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allow the sky frame to be specified

Colm Talbot requested to merge sampling-frame into master

This MR adds two new related features to the GravitationalWaveTransient class.

These are a reference_frame and a time_reference.

The first specifies how the sky should be parameterised. If left as the default sky, the likelihood expects the RA/dec to be specified as is currently the case. Alternatively, the user can pass a pair of interferometers or a pair of known interferometer names and the sampling is done in parameters zenith and azimuth which zenith and azimuthal angles in a frame where the z-axis is parallel to the line connecting the two detectors.

The other specifies what reference time should be used for the sampler, this can either be geocenter which will keep the previous behaviour of sampling in the time at the geocenter or the name of an interferometer, in which case the time at that interferometer will be measured.

This is a more natural parameterization of the problem, especially when there are only two detectors contributing as kappa is trivially related to the time delay between the two detectors, which is typically a well-measured quantity, leaving just one relatively unconstrained parameter.

I intend to add an example/documentation.

This is the posterior on geocenter time, RA, dec, H1 time, eta, and kappa for GW170823 with the detector frame defined by Hanford and Livingston. The most obvious difference is that the time in Hanford is completely uncorrelated with all of the sky parameters and the shape of the kappa-eta posterior is closer to a bimodal Gaussian than the ra-dec posterior.

image

This is the posterior for the geocenter time, RA, and declination using the current sampling frame ("sky") and the detector-based frame ("H1L1").

image

The prior to use for the new parameters is

azimuth = Uniform(name='azimuth', minimum=0, maximum=2 * np.pi, boundary='periodic', latex_label="\\epsilon")
zenith = Sine(name='zenith', latex_label="$\\kappa$")
Edited by Colm Talbot

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