Bayesian analysis of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>f</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>T</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:math>gravity using<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi>f</mml:mi><mml:msub><mml:mrow><mml:mi>σ</mml:mi></mml:mrow><mml:mrow><mml:mn>8</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math>data

We use observational data from the Pantheon supernovae sample, direct Hubble constant measurements with cosmic chronometers, the cosmic microwave background shift parameter ${\mathrm{CMB}}_{\text{shift}}$, and redshift-space distortion ($f{\ensuremath{\sigma}}_{8}$) measurements, in order to constrain $f(T)$ gravity. We do not follow the common $\ensuremath{\gamma}$ parametrization within the semianalytical approximation of the growth rate, in order to avoid model-dependent uncertainties. To our knowledge this is the first time that $f(T)$ gravity has been 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 adequately describe the $f{\ensuremath{\sigma}}_{8}$ data. Furthermore, by 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 the $\mathrm{\ensuremath{\Lambda}}\mathrm{CDM}$ paradigm.

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