{
localUrl: '../page/bayes_rule_proof.html',
arbitalUrl: 'https://arbital.com/p/bayes_rule_proof',
rawJsonUrl: '../raw/1xr.json',
likeableId: 'JoaqunIvona',
likeableType: 'page',
myLikeValue: '0',
likeCount: '3',
dislikeCount: '0',
likeScore: '3',
individualLikes: [
'EricBruylant',
'NateSoares',
'JacksonFriess'
],
pageId: 'bayes_rule_proof',
edit: '23',
editSummary: '',
prevEdit: '22',
currentEdit: '23',
wasPublished: 'true',
type: 'wiki',
title: 'Proof of Bayes' rule',
clickbait: 'Proofs of Bayes' rule, with graphics',
textLength: '3713',
alias: 'bayes_rule_proof',
externalUrl: '',
sortChildrenBy: 'likes',
hasVote: 'false',
voteType: '',
votesAnonymous: 'false',
editCreatorId: 'NateSoares',
editCreatedAt: '2016-07-10 21:24:01',
pageCreatorId: 'EliezerYudkowsky',
pageCreatedAt: '2016-02-09 20:59:26',
seeDomainId: '0',
editDomainId: 'AlexeiAndreev',
submitToDomainId: '0',
isAutosave: 'false',
isSnapshot: 'false',
isLiveEdit: 'true',
isMinorEdit: 'false',
indirectTeacher: 'false',
todoCount: '0',
isEditorComment: 'false',
isApprovedComment: 'true',
isResolved: 'false',
snapshotText: '',
anchorContext: '',
anchorText: '',
anchorOffset: '0',
mergedInto: '',
isDeleted: 'false',
viewCount: '2076',
text: 'Bayes' rule (in the [1x5 odds form]) says that, for every pair of hypotheses $H_i$ and $H_j$ and piece of evidence $e,$\n\n$$\\dfrac{\\mathbb P(H_i)}{\\mathbb P(H_j)} \\times \\dfrac{\\mathbb P(e \\mid H_i)}{\\mathbb P(e \\mid H_j)} = \\dfrac{\\mathbb P(H_i \\mid e)}{\\mathbb P(H_j \\mid e)}.$$\n\nBy the definition of [1rj conditional probability], $\\mathbb P(e \\land H)$ $=$ $\\mathbb P(H) \\cdot \\mathbb P(e \\mid H),$ so\n\n$$ \\dfrac{\\mathbb P(H_i)}{\\mathbb P(H_j)} \\times \\dfrac{\\mathbb P(e\\mid H_i)}{\\mathbb P(e\\mid H_j)} = \\dfrac{\\mathbb P(e \\wedge H_i)}{\\mathbb P(e \\wedge H_j)} $$\n\nDividing both the numerator and the denominator by $\\mathbb P(e),$ we have\n\n$$ \\dfrac{\\mathbb P(e \\wedge H_i)}{\\mathbb P(e \\wedge H_j)} = \\dfrac{\\mathbb P(e \\wedge H_i) / \\mathbb P(e)}{\\mathbb P(e \\wedge H_j) / \\mathbb P(e)} $$\n\nInvoking the definition of conditional probability again,\n\n$$ \\dfrac{\\mathbb P(e \\wedge H_i) / \\mathbb P(e)}{\\mathbb P(e \\wedge H_j) / \\mathbb P(e)} = \\dfrac{\\mathbb P(H_i\\mid e)}{\\mathbb P(H_j\\mid e)}.$$\n\nDone.\n\n---\n\nOf note is the equality\n\n$$\\frac{\\mathbb P(H_i\\mid e)}{\\mathbb P(H_j\\mid e)} = \\frac{\\mathbb P(H_i \\land e)}{\\mathbb P(H_j \\land e)},$$\n\nwhich says that the posterior odds (on the left) for $H_i$ (vs $H_j$) given evidence $e$ is exactly equal to the prior odds of $H_i$ (vs $H_j$) in the parts of $\\mathbb P$ where $e$ was already true. $\\mathbb P(x \\land e)$ is the amount of probability mass that $\\mathbb P$ allocated to worlds where both $x$ and $e$ are true, and the above equation says that after observing $e,$ your belief in $H_i$ relative to $H_j$ should be equal to $H_i$'s odds relative to $H_j$ _in those worlds._ In other words, Bayes' rule can be interpreted as saying: "Once you've seen $e$, simply throw away all probability mass except the mass on worlds where $e$ was true, and then continue reasoning according to the remaining probability mass." See also [1y6].