GRF Shear prior

[b-remy]

This issue is to track the development of a varying shear model.

In this model, instead of sampling shear values, we sample convergence map from a Gaussian Random Field.

Assuming a cosmology and a redshift distribution, we create a GRF prior for the E-mode of the convergence (and assume the B-mode is zero). Shear maps are then computed using KS transformation, and shear is measured on galaxy position by interpolation. Here is the related code (forward model, sampling shear maps).

As a first try, I simulated observations by sampling:

• a 16x16 convergence map of resultion 5 arcmin/pixel
• 3600 Gaussian galaxies on a regular grid (params: hlr and ellipticities) which is equivalent of 14 galaxies per pixel.

MAP

Initialization was done sampling from the prior distribution.

As decribed in #issue-vi, optimization is in two steps:

1. Adam(lr=1e-1) for 100 iterations:

2. Adam(lr=1e-2) for 100 iterations:

Here as well, the hlr parameter is well fitted, but galaxy ellipticities and shear field are a bit off.

Expected shear

Obtained shear

I need to try with more galaxies per pixel to see if it constrains more the model. But I wanted to ask you if the size and resolution of the map were not problematic @EiffL .

VI

I haven't started to run VI with the varying shear field.

[b-remy]

Update result for the MAP: rescaling the parameters to the same scale helps the inference.

• 3600 gaussian galaxies on a regular grid
• GRF shear (16x16, resolution = 1 arcmin/pixel)
• sigma_pix = 0.003

With Adam(lr=1e-2) for 300 steps

Here is the convergence MAP (kB is zero by construction):

An the associated shear maps