adjusting priors with getdist

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Petruta Stefanescu
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Joined: July 02 2008
Affiliation: Institute for Space Science
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adjusting priors with getdist

Post by Petruta Stefanescu » July 24 2008

Dear all,

I am trying to use the adjust priors option of Getdist to add constraints from a new dataset to the cosmological parameters distributions obtained only for WMAP-5. Following the example of the corresponding routine in Getdist, I calculated the chi^2 for the new dataset for the corresponding combinations of the cosmological parameters from .txt files.

In order to calculate the likelihoods for WMAP-5 + the new dataset I have to modify the first two columns of the .txt files.

My questions is how is the right way to do that? It seems to be logical to add to the column 2 the entire chi^2/2, but if I multiply the first column by exp(-chi^2/2) the weights are too small. Should I use the chi^2 reduced by the number of independent data points or/and a kind of offset for the first column?

Thanks,

Petruta.

Antony Lewis
Posts: 1501
Joined: September 23 2004
Affiliation: University of Sussex
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Re: adjusting priors with getdist

Post by Antony Lewis » July 24 2008

If you are using cosmomc to post-process there is an input option redo_likeoffset to re-scale the log likelihood.

In GetDist you can add any constant you like to the log likelihood. But if the scatter of weights is too large that's telling you that you need to run new chains (importance sampling only works well if the new distribution is subset and similar).

Petruta Stefanescu
Posts: 3
Joined: July 02 2008
Affiliation: Institute for Space Science
Contact:

adjusting priors with getdist

Post by Petruta Stefanescu » July 24 2008

Dear Antony,

Thanks for your prompt reply!

Please, could you tell me if I have understood right? Is the outlier
fraction given by getdist a measure of the scatter of weights so that if
it is not too large I can use the distributions obtained by
running getdist on the original chains with the adjust priors option?

From running getdist without and with the adjust prior I have obtained:

case 1) without adjust priors

Number of chains used = 8
var(mean)/mean(var), 1/2 chains, worst e-value: R-1 = 0.0182
RL: Thin for Markov: 45
RL: Thin for indep samples: 89
RL: Estimated burn in steps: 480 (137 rows)
mean input multiplicity = 3.502123
using 41914 rows, processing 13 parameters
Approx indep samples: 1649
...

case 2) with adjust priors - using the entire chi^2

Adjusting priors
outlier fraction 2.3858376E-05
Number of chains used = 8
var(mean)/mean(var), 1/2 chains, worst e-value: R-1 = 0.0290
Prior removed 17313 models
mean input multiplicity = 7.1085290E-11
using 24601 rows, processing 13 parameters
effective number of samples (assuming indep): 499
...

case 3) with adjust priors - using the chi^2 divided by the number
of indep. data points

Adjusting priors
Number of chains used = 8
var(mean)/mean(var), 1/2 chains, worst e-value: R-1 = 0.0093
mean input multiplicity = 0.8225374
using 41914 rows, processing 13 parameters
effective number of samples (assuming indep): 2053
...

My question is: may be one of the cases 2) and 3) OK from this point of
view or the solution is to use cosmomc to post-process the chains or to
make new chains using both the datasets?

Thanks,

Petruta.

Antony Lewis
Posts: 1501
Joined: September 23 2004
Affiliation: University of Sussex
Contact:

Re: adjusting priors with getdist

Post by Antony Lewis » July 24 2008

chi^2 is log likelihood, so you should only add or subtract a constant, not multiply or divide.

The outlier fraction just gives some idea of large variations. It's usually obvious from looking at the plots whether importance sampling is working well or not.

Petruta Stefanescu
Posts: 3
Joined: July 02 2008
Affiliation: Institute for Space Science
Contact:

adjusting priors with getdist

Post by Petruta Stefanescu » July 24 2008

Thank you very much!

Petruta.

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