\n\n## Illustration (using the Diseasitis example)\n\nSpecializing to the [22s Diseasitis] problem, using red for sick, blue for healthy, and + signs for positive test results, the proof above can be visually depicted as follows:\n\n\n\nThis visualization can be read as saying: The ratio of the initial sick population (red) to the initial healthy population (blue), times the ratio of positive results (+) in the sick population to positive results in the blue population, equals the ratio of the positive-and-red population to positive-and-blue population. Thus we can divide both into the proportion of the whole population which got positive results (grey and +), yielding the posterior odds of sick (red) vs healthy (blue) among only those with positive results.\n\n\nThe corresponding numbers are:\n\n$$\\dfrac{20\\%}{80\\%} \\times \\dfrac{90\\%}{30\\%} = \\dfrac{18\\%}{24\\%} = \\dfrac{0.18 / 0.42}{0.24 / 0.42} = \\dfrac{3}{4}$$\n\nfor a final probability $\\mathbb P(sick)$ of $\\frac{3}{7} \\approx 43\\%.$\n\n## Generality\n\nThe [1x5 odds] and [1zm proportional] forms of Bayes' rule talk about the *relative* probability of two hypotheses $H_i$ and $H_j.$ In the particular example of Diseasitis it happens that [1rd every patient is either sick or not-sick], so that we can [1rk normalize] the final odds 3 : 4 to probabilities of $\\frac{3}{7} : \\frac{4}{7}.$ However, the proof above shows that even if we were talking about two different possible diseases and their total prevalances did not sum to 1, the equation above would still hold between the *relative* prior odds for $\\frac{\\mathbb P(H_i)}{\\mathbb P(H_j)}$ and the *relative* posterior odds for $\\frac{\\mathbb P(H_i\\mid e)}{\\mathbb P(H_j\\mid e)}.$\n\nThe above proof can be specialized to the probabilistic case; see [56j].\n\n',
metaText: '',
isTextLoaded: 'true',
isSubscribedToDiscussion: 'false',
isSubscribedToUser: 'false',
isSubscribedAsMaintainer: 'false',
discussionSubscriberCount: '1',
maintainerCount: '1',
userSubscriberCount: '0',
lastVisit: '2016-02-21 13:17:05',
hasDraft: 'false',
votes: [],
voteSummary: [
'0',
'0',
'0',
'0',
'0',
'0',
'0',
'0',
'0',
'0'
],
muVoteSummary: '0',
voteScaling: '0',
currentUserVote: '-2',
voteCount: '0',
lockedVoteType: '',
maxEditEver: '0',
redLinkCount: '0',
lockedBy: '',
lockedUntil: '',
nextPageId: '',
prevPageId: '',
usedAsMastery: 'true',
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: {
Summary: 'Bayes' rule (in the [1x5 odds form]) says that, for every pair of hypotheses $H_i$ and $H_j$ and piece of evidence $e,$'
},
creatorIds: [
'EliezerYudkowsky',
'NateSoares'
],
childIds: [
'bayes_rule_probability_proof'
],
parentIds: [
'bayes_rule'
],
commentIds: [],
questionIds: [],
tagIds: [
'b_class_meta_tag'
],
relatedIds: [],
markIds: [],
explanations: [
{
id: '6510',
parentId: 'bayes_rule_proof',
childId: 'bayes_rule_odds_intro',
type: 'subject',
creatorId: 'EliezerYudkowsky',
createdAt: '2016-10-01 05:33:20',
level: '2',
isStrong: 'true',
everPublished: 'true'
},
{
id: '5183',
parentId: 'bayes_rule_proof',
childId: 'bayes_rule_proof',
type: 'subject',
creatorId: 'NateSoares',
createdAt: '2016-07-10 23:38:40',
level: '2',
isStrong: 'true',
everPublished: 'true'
},
{
id: '6500',
