Getdist: values in the .margestats file

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 Joined: September 28 2004
 Affiliation: Max Planck Institute for Extraterrestrial Physics
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Getdist: values in the .margestats file
Hi,
I am using the COSMOMC code to obtain constraints on cosmological parameters and GETDIST to analise the output files. I have been comparing my results with the outputs from other code and the results for simple six parameter models agree quite well in general, but with some subtleties. I have a doubt about what do the values quoted in the .margestats file really mean. I have interpreted those values as the mean value, the standard deviation, and the limits of the allowed regions for the parameters correspondent to the values given by the parameters "contour1" and "contour2" in the distparams.ini file (by default 68% and 95%). Is that correct?
I will also like to know the precise definition of the limits, that is: how are they calculated?
I hope you can help me. Thanks in advance
Ariel Sanchez
I am using the COSMOMC code to obtain constraints on cosmological parameters and GETDIST to analise the output files. I have been comparing my results with the outputs from other code and the results for simple six parameter models agree quite well in general, but with some subtleties. I have a doubt about what do the values quoted in the .margestats file really mean. I have interpreted those values as the mean value, the standard deviation, and the limits of the allowed regions for the parameters correspondent to the values given by the parameters "contour1" and "contour2" in the distparams.ini file (by default 68% and 95%). Is that correct?
I will also like to know the precise definition of the limits, that is: how are they calculated?
I hope you can help me. Thanks in advance
Ariel Sanchez

 Posts: 1636
 Joined: September 23 2004
 Affiliation: University of Sussex
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Re: Getdist: values in the .margestats file
Yes, that is correct.
Unless you have set one of the limitsxxx parameters to impose a prior on one of the parameters (e.g. that [tex]m_\nu > 0[/tex]), the limits are twotail limits. Otherwise they are onetail.
For the 95% limits this means that 2.5% of the samples are larger than the upper limit, 2.5% are lower than the lower limit. For a one tailed test, it would mean 5% of the samples larger than the upper limit.
So the limits are integrated probabilities. In particular, the marginalized probability value at the two limiting points will not in general be the same (unless the posterior is symmetrical). An alternative protocol would be to choose limits so that they have the same marginalized probability, with a given total area outside them (so the integrals at the upper and lower ends would not be the same). GetDist does not to this, largely because it is much harder as it requires an estimate of the marginalized probability density at a point (rather than just counting samples).
Unless you have set one of the limitsxxx parameters to impose a prior on one of the parameters (e.g. that [tex]m_\nu > 0[/tex]), the limits are twotail limits. Otherwise they are onetail.
For the 95% limits this means that 2.5% of the samples are larger than the upper limit, 2.5% are lower than the lower limit. For a one tailed test, it would mean 5% of the samples larger than the upper limit.
So the limits are integrated probabilities. In particular, the marginalized probability value at the two limiting points will not in general be the same (unless the posterior is symmetrical). An alternative protocol would be to choose limits so that they have the same marginalized probability, with a given total area outside them (so the integrals at the upper and lower ends would not be the same). GetDist does not to this, largely because it is much harder as it requires an estimate of the marginalized probability density at a point (rather than just counting samples).

 Posts: 4
 Joined: June 17 2015
 Affiliation: Federal University of Bahia / Imperial College London
Getdist: values in the .margestats file
Dear Antony,
One question about this topic: if I have a parameter with a limit and which PDF doesn't peak at that limit (and isn't a tail in fact), how would be the best way to proceed? Both one or two tails procedures you described don't seem to fit well to this case. Wouldn't it be possible to evaluate the cumulative probability density from the peak?
Thank you.
Cassio
One question about this topic: if I have a parameter with a limit and which PDF doesn't peak at that limit (and isn't a tail in fact), how would be the best way to proceed? Both one or two tails procedures you described don't seem to fit well to this case. Wouldn't it be possible to evaluate the cumulative probability density from the peak?
Thank you.
Cassio

 Posts: 1636
 Joined: September 23 2004
 Affiliation: University of Sussex
 Contact:
Re: Getdist: values in the .margestats file
The latest GetDist follows the recipe outlined in the Planck 2013 parameter paper for whether to quote 1, 2 or notail limits for bounded parameters, depending on the marginalized density at the boundary.