## [GetDist] Probability densities and confidence limits in cases with hard parameters boundaries from priors

Use of Cobaya. camb, CLASS, cosmomc, compilers, etc.
Minh Nguyen
Posts: 15
Joined: March 21 2016
Affiliation: Leinweber Center for Theoretical Physics, University of Michigan
Contact:

### [GetDist] Probability densities and confidence limits in cases with hard parameters boundaries from priors

The attachment no_boundary_case.png is no longer available
Hi,

I know that getdist corrects for the bias introduced by smoothing over parameter hard boundaries. But I'm still failing to see how this significantly changes the answer I am getting in the scenario below.

Given a

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getdist.mcsamples.MCSamples
, suppose I want to compute how much of the posterior mass is there where P(theta|data) > P(theta0|data), where theta0 is the fiducial point in parameter space. I can get P(theta0|data) by interpolating the

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getdist.densities.Density2D
*.

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getdist_Density2D=getdist_samples.get2DDensity(pars[0],pars[1],normalized=False)
interpolator = RectBivariateSpline(getdist_Density2D.x, getdist_Density2D.y, getdist_Density2D.P)
Ptheta0 = interpolator.ev(fiducial_point[0], fiducial_point[1])
Once I have P(theta0|data), I can compute a bunch of contour levels, calling

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getdist.densities.Density2D. getContourLevels()
, and (adaptively) search for the contour levels with P(theta|data) ~ P(theta0|data) till reaching a convergence target.
For visual inspection, I can plot the found CL and it should be very close to the fiducial point, looking like the attached no_boundary_case.png, for example.

However, this procedure would fail when parameters have hard boundaries imposed by their priors, e.g. [w0,wa]. The situation then looks like the with_boundary_case.png attached.

FWIW, here is the jupyter notebook:
https://github.com/MinhMPA/getdist/blob/master/getdist_analysis_pipelines_and_tutorials/compute_significance_from_chains.ipynb
with the full routine. The result in the notebook corresponds to the case without boundaries.

*I know that getdist.densities.Density2D is supposed to support this procedure directly through the method Prob() but it never works for me in 2D as it returns None always.

Any insight would be greatly appreciated.
Attachments
Case with hard boundaries
with_boundary_case.png (41.15 KiB) Viewed 1362 times
Case without boundary
no_boundary_case.png (83.92 KiB) Viewed 1363 times
Antony Lewis
Posts: 1973
Joined: September 23 2004
Affiliation: University of Sussex
Contact:

### Re: [GetDist] Probability densities and confidence limits in cases with hard parameters boundaries from priors

I fixed the missing return in Prob() on latest getdist master:
https://github.com/cmbant/getdist/commit/d2dbc9797e4f90ab3605696a831a6856a5f19d54
Minh Nguyen
Posts: 15
Joined: March 21 2016
Affiliation: Leinweber Center for Theoretical Physics, University of Michigan
Contact:

### Re: [GetDist] Probability densities and confidence limits in cases with hard parameters boundaries from priors

Thank you very much, Antony! Now that the interpolation step is handled internally by getdist, I'm getting consistent results.