  We analyze primordial tensor perturbations using the latest cosmic microwave
background and gravitational waves data, focusing on the tensor-to-scalar
ratio, $r$, and the tensor spectral tilt, $n_t$. Utilizing data from Planck
PR4, BICEP/Keck, and LIGO-Virgo-KAGRA, we employ both Bayesian and frequentist
methods to provide robust constraints on these parameters. Our results indicate
more conservative upper limits for $r$ with profile likelihoods compared to
Bayesian credible intervals, highlighting the influence of prior selection and
volume effects. The profile likelihood for $n_t$ shows that the current data do
not provide sufficient information to derive quantitative bounds, unless extra
assumptions on $r$ are used. Additionally, we conduct a 2D profile likelihood
analysis of $r$ and $n_t$, indicating a closer agreement between both
statistical methods for the largest values of $r$. This study not only updates
our understanding of the tensor perturbations but also highlights the
importance of employing both statistical methods to explore less constrained
parameters, crucial for future explorations in cosmology.
