Inference Semantics

[davidthomas5412]

The code for comparing the 'true' ray traced reduced shear (g_i_true) of a background galaxy to its Pangloss predicted ellipticity (e_i_predicted) still confuses me.

1) How I think it should be:

• The method lens_by_map extracts g_i_true from the Hilbert et al ray traced pangloss.KAPPA_FILE, pangloss.GAMMA_1_FILE, pangloss.GAMMA_2_FILE.
• We compute g_i_predicted and then use it to compute e_i_predicted in the method lens_by_halos.
• Compare g_i_true with e_i_predicted.

2) How it is now:

• The method lens_by_halos computes g_i_predicted and then uses it to compute e_i_predicted.
• Compare g_i_predicted with e_i_predicted.

Lines 919-926 in background.py on 'wl' branch are good reference. What am I missing?

[drphilmarshall]

Good: the names of things are important. There are several different comparisons that we might want to do.

A. Compare shapes of background galaxies lensed by a realistic density field (as captured by the MS maps) with the shapes of background galaxies lensed by a set of halos extracted from that density field (ie each with known Mhalo). This is the test that Spencer was doing, and answers the question, how good can the halo model possibly be? The comparison can be done either in g or e, but either way we should:

• Get g_true for each background galaxy with lens_by_maps, apply to e_int to get e_true
• Get g_predicted for each background galaxy with lens_by_halos, apply to e_int to get e_preditced
• Compare g or e true with g or e using correlation functions to summarize the data in each case

B. Compare observed (fixed) and model-predicted galaxy shapes, in order to infer the halo masses. This is what we are now trying to do. Here, the comparison must be between e_obs (which is fixed) and e_predicted (which we compute using the halos). However, we are still doing functional tests, so we make the e_obs ourselves, using our realistic density field from teh MS maps.

• Get g_true for each background galaxy with lens_by_maps, apply to e_int to get e_true and add noise to get e_obs
• For each choice of halo masses, compute g_predicted for each background galaxy with lens_by_halos
• Compare g_predicted with e_obs using the log likelihood function
• See whether the inferred Mhalo values match the true halo masses in the MS catalog.

On Sun, Nov 6, 2016 at 5:09 PM, David Thomas notifications@github.com wrote:

The code for comparing the 'true' ray traced reduced shear (g_i_true) of a background galaxy to its Pangloss predicted ellipticity (e_i_predicted) either has a bug or my understanding requires correcting.

1. How I think it should be:
   • The method lens_by_map extracts g_i_true from the Hilbert et al ray traced pangloss.KAPPA_FILE, pangloss.GAMMA_1_FILE, pangloss.GAMMA_2_FILE.
   • We compute g_i_predicted and then use it to compute e_i_predicted in the method lens_by_halos.
   • Compare g_i_true with e_i_predicted.
2. How it is now:
   • The method lens_by_halos computes g_i_predicted and then uses it to compute e_i_predicted.
   • Compare g_i_predicted with e_i_predicted.

Lines 919-926 in background.py on 'wl' branch are good reference.

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[davidthomas5412]

The names in my original post are fictitious and exist solely for the purpose of simplifying communication. My confusion was not with names, but rather that the 'calculate_log_likelihood' method, which currently computes neither A nor B. A simple way to see this is that the 'calculate_log_likelihood' method only ever makes a comparison with variables computed with lens_by_halos or lens_by_map but never compares variables across both (see lines 920-928 in background.py).

It seems like the conclusion is that we should (i) write a method that computes B, and (ii) use this method in our inference notebooks.