⚡️ Inference ⚡️

After performing a joint fit following the example here, 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) ).

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) . The sample script for this is included in the 2D_marginalize1D script .

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 .

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 .

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) . The sample script for this is included in the 4D_marginalize3D script . Other variants of conditioning can be coded up as well.