## Problem: H0 marginalization in the supernovae_Union2.f90

Use of Healpix, camb, CLASS, cosmomc, compilers, etc.
MingJian Zhang
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 = AT-BT**2/sn_sumninv. This form is what we usually used formula: chi^2 = A-B^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 = AT-BT**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

Antony Lewis
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.

Savvas Nesseris
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

MingJian Zhang
Posts: 3
Joined: October 19 2015
Affiliation: Beijing Normal University

### Re: Problem: H0 marginalization in the supernovae_Union2.f90

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
Dear Nesseris,
Thanks very much for your help. Your advice is very useful for me. I will check it.