分类:Simultaneous and selective inference: Current successes and future challenges

Benjamini, Y. (2010), Simultaneous and selective inference: Current successes and future challenges. Biom. J., 52: 708-721. doi:10.1002/bimj.200900299

Abstract

The previous decade can be viewed as a second golden for era Multiple Comparisons research. I argue that much of the success stems from our being able to address real current needs. At the same time, this success generated a plethora of concepts for error rate and power, as well as multiplicity of methods for addressing them. These confuse the users of our methodology and pose a threat. To avoid the threat, it is our responsibility to match our theoretical goals to the goals of the users of statistics. Only then should we match the methods to the theoretical goals. Considerations related to such needs are discussed: simultaneous inference or selective inference, testing or estimation, decision making or scientific reporting. I then further argue that the vitality of our field in the future – as a research area – depends upon our ability to continue and address the real needs of statistical analyses in current problems. Two application areas offering new challenges have received less attention in our community to date are discussed. Safety analysis in clinical trials, where I offer an aggregated safety assessment methodology and functional Magnetic Resonance Imaging.

总结和评论

如果我们要从多个角度来对比两组数据，我们可以从每一个角度来单独做一下这个对比，然后各自汇报结果。例如对比实验组和对照组的高矮、胖瘦、智力发展程度、颜值等等。但是，如果能够给出来一个整体的两组是否存在差别的报告，就更好了。这个问题就叫做多重比较问题^{[1] [2]}。如果每一个比较都是独立的，还比较好办，可以说，给出来一个有差别的比例（有差别的比较结果占总比较指标的比例）也还算凑活。如果每一个比较的指标可能不是完全独立的，就不好办了。统计学里面专门有一个分支学科就研究这个多重比较问题，见文献^{[1] [2]}，以及Wikipedia词条“Multiple comparisons problem”。

参考文献