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I propose that this concept be called "unex..."', clickbait: '', textLength: '2691', alias: '7qs', externalUrl: '', sortChildrenBy: 'recentFirst', hasVote: 'false', voteType: '', votesAnonymous: 'false', editCreatorId: 'LeonD', editCreatedAt: '2017-02-17 05:51:59', pageCreatorId: 'LeonD', pageCreatedAt: '2017-02-03 04:47:51', seeDomainId: '0', editDomainId: '1297', submitToDomainId: '0', isAutosave: 'false', isSnapshot: 'false', isLiveEdit: 'true', isMinorEdit: 'false', indirectTeacher: 'false', todoCount: '0', isEditorComment: 'false', isApprovedComment: 'false', isResolved: 'false', snapshotText: '', anchorContext: '', anchorText: '', anchorOffset: '0', mergedInto: '', isDeleted: 'false', viewCount: '339', 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 $d$.', metaText: '', isTextLoaded: 'true', isSubscribedToDiscussion: 'false', isSubscribedToUser: 'false', isSubscribedAsMaintainer: 'false', discussionSubscriberCount: '1', maintainerCount: '1', userSubscriberCount: '0', lastVisit: '', hasDraft: 'false', votes: [], voteSummary: 'null', muVoteSummary: '0', voteScaling: '0', currentUserVote: '-2', voteCount: '0', lockedVoteType: '', maxEditEver: '0', redLinkCount: '0', lockedBy: '', lockedUntil: '', nextPageId: '', prevPageId: '', usedAsMastery: 'false', proposalEditNum: '0', permissions: { edit: { has: 'false', reason: 'You don't have domain permission to edit this page' }, proposeEdit: { has: 'true', reason: '' }, delete: { has: 'false', reason: 'You don't have domain permission to delete this page' }, comment: { has: 'false', reason: 'You can't comment in this domain because you are not a member' }, proposeComment: { has: 'true', reason: '' } }, summaries: {}, creatorIds: [ 'LeonD' ], childIds: [], parentIds: [ 'strictly_confused' ], commentIds: [], questionIds: [], tagIds: [], relatedIds: [], markIds: [], explanations: [], learnMore: [], requirements: [], subjects: [], lenses: [], lensParentId: '', pathPages: [], learnMoreTaughtMap: {}, learnMoreCoveredMap: {}, learnMoreRequiredMap: {}, editHistory: {}, domainSubmissions: {}, answers: [], answerCount: '0', commentCount: '0', newCommentCount: '0', linkedMarkCount: '0', changeLogs: [ { likeableId: '0', likeableType: 'changeLog', myLikeValue: '0', likeCount: '0', dislikeCount: '0', likeScore: '0', individualLikes: [], id: '22064', pageId: '7qs', userId: 'LeonD', edit: '2', type: 'newEdit', createdAt: '2017-02-17 05:51:59', auxPageId: '', oldSettingsValue: '', newSettingsValue: '' }, { likeableId: '0', likeableType: 'changeLog', myLikeValue: '0', likeCount: '0', dislikeCount: '0', likeScore: '0', individualLikes: [], id: '21924', pageId: '7qs', userId: 'LeonD', edit: '1', type: 'newEdit', createdAt: '2017-02-03 04:47:51', auxPageId: '', oldSettingsValue: '', newSettingsValue: '' } ], feedSubmissions: [], searchStrings: {}, hasChildren: 'false', hasParents: 'true', redAliases: {}, improvementTagIds: [], nonMetaTagIds: [], todos: [], slowDownMap: 'null', speedUpMap: 'null', arcPageIds: 'null', contentRequests: {} }