parentId: 'bayes_rule_proof',
childId: 'bayes_rule_fast_intro',
type: 'subject',
creatorId: 'EliezerYudkowsky',
createdAt: '2016-09-29 04:41:48',
level: '2',
isStrong: 'true',
everPublished: 'true'
}
],
learnMore: [
{
id: '5641',
parentId: 'bayes_rule_proof',
childId: 'bayes_rule_probability_proof',
type: 'subject',
creatorId: 'AlexeiAndreev',
createdAt: '2016-07-26 17:07:57',
level: '2',
isStrong: 'false',
everPublished: 'true'
}
],
requirements: [
{
id: '2095',
parentId: 'conditional_probability',
childId: 'bayes_rule_proof',
type: 'requirement',
creatorId: 'AlexeiAndreev',
createdAt: '2016-06-17 21:58:56',
level: '2',
isStrong: 'true',
everPublished: 'true'
},
{
id: '5118',
parentId: 'bayes_rule',
childId: 'bayes_rule_proof',
type: 'requirement',
creatorId: 'NateSoares',
createdAt: '2016-07-10 21:13:31',
level: '2',
isStrong: 'true',
everPublished: 'true'
},
{
id: '5119',
parentId: 'math1',
childId: 'bayes_rule_proof',
type: 'requirement',
creatorId: 'NateSoares',
createdAt: '2016-07-10 21:13:50',
level: '3',
isStrong: 'true',
everPublished: 'true'
}
],
subjects: [
{
id: '5122',
parentId: 'bayes_rule',
childId: 'bayes_rule_proof',
type: 'subject',
creatorId: 'NateSoares',
createdAt: '2016-07-10 21:27:11',
level: '2',
isStrong: 'false',
everPublished: 'true'
},
{
id: '5183',
parentId: 'bayes_rule_proof',
childId: 'bayes_rule_proof',
type: 'subject',
creatorId: 'NateSoares',
createdAt: '2016-07-10 23:38:40',
level: '2',
isStrong: 'true',
everPublished: 'true'
}
],
lenses: [],
lensParentId: '',
pathPages: [],
learnMoreTaughtMap: {
'1xr': [
'56j'
]
},
learnMoreCoveredMap: {
'1lz': [
'1yc',
'1zh',
'1zm',
'220',
'552',
'56j',
'6cj'
]
},
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: '19807',
pageId: 'bayes_rule_proof',
userId: 'EliezerYudkowsky',
edit: '0',
type: 'newTeacher',
createdAt: '2016-10-01 05:33:20',
auxPageId: 'bayes_rule_odds_intro',
oldSettingsValue: '',
newSettingsValue: ''
},
{
likeableId: '0',
likeableType: 'changeLog',
myLikeValue: '0',
likeCount: '0',
dislikeCount: '0',
likeScore: '0',
individualLikes: [],
id: '19750',
pageId: 'bayes_rule_proof',
userId: 'EliezerYudkowsky',
edit: '0',
type: 'newTeacher',
createdAt: '2016-09-29 04:41:49',
auxPageId: 'bayes_rule_fast_intro',
oldSettingsValue: '',
newSettingsValue: ''
},
{
likeableId: '0',
likeableType: 'changeLog',
myLikeValue: '0',
likeCount: '0',
dislikeCount: '0',
likeScore: '0',
individualLikes: [],
id: '18225',
pageId: 'bayes_rule_proof',
userId: 'EricBruylant',
edit: '0',
type: 'newTag',
createdAt: '2016-08-03 16:32:34',
auxPageId: 'b_class_meta_tag',
oldSettingsValue: '',
newSettingsValue: ''
},
{
likeableId: '0',
likeableType: 'changeLog',
myLikeValue: '0',
likeCount: '0',
dislikeCount: '0',
likeScore: '0',
individualLikes: [],
id: '17970',
pageId: 'bayes_rule_proof',
userId: 'AlexeiAndreev',
edit: '0',
type: 'deleteSubject',
createdAt: '2016-08-02 00:17:17',
auxPageId: 'bayes_rule_odds',
oldSettingsValue: '',
newSettingsValue: ''
},
{
likeableId: '0',
likeableType: 'changeLog',
myLikeValue: '0',
likeCount: '0',
dislikeCount: '0',
likeScore: '0',
individualLikes: [],
id: '17542',
pageId: 'bayes_rule_proof',
userId: 'AlexeiAndreev',
edit: '0',
type: 'newTeacher',
createdAt: '2016-07-26 17:07:58',
