False Discovery Control, Balance Between Risk and Utility, Connection Between Theory and Application

Yilun He, The University of Sydney

My supervisor introduced the idea of false discoveries to me last year. In statistics, almost every practical decision has a chance to be wrong, due to the randomness of real world. One important job of statisticians is to control such risk at appropriate level. If a decision method is too conservative, it will be useless because it will never give you positive statement. If a decision method does not achieve the safety level it claims, it may lead to catastrophic errors.

The idea of false discovery control was initially invented to mitigate the problem that, when people require a large number statistical decision at the same time, it is almost not possible to guarantee correctness for all of them. Playing russian roulette once does not guarantee your death, but if you play it ten times a day you are not likely to survive. Traditionally in such scenario, no one can make any useful statement. False discovery control saved it, and statistical decisions can be made in such scenario.

But being able to join the gamble is not always a good thing. You have to know about the game rules. Statisticians provide those tools and advertise their effect, and sometimes people use this tool before they learn about the risk. The nature of false discovery rate control is potentially dangerous, and many statisticians are aware of it, but the application side are not warned.

I studied, implemented and tested a few methods that find better balance between risk and utility. This reminds me of some ancient Chinese wisdom. The idea of Yin and Yang is mainly about balance, and it acts as the core of Chinese philosophy.

It also inspired much critical thinking about statistics. How do we define an appropriate confidence level? If we make many decisions in our life, can we afford a solid proportion to be totally wrong? This invaluable experience will surely take me further into the realm of mathematics and statistics.

Yilun He was one of the recipients of a 2017/18 AMSI Vacation Research Scholarship.

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