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  title: '"1.  I propose that this concept be called "unex..."',
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  text: '1.  I propose that this concept be called "unexpected surprise" rather than "strictly confused":\n\n-   "Strictly confused" suggests logical incoherence.\n-   "Unexpected surprise" can be motivated the following way: let $$ s(d) = \\textrm{surprise}(d \\mid H) = - \\log \\Pr (d \\mid H) $$ 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. \n\n    This terminology is nice because the average of $s$ under $H$ is the entropy or expected surprise in $(d \\mid H)$. It also connects with Bayes, since $$\\textrm{log-likelihood} = -\\textrm{surprise}$$ is the evidential support $d$ gives $H$.\n\n2.  The section on "Distinction from frequentist p-values" is, I think, both technically incorrect and a bit uncharitable.\n    \n    -   It's technically incorrect because the following isn't true:\n        > The classical frequentist test for rejecting the null hypothesis involves considering the probability assigned to particular 'obvious'-seeming partitions of the data, and asking if we ended up inside a low-probability partition.\n\n        Actually, the classical frequentist test involves specifying an obvious-seeming measure of surprise $t(d)$, and seeing whether $t$ is higher than expected on $H$. This is even more arbitrary than the above.\n    -   On the other hand, it's uncharitable because it's widely acknowledged one should try to choose $t$ to be _sufficient_, which is exactly the condition that the partition induced by $t$ is "compatible" with $\\Pr(d \\mid H)$ for different $H$, in the sense that $$\\Pr(H \\mid d) = \\Pr(H \\mid t(d))$$ for all the considered $H$.\n\n        Clearly $s$ is sufficient in this sense. But there might be simpler functions of $d$ that do the job too ("minimal sufficient statistics"). \n\n        Note that $t$ being sufficient doesn't make it non-arbitrary, as it may not be a monotone function of $s$.\n\n3.  Finally, I think that this concept is clearly "extra-Bayesian", in the sense that it's about non-probabilistic ("Knightian") uncertainty over $H$, and one is considering probabilities attached to unobserved $d$ (i.e., not conditioning on the observed $d$).\n\n    I don't think being "extra-Bayesian" in this sense is problematic. But I think it should be owned-up to.\n\n    Actually, "unexpected surprise" reveals a nice connection between Bayesian and sampling-based uncertainty intervals: \n    \n    -   To get a (HPD) credible interval, exclude those $H$ that are relatively surprised by the observed $d$ (or which are *a priori* surprising).\n    -   To get a (nice) confidence interval, exclude those $H$ that are "unexpectedly surprised" by $d$.',
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