auxPageId: 'bayes_rule_probability_proof',
oldSettingsValue: '',
newSettingsValue: ''
},
{
likeableId: '0',
likeableType: 'changeLog',
myLikeValue: '0',
likeCount: '0',
dislikeCount: '0',
likeScore: '0',
individualLikes: [],
id: '16548',
pageId: 'bayes_rule_proof',
userId: 'NateSoares',
edit: '0',
type: 'newTeacher',
createdAt: '2016-07-10 23:38:41',
auxPageId: 'bayes_rule_proof',
oldSettingsValue: '',
newSettingsValue: ''
},
{
likeableId: '0',
likeableType: 'changeLog',
myLikeValue: '0',
likeCount: '0',
dislikeCount: '0',
likeScore: '0',
individualLikes: [],
id: '16549',
pageId: 'bayes_rule_proof',
userId: 'NateSoares',
edit: '0',
type: 'newSubject',
createdAt: '2016-07-10 23:38:41',
auxPageId: 'bayes_rule_proof',
oldSettingsValue: '',
newSettingsValue: ''
},
{
likeableId: '0',
likeableType: 'changeLog',
myLikeValue: '0',
likeCount: '0',
dislikeCount: '0',
likeScore: '0',
individualLikes: [],
id: '16535',
pageId: 'bayes_rule_proof',
userId: 'NateSoares',
edit: '0',
type: 'deleteRequiredBy',
createdAt: '2016-07-10 23:00:57',
auxPageId: 'bayes_guide_end',
oldSettingsValue: '',
newSettingsValue: ''
},
{
likeableId: '0',
likeableType: 'changeLog',
myLikeValue: '0',
likeCount: '0',
dislikeCount: '0',
likeScore: '0',
individualLikes: [],
id: '16532',
pageId: 'bayes_rule_proof',
userId: 'NateSoares',
edit: '0',
type: 'deleteRequiredBy',
createdAt: '2016-07-10 22:59:04',
auxPageId: 'bayes_guide_end',
oldSettingsValue: '',
newSettingsValue: ''
},
{
likeableId: '0',
likeableType: 'changeLog',
myLikeValue: '0',
likeCount: '0',
dislikeCount: '0',
likeScore: '0',
individualLikes: [],
id: '16466',
pageId: 'bayes_rule_proof',
userId: 'NateSoares',
edit: '0',
type: 'deleteRequiredBy',
createdAt: '2016-07-10 21:58:02',
auxPageId: 'bayes_rule_details',
oldSettingsValue: '',
newSettingsValue: ''
},
{
likeableId: '0',
likeableType: 'changeLog',
myLikeValue: '0',
likeCount: '0',
dislikeCount: '0',
likeScore: '0',
individualLikes: [],
id: '16405',
pageId: 'bayes_rule_proof',
userId: 'NateSoares',
edit: '0',
type: 'newSubject',
createdAt: '2016-07-10 21:27:23',
auxPageId: 'bayes_rule_odds',
oldSettingsValue: '',
newSettingsValue: ''
},
{
likeableId: '0',
likeableType: 'changeLog',
myLikeValue: '0',
likeCount: '0',
dislikeCount: '0',
likeScore: '0',
individualLikes: [],
id: '16403',
pageId: 'bayes_rule_proof',
userId: 'NateSoares',
edit: '0',
type: 'newSubject',
createdAt: '2016-07-10 21:27:12',
auxPageId: 'bayes_rule',
oldSettingsValue: '',
newSettingsValue: ''
},
{
likeableId: '0',
likeableType: 'changeLog',
myLikeValue: '0',
likeCount: '0',
dislikeCount: '0',
likeScore: '0',
individualLikes: [],
id: '16399',
pageId: 'bayes_rule_proof',
userId: 'NateSoares',
edit: '0',
type: 'deleteChild',
createdAt: '2016-07-10 21:24:22',
auxPageId: 'bayes_rule_proof_math1',
oldSettingsValue: '',
newSettingsValue: ''
},
{
likeableId: '0',
likeableType: 'changeLog',
myLikeValue: '0',
likeCount: '0',
dislikeCount: '0',
likeScore: '0',
individualLikes: [],
id: '16398',
pageId: 'bayes_rule_proof',
userId: 'NateSoares',
edit: '23',
type: 'newEdit',
createdAt: '2016-07-10 21:24:01',
auxPageId: '',
oldSettingsValue: '',
newSettingsValue: ''
},
{
likeableId: '0',
likeableType: 'changeLog',
myLikeValue: '0',
