  We derive a new upper bound on the tensor-to-scalar ratio parameter $r$ using
the frequentist profile likelihood method. We vary all the relevant
cosmological parameters of the $\Lambda$CDM model, as well as the nuisance
parameters. Unlike the Bayesian analysis using Markov Chain Monte Carlo (MCMC),
our analysis is independent of the choice of priors. Using $Planck$ Public
Release 4, BICEP/Keck Array 2018, $Planck$ CMB lensing, and BAO data, we find
an upper limit of $r<0.037$ at 95% C.L., similar to the Bayesian MCMC result of
$r<0.038$ for a flat prior on $r$ and a conditioned $Planck$ lowlEB covariance
matrix.
