Bayesian analysis of $f(T)$ gravity using $f\sigma_8$ data
  We use observational data from Supernovae (SNIa) Pantheon sample, from direct
Hubble constant measurements with cosmic chronometers (CC), from the Cosmic
Microwave Background shift parameter $\text{CMB}_{\text{shift}}$, and from
redshift space distortion ($f\sigma_8$) measurements, in order to constrain
$f(T)$ gravity. We do not follow the common $\gamma$ parameterization within
the semi-analytical approximation of the growth rate, in order to avoid
model-dependent uncertainties. Up to our knowledge this is the first time that
$f(T)$ gravity is analyzed within a Bayesian framework, and with background and
perturbation behaviour considered jointly. We show that all three examined
$f(T)$ models are able to describe adequately the $f\sigma_8$ data.
Furthermore, applying the Akaike, Bayesian and Deviance Information Criteria,
we conclude that all considered models are statistically equivalent, however
the most efficient candidate is the exponential model, which additionally
presents a small deviation from $\Lambda$CDM paradigm.
