CosmoMC: A_s pivot point

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Antony Lewis
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Joined: September 23 2004
Affiliation: University of Sussex
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CosmoMC: A_s pivot point

Post by Antony Lewis » March 11 2008

Just a note about changing the pivot point for the primoridal power spectrum. WMAP5 use k0=0.002/Mpc whereas CosmoMC's default is 0.05. The correlation between n_s and A_s is quite different in the former case, so if you change the pivot point the supplied proposal covariance matrix won't work very well.

When changing the pivot point but using an old covariance matrix it's a good idea to increase MPI_Max_R_ProposeUpdate, e.g. to 50. Or, even better, post-process your original chain to the new pivot point, calculate a covariance matrix from that, and use that for the new proposal.

In case of use here is a k=0.002 .covmat for a basic 7-parameter model (normal+A_{SZ})

Code: Select all

    0.37746E-06    0.47512E-06    0.12444E-05    0.26567E-05    0.00000E+00    0.00000E+00    0.00000E+00    0.70331E-05    0.00000E+00    0.00000E+00   -0.11470E-04    0.00000E+00    0.32868E-04
    0.47512E-06    0.38350E-04    0.48219E-05   -0.21296E-04    0.00000E+00    0.00000E+00    0.00000E+00   -0.83625E-05    0.00000E+00    0.00000E+00    0.14088E-03    0.00000E+00   -0.22025E-03
    0.12444E-05    0.48219E-05    0.95613E-05    0.67625E-05    0.00000E+00    0.00000E+00    0.00000E+00    0.26676E-04    0.00000E+00    0.00000E+00   -0.33425E-04    0.00000E+00   -0.49732E-05
    0.26567E-05   -0.21296E-04    0.67625E-05    0.29354E-03    0.00000E+00    0.00000E+00    0.00000E+00    0.91830E-04    0.00000E+00    0.00000E+00    0.24973E-03    0.00000E+00   -0.23492E-03
    0.00000E+00    0.00000E+00    0.00000E+00    0.00000E+00    0.00000E+00    0.00000E+00    0.00000E+00    0.00000E+00    0.00000E+00    0.00000E+00    0.00000E+00    0.00000E+00    0.00000E+00
    0.00000E+00    0.00000E+00    0.00000E+00    0.00000E+00    0.00000E+00    0.00000E+00    0.00000E+00    0.00000E+00    0.00000E+00    0.00000E+00    0.00000E+00    0.00000E+00    0.00000E+00
    0.00000E+00    0.00000E+00    0.00000E+00    0.00000E+00    0.00000E+00    0.00000E+00    0.00000E+00    0.00000E+00    0.00000E+00    0.00000E+00    0.00000E+00    0.00000E+00    0.00000E+00
    0.70331E-05   -0.83625E-05    0.26676E-04    0.91830E-04    0.00000E+00    0.00000E+00    0.00000E+00    0.20327E-03    0.00000E+00    0.00000E+00   -0.38090E-03    0.00000E+00   -0.83922E-03
    0.00000E+00    0.00000E+00    0.00000E+00    0.00000E+00    0.00000E+00    0.00000E+00    0.00000E+00    0.00000E+00    0.00000E+00    0.00000E+00    0.00000E+00    0.00000E+00    0.00000E+00
    0.00000E+00    0.00000E+00    0.00000E+00    0.00000E+00    0.00000E+00    0.00000E+00    0.00000E+00    0.00000E+00    0.00000E+00    0.00000E+00    0.00000E+00    0.00000E+00    0.00000E+00
   -0.11470E-04    0.14088E-03   -0.33425E-04    0.24973E-03    0.00000E+00    0.00000E+00    0.00000E+00   -0.38090E-03    0.00000E+00    0.00000E+00    0.21115E-02    0.00000E+00   -0.61157E-03
    0.00000E+00    0.00000E+00    0.00000E+00    0.00000E+00    0.00000E+00    0.00000E+00    0.00000E+00    0.00000E+00    0.00000E+00    0.00000E+00    0.00000E+00    0.00000E+00    0.00000E+00
    0.32868E-04   -0.22025E-03   -0.49732E-05   -0.23492E-03    0.00000E+00    0.00000E+00    0.00000E+00   -0.83922E-03    0.00000E+00    0.00000E+00   -0.61157E-03    0.00000E+00    0.32622E+00

Ana Vasile
Posts: 25
Joined: March 26 2006
Affiliation: Institute for Space Sciences
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CosmoMC: A_s pivot point

Post by Ana Vasile » April 02 2008

Anthony,

I'm not sure I understood correctly: if I have some chains at some pivot post-processing them at another pivot would be the equivalent to creating new chains with the new pivot? (in other words: is post-processing enough to get results with new pivot?)

Antony Lewis
Posts: 1503
Joined: September 23 2004
Affiliation: University of Sussex
Contact:

Re: CosmoMC: A_s pivot point

Post by Antony Lewis » April 02 2008

Yes (given flat priors in the original parameters; if you want flat priors on the new parameters you might need to put in a Jacobian weighting too - but the effect is usually small). See e.g. appendix of astro-ph/0205436.

Ana Vasile
Posts: 25
Joined: March 26 2006
Affiliation: Institute for Space Sciences
Contact:

CosmoMC: A_s pivot point

Post by Ana Vasile » April 02 2008

OK, now It's clear for me, thank you Antony.

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