Implement better HOD prior fitting

[maho3]

We are currently using SimBIG-like wide HOD priors. However, there are lot of unphysical prior regions, affecting our sampling efficiency. We can be smarter about how we constrain these HOD priors.

Things to look into:

• [ ] Constrain HOD priors from the real observational P(k), marginalizing over cosmology
• [ ] Fix cosmology, and compare HOD parameters against Patchy mocks to set HOD priors

Also, it is unclear whether we need to take into account HOD redshift dependence. Things to consider:

• [ ] Check MTNG, Abacus papers on HOD constraints for impact of HOD redshift dependence.
• [ ] Do HOD inference on multiple slices of real data. See how much HOD constraints change. This

[maho3]

From Chirag:

So this is the code that evaluates the mean of the 2 mass dependent HOD priors given a halo catalog, mean \nbar and fiducial values of other HOD parameters https://github.com/modichirag/contrastive_cosmology/blob/main/src/hodtools.py#L9 This function then samples the prior to generate HOD values https://github.com/modichirag/contrastive_cosmology/blob/main/src/hodtools.py#L54 These are used in this file https://github.com/modichirag/contrastive_cosmology/blob/main/scripts/hod_scripts/make_hod.py#L103 and line 117.