You are correct that precision is (in general) higher than the threshold. So if Alice publishes anything with at least 10% likelihood of being good, then more than 10% of her poems will be good. Whereas, if Alice aims for a precision of 10% then her promising threshold will be less than 10%.
Unless I’ve made a typo somewhere (and please let me know if I have), I don’t claim the optimal promising threshold τ⋆ = 10%. You can see in Graph 5 that I propose a promising threshold of 3.5%, which gives a precision of 10%.
I’ll edit the article to dispel any confusion. I was wary of giving exact values for the promising threshold, because τ⋆=3.5 yields 10% precision only for these graphs, which are of course invented for illustrative purposes.
You are correct that precision is (in general) higher than the threshold. So if Alice publishes anything with at least 10% likelihood of being good, then more than 10% of her poems will be good. Whereas, if Alice aims for a precision of 10% then her promising threshold will be less than 10%.
Unless I’ve made a typo somewhere (and please let me know if I have), I don’t claim the optimal promising threshold τ⋆ = 10%. You can see in Graph 5 that I propose a promising threshold of 3.5%, which gives a precision of 10%.
I’ll edit the article to dispel any confusion. I was wary of giving exact values for the promising threshold, because τ⋆=3.5 yields 10% precision only for these graphs, which are of course invented for illustrative purposes.
You’re right, my mistake