Constraints on Cosmic Opacity from Bayesian Machine Learning: The hidden
  side of the $H_{0}$ tension problem
  Bayesian (Probabilistic) Machine Learning is used to probe the opacity of the
Universe. It relies on a generative process where the model is the key object
to generate the data involving the unknown parameters of the model, our prior
beliefs, and allows us to get the posterior results. The constraints on the
cosmic opacity are determined for two flat models, $\Lambda$CDM and XCDM (this
having $\omega_{de} \neq -1$), for three redshift ranges, $z\in[0,2.5]$, $z
\in[0,5]$, and $z\in[0,10]$, in each case. This is to understand how the
constraints on the cosmic opacity could change in the very deep Universe, and
also to check to what extent there is a redshift-range dependence. The
following forms for the opacity, $\tau(z) = 2\epsilon z$ and $\tau(z) =
(1+z)^{2\epsilon} -1$, corresponding to an observer at $z=0$ and a source at
$z$, are considered. The results of our analysis show that the Universe is not
fully transparent, and this may have a significant impact on the $H_{0}$
tension problem. In the generative process, the fact that, owing to cosmic
opacity, the flux received by the observer is reduced has been taken into
account. In the analysis, the luminosity distance associated with the
cosmological model has been employed.
