Earlier quoted context omitted.
The following is a response to only your first paragraph: Huh? If the distributions of bone densities among “people you would visually identify as ‘race X’ ” and “people you would visually identify as ‘race Y’ ” differ, then knowing that an individual would be someone you would visually identify as ‘race X’, gives you some amount of statistical information about their bone density. I guess you just mean that you can’…
> If the distributions of bone densities among “people you would visually identify as ‘race X’ ” and “people you would visually identify as ‘race Y’ ” differ, then knowing that an individual would be someone you would visually identify as ‘race X’, gives you some amount of statistical information about their bone density. Only if they differ substantially . If they look like https://evergreenleadership.com/wp-content…
I interpreted "conclude anything from" as "have a different posterior probability distribution" rather than "have a significantly different posterior probability distribution". This was an error on my part.
Thanks for the elaboration.