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

[Minh Nguyen]

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.

[Antony Lewis]

I fixed the missing return in Prob() on latest getdist master:
https://github.com/cmbant/getdist/commit/d2dbc9797e4f90ab3605696a831a6856a5f19d54

[Minh Nguyen]

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