After yet another failed fellowship application I considered if I should leave research. I now have seven fellowship failures and no successes, and that seems like a lot.
Success rates for grants are nose-diving and even the former head of the NHMRC says that researchers should be considering other careers. I’ve spent a lot of time running research projects for no money, but working for no money is a luxury I can’t afford.
As a statistician I knew I could get a more objective answer of whether seven failures really is a lot. I used a Bayesian approach by creating a prior distribution of researchers and then adding my own data to get a posterior probability that I should quit. I decided I would quit if there was a more than 90% probability that I am in the bottom half of the talent pool. In other words, if there’s a high probability that I am below average.
My prior distribution aimed to capture the likely range in researcher quality. So I needed to think of the average researcher and the range in ability. If you think it’s a horrible idea to assign a number to researcher quality, then you should never apply for research funding. As a compromise we can call it the prior the distribution of researchers’ ability to write a good fellowship application, without opening the can of snakes of whether that’s actually well correlated with talent.
Here’s my prior:
I wanted to have an average probability of success of 0.2, as that was about the average success of the schemes I had applied to. Then it’s logical to think of a few brilliant researchers, a few less than brilliant ones and most clumped around the mean. By trial and error I created the above prior, which is a Beta distribution (1,4), meaning that an average researcher would have 1 success and 5 attempts. If you understand this perfectly then you’re probably in the top half of the distribution.
Combining my data and the prior gives me this posterior:
There is a 77% probability that I am in the bottom half, so I stay in research by a margin of 13%. Sadly the evidence tells me that there’s an almost zero probability that I am a genius, and a relatively high probability that I am a plodder. Twelve failures are needed to reach the 90% margin, so the message for other people who have had multiple failures is: don’t give up hope yet.
Of course if (when) I do reach the 90% probability threshold then I’ll just move the goalposts to being 95% sure, which moves the failure threshold up to 16. Or if I do eventually quit research at least it will be a partly evidence-based decision.