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Bayesian (Probabilistic) Machine Learning is used to probe the opacity of theUniverse. It relies on a generative process where the model is the key objectto generate the data involving the unknown parameters of the model, our priorbeliefs, and allows us to get the posterior results. The constraints on thecosmic opacity are determined for two flat models, $\Lambda$CDM and XCDM (thishaving $\omega_{de} \neq -1$), 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 theconstraints on the cosmic opacity could change in the very deep Universe, andalso to check to what extent there is a redshift-range dependence. Thefollowing 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 notfully transparent, and this may have a significant impact on the $H_{0}$tension problem. In the generative process, the fact that, owing to cosmicopacity, the flux received by the observer is reduced has been taken intoaccount. In the analysis, the luminosity distance associated with thecosmological model has been employed.

Constraints on Cosmic Opacity from Bayesian Machine Learning: The hidden side of the $H_{0}$ tension problem