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We perform extensive Monte Carlo simulations to systematically compare thefrequentist and Bayesian treatments of the Lomb--Scargle periodogram. The goalis to investigate whether the Bayesian period search is advantageous over thefrequentist one in terms of the detection efficiency, how much if yes, and howsensitive it is regarding the choice of the priors, in particular in case of amisspecified prior (whenever the adopted prior does not match the actualdistribution of physical objects). We find that the Bayesian and frequentistanalyses always offer nearly identical detection efficiency in terms of theirtradeoff between type-I and type-II mistakes. Bayesian detection may reveal aformal advantage if the frequency prior is nonuniform, but this results in only$\sim 1$ per cent extra detected signals. In case if the prior was misspecified(adopting nonuniform one over the actual uniform) this may turn into anopposite advantage of the frequentist analysis. Finally, we revealed that Bayesfactor of this task appears rather overconservative if used without acalibration against type-I mistakes (false positives), thereby necessitatingsuch a calibration in practice.

Comparing the frequentist and Bayesian periodic signal detection: rates of statistical mistakes and sensitivity to priors