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A number of recent analyses of cosmological data have reported hints for thepresence of extra radiation beyond the standard model expectation. In order totest the robustness of these claims under different methods of constructingparameter constraints, we perform a Bayesian posterior-based and a likelihoodprofile-based analysis of current data. We confirm the presence of a slightdiscrepancy between posterior- and profile-based constraints, with themarginalised posterior preferring higher values of the effective number ofneutrino species N_eff. This can be traced back to a volume effect occurringduring the marginalisation process, and we demonstrate that the effect isrelated to the fact that cosmic microwave background (CMB) data constrain N_effonly indirectly via the redshift of matter-radiation equality. Once present CMBdata are combined with external information about, e.g., the Hubble parameter,the difference between the methods becomes small compared to the uncertainty ofN_eff. We conclude that the preference of precision cosmological data forexcess radiation is "real" and not an artifact of a specific choice ofcredible/confidence interval construction.

Evidence for extra radiation? Profile likelihood versus Bayesian posterior