The DESI galaxy survey has recently placed the tightest constraint on the sum of neutrino masses to date. For such effects “below the detection limit”, where data can only infer upper bounds, Bayesian and frequentist methods can give important complimentary information. I will begin with an overview of the frequentist profile-likelihood method, its advantages and limitations. Using a frequentist and Bayesian toolbox, I will discuss neutrino mass constraints from Planck and DESI data. In particular, I will focus on the impact of different assumptions about the neutrino mass hierarchy on the inferred mass bounds. Further, I will compare Bayesian and frequentist constraints on evolving dark energy from recent cosmological data.