It seems that if I were an anosognosic, I would make some observations only indirectly related to the affected limb that they don't seem impaired at making. For instance, even if I didn't notice that I was typing with one hand, I would probably remember having been to the hospital, or hearing a friend point out that one of my limbs looks awfully limp (even if I didn't know what they were talking about). Since I haven't made such observations, my probability that I'm anosognosic (at least about a limb or anything that observable) is lower than the prior.
Followup to: The Strangest Thing An AI Could Tell You
Brain damage patients with anosognosia are incapable of considering, noticing, admitting, or realizing even after being argued with, that their left arm, left leg, or left side of the body, is paralyzed. Again I'll quote Yvain's summary:
A brief search didn't turn up a base-rate frequency in the population for left-arm paralysis with anosognosia, but let's say the base rate is 1 in 10,000,000 individuals (so around 670 individuals worldwide).
Supposing this to be the prior, what is your estimated probability that your left arm is currently paralyzed?
Added: This interests me because it seems to be a special case of the same general issue discussed in The Modesty Argument and Robin's reply Sleepy Fools - when pathological minds roughly similar to yours update based on fabricated evidence to conclude they are not pathological, under what circumstances can you update on different-seeming evidence to conclude that you are not pathological?