wrote this module.

 Posts: 70
 Joined: April 05 2005
 Affiliation: UAM/IFT
 Contact:
Problem: H0 marginalization in the supernovae_Union2.f90
Hi,
Check Appendix C in http://arxiv.org/abs/1004.1711, where they derive a new inverse covariance matrix that contains the corrections due to the marginalization/minimization. This new inverse covariance matrix is the one given in the CosmoMC module.
I remember checking this some time ago (95% sure!).
Cheers,
Savvas
Check Appendix C in http://arxiv.org/abs/1004.1711, where they derive a new inverse covariance matrix that contains the corrections due to the marginalization/minimization. This new inverse covariance matrix is the one given in the CosmoMC module.
I remember checking this some time ago (95% sure!).
Cheers,
Savvas

 Posts: 3
 Joined: October 19 2015
 Affiliation: Beijing Normal University
Re: Problem: H0 marginalization in the supernovae_Union2.f90
Dear Nesseris,Savvas Nesseris wrote:Hi,
Check Appendix C in http://arxiv.org/abs/1004.1711, where they derive a new inverse covariance matrix that contains the corrections due to the marginalization/minimization. This new inverse covariance matrix is the one given in the CosmoMC module.
I remember checking this some time ago (95% sure!).
Cheers,
Savvas
Thanks very much for your help. Your advice is very useful for me. I will check it.