Cosmological parameter estimation is traditionally performed in the Bayesian context. By adopting an “agnostic” statistical point of view, we show the interest of confronting the Bayesian results to a frequentist approach based on profile-likelihoods. To this purpose, we have developed the _Cosmological Analysis with a Minuit Exploration of the Likelihood_ () software. Written from scratch in pure C++, emphasis was put in building a clean and carefully-designed project where new data and/or cosmological computations can be easily included. CAMEL incorporates the latest cosmological likelihoods and gives access _from the very same input file_ to several estimation methods: - A high quality Maximum Likelihood Estimate (a.k.a “best fit”) using , - profile likelihoods, - a new implementation of an Adaptive Metropolis MCMC algorithm that relieves the burden of reconstructing the proposal distribution. We present here those various statistical techniques and roll out a full use-case that can then used as a tutorial. We revisit the parameters determination with the latest data and give results with both methodologies. Furthermore, by comparing the Bayesian and frequentist approaches, we discuss a “likelihood volume effect” that affects the optical reionization depth when analyzing the high multipoles part of the data. The software, used in several data analyzes, is available from http://camel.in2p3.fr. Using it does not require advanced C++ skills.