I propose that this concept be called "unexpected surprise" rather than "strictly confused":
"Strictly confused" suggests logical incoherence.
"Unexpected surprise" can be motivated the following way: let s(d)=surprise(d∣H)=−logPr(d∣H) be how surprising data d is on hypothesis H. Then one is "strictly confused" if the observed s is larger than than one would expect assuming a H holds.
This terminology is nice because the average of s under H is the entropy or expected surprise in (d∣H). It also connects with Bayes, since log-likelihood=−surprise is the
- "Strictly confused" suggests logical incoherence.
- "Unexpected surprise" can be motivated the following way: let s(d)=surprise(d∣H)=−logPr(d∣H) be how surprising data d is on hypothesis H. Then one is "strictly confused" if the observed s is larger than than one would expect assuming a H holds.
... (read more)I propose that this concept be called "unexpected surprise" rather than "strictly confused":
This terminology is nice because the average of s under H is the entropy or expected surprise in (d∣H). It also connects with Bayes, since log-likelihood=−surprise is the