.. _inference:

⚡️ Inference ⚡️
=================================

After performing a joint fit following the example :ref:`here <fitting>`, ``MRExo`` can be used to condition the joint probability distribution (PDF) to predict one set of variable/s from the others. 
The user can also condition the  Joint PDFs from the Monte-Carlo or Bootstrap simulations to obtain posteriors quantifying the impact of measurement uncertainties or finite sample size (see `Kanodia et al. (2023) <https://ui.adsabs.harvard.edu/abs/2023arXiv230810615K>`_ ).

2D Distributions
-----------------------
For 2D fits, say --- *f(x, y)* ---,  the 2D PDF can be conditioned on a given measurement Y,  *y=Y*, to obtain the 1D PDF --- *f(x|y=Y)*, from which the user can obtain the expectation and variance of the distribution.   
Here *x, y* can refer to any two measured quantities. 

Example is Figure 2 in `Kanodia et al. (2023) <https://ui.adsabs.harvard.edu/abs/2023arXiv230810615K>`_  . The sample script for this is included in the `2D_marginalize1D script <https://github.com/shbhuk/mrexo/blob/master/sample_scripts/2D_marginalize1Dplot.py>`_  . 

3D Distributions conditioned on 1D 
--------------------------------------------------------
For 3D fits, say --- *f(x, y, z)* ---,  the 3D PDF can be conditioned on a given measurement Z,  *z=Z*, to obtain the  2D PDF --- *f(x, y|z=Z)*, from which the user can obtain the expectation and variance of the distribution.   
Here *x, y, z* can refer to any three measured quantities. 

Example, fitting a *f(m,r,insol)* 3D PDF, and obtaining the *f(m,r)* plane by conditioning on *f(m,r|insol=Insol)*. The sample script for this is included in the `3D_marginalize1D script <https://github.com/shbhuk/mrexo/blob/master/sample_scripts/3D_marginalize1Dplot.py>`_  . 


3D Distributions conditioned on 2D 
--------------------------------------------------------
For 3D fits, say --- *f(x, y, z)* ---,  the 3D PDF can be conditioned on given measurements Y, Z,  *y=Y, z=Z*, to obtain the  1D PDF --- *f(x|y=Y,  z=Z)*, from which the user can obtain the expectation and variance of the distribution.  
Here *x, y, z* can refer to any three measured quantities.

Example, fitting a *f(m,r,insol)* 3D PDF, and obtaining the *f(m)* PDF by conditioning on *f(m|r=Rp, insol=Insol)*.  The sample script for this is included in the `3D_marginalize2D script <https://github.com/shbhuk/mrexo/blob/master/sample_scripts/3D_marginalize2Dplot.py>`_  . 


4D Distributions conditioned on 3D 
--------------------------------------------------------
For 4D fits, say --- *f(x, y, z, t)* ---,  the 4D PDF can be conditioned on given measurements Y, Z, T  *y=Y, z=Z, t=T*, to obtain the  1D PDF --- *f(x|y=Y,  z=Z, t=T)*, from which the user can obtain the expectation and variance of the distribution. 
Here *x, y, z, t* can refer to any four measured quantities. 

Example is Figure 4 or 5 in `Kanodia et al. (2023) <https://ui.adsabs.harvard.edu/abs/2023arXiv230810615K>`_  . The sample script for this is included in the `4D_marginalize3D script <https://github.com/shbhuk/mrexo/blob/master/sample_scripts/4D_marginalize3Dplot.py>`_  .  Other variants of conditioning can be coded up as well.