I think the best antidote to “cowardice” is thinking about probabilities on a log scale once you get close to 0 or 1. The same likelihood ratio moves your log odds the same amount no matter the starting point, which basically means that going from 90% to 99% and going from 99% to 99.9% are steps of the same size.
Thus, I present the “number of nines” technique. Probability 0.9 (a.k.a. 90%) is one nine. Once you’re at one nine, further evidence should be measured in “number of nines” (number of powers of 10 in the likelihood ratio) E.g. “the growth rate data from Denmark and the UK provides about 1.3 nines of evidence (likelihood ratio something like 15:1) that Omicron is taking over before the end of the year.” Then to add up your evidence, you just add up the number of nines. Four nines = probability 0.9999.
It’s easy to end up over-confident with this technique if you accidentally double-count evidence, but it’s a really good antidote to feeling like you have to stop all of your probability estimates at 99%. Between seeing South Africa and Denmark and UK data, I think we are at >3 nines for Omicron being more than 1% in western countries by the end of the year.
I think the best antidote to “cowardice” is thinking about probabilities on a log scale once you get close to 0 or 1. The same likelihood ratio moves your log odds the same amount no matter the starting point, which basically means that going from 90% to 99% and going from 99% to 99.9% are steps of the same size.
Thus, I present the “number of nines” technique. Probability 0.9 (a.k.a. 90%) is one nine. Once you’re at one nine, further evidence should be measured in “number of nines” (number of powers of 10 in the likelihood ratio) E.g. “the growth rate data from Denmark and the UK provides about 1.3 nines of evidence (likelihood ratio something like 15:1) that Omicron is taking over before the end of the year.” Then to add up your evidence, you just add up the number of nines. Four nines = probability 0.9999.
It’s easy to end up over-confident with this technique if you accidentally double-count evidence, but it’s a really good antidote to feeling like you have to stop all of your probability estimates at 99%. Between seeing South Africa and Denmark and UK data, I think we are at >3 nines for Omicron being more than 1% in western countries by the end of the year.