频率学派与贝叶斯周期信号检测的比较：统计错误率及对先验的敏感性
Comparing the frequentist and Bayesian periodic signal detection: rates of statistical mistakes and sensitivity to priors
AI总结：
本研究通过蒙特卡洛模拟比较频率学派与贝叶斯的Lomb--Scargle周期图检测方法，发现二者检测效率相近，非均匀先验仅让贝叶斯方法多检测约1%信号，先验错配时频率学派更优，且贝叶斯因子需经假阳性校准。
摘要：
我们开展了大量蒙特卡洛模拟，系统比较了Lomb--Scargle（隆布-斯卡格尔）周期图的频率学派与贝叶斯处理方式。研究目标是探究贝叶斯周期搜索在检测效率上是否优于频率学派方法，若存在优势则量化其幅度，同时分析该方法对先验选择的敏感性，尤其是在先验设定错误（即所采用的先验与物理天体的实际分布不匹配）的情况下的表现。我们发现，贝叶斯分析与频率学派分析在第一类错误与第二类错误的权衡层面，始终呈现出几乎一致的检测效率。若频率先验为非均匀分布，贝叶斯检测可能体现出形式上的优势，但这仅能多检测约1%的信号。若先验设定错误（采用非均匀先验但实际分布为均匀分布），则可能转而呈现频率学派分析的反向优势。最后我们发现，该任务中的贝叶斯因子若未经过第一类错误（假阳性）校准就使用，会显得过于保守，因此实际应用中必须进行此类校准。
英文摘要：
We perform extensive Monte Carlo simulations to systematically compare the frequentist and Bayesian treatments of the Lomb--Scargle periodogram. The goal is to investigate whether the Bayesian period search is advantageous over the frequentist one in terms of the detection efficiency, how much if yes, and how sensitive it is regarding the choice of the priors, in particular in case of a misspecified prior (whenever the adopted prior does not match the actual distribution of physical objects). We find that the Bayesian and frequentist analyses always offer nearly identical detection efficiency in terms of their tradeoff between type-I and type-II mistakes. Bayesian detection may reveal a formal 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 an opposite advantage of the frequentist analysis. Finally, we revealed that Bayes factor of this task appears rather overconservative if used without a calibration against type-I mistakes (false positives), thereby necessitating such a calibration in practice.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