likeCount: '0',
dislikeCount: '0',
likeScore: '0',
individualLikes: [],
id: '16394',
pageId: 'bayes_rule_proof',
userId: 'NateSoares',
edit: '0',
type: 'newRequirement',
createdAt: '2016-07-10 21:13:50',
auxPageId: 'math1',
oldSettingsValue: '',
newSettingsValue: ''
},
{
likeableId: '0',
likeableType: 'changeLog',
myLikeValue: '0',
likeCount: '0',
dislikeCount: '0',
likeScore: '0',
individualLikes: [],
id: '16393',
pageId: 'bayes_rule_proof',
userId: 'NateSoares',
edit: '0',
type: 'deleteRequirement',
createdAt: '2016-07-10 21:13:38',
auxPageId: 'math3',
oldSettingsValue: '',
newSettingsValue: ''
},
{
likeableId: '0',
likeableType: 'changeLog',
myLikeValue: '0',
likeCount: '0',
dislikeCount: '0',
likeScore: '0',
individualLikes: [],
id: '16391',
pageId: 'bayes_rule_proof',
userId: 'NateSoares',
edit: '0',
type: 'newRequirement',
createdAt: '2016-07-10 21:13:32',
auxPageId: 'bayes_rule',
oldSettingsValue: '',
newSettingsValue: ''
},
{
likeableId: '0',
likeableType: 'changeLog',
myLikeValue: '0',
likeCount: '0',
dislikeCount: '0',
likeScore: '0',
individualLikes: [],
id: '16380',
pageId: 'bayes_rule_proof',
userId: 'NateSoares',
edit: '0',
type: 'deleteTeacher',
createdAt: '2016-07-10 21:05:01',
auxPageId: 'bayes_rule_proof_math1',
oldSettingsValue: '',
newSettingsValue: ''
},
{
likeableId: '0',
likeableType: 'changeLog',
myLikeValue: '0',
likeCount: '0',
dislikeCount: '0',
likeScore: '0',
individualLikes: [],
id: '16213',
pageId: 'bayes_rule_proof',
userId: 'NateSoares',
edit: '0',
type: 'deleteTeacher',
createdAt: '2016-07-08 15:44:00',
auxPageId: '1x9',
oldSettingsValue: '',
newSettingsValue: ''
},
{
likeableId: '0',
likeableType: 'changeLog',
myLikeValue: '0',
likeCount: '0',
dislikeCount: '0',
likeScore: '0',
individualLikes: [],
id: '16174',
pageId: 'bayes_rule_proof',
userId: 'NateSoares',
edit: '0',
type: 'deleteTeacher',
createdAt: '2016-07-08 15:28:47',
auxPageId: 'bayes_rule_odds_intro',
oldSettingsValue: '',
newSettingsValue: ''
},
{
likeableId: '0',
likeableType: 'changeLog',
myLikeValue: '0',
likeCount: '0',
dislikeCount: '0',
likeScore: '0',
individualLikes: [],
id: '15898',
pageId: 'bayes_rule_proof',
userId: 'NateSoares',
edit: '22',
type: 'newEdit',
createdAt: '2016-07-07 01:47:55',
auxPageId: '',
oldSettingsValue: '',
newSettingsValue: ''
},
{
likeableId: '0',
likeableType: 'changeLog',
myLikeValue: '0',
likeCount: '0',
dislikeCount: '0',
likeScore: '0',
individualLikes: [],
id: '15891',
pageId: 'bayes_rule_proof',
userId: 'NateSoares',
edit: '21',
type: 'newEdit',
createdAt: '2016-07-07 01:42:56',
auxPageId: '',
oldSettingsValue: '',
newSettingsValue: 'Split off the probability proof, and cleaned up the notation a bit.'
},
{
likeableId: '0',
likeableType: 'changeLog',
myLikeValue: '0',
likeCount: '0',
dislikeCount: '0',
likeScore: '0',
individualLikes: [],
id: '15890',
pageId: 'bayes_rule_proof',
userId: 'NateSoares',
edit: '0',
type: 'lensOrderChanged',
createdAt: '2016-07-07 01:42:38',
auxPageId: '',
oldSettingsValue: '',
newSettingsValue: ''
},
{
likeableId: '0',
likeableType: 'changeLog',
myLikeValue: '0',
likeCount: '0',
dislikeCount: '0',
likeScore: '0',
individualLikes: [],
id: '15888',
pageId: 'bayes_rule_proof',
userId: 'NateSoares',
edit: '0',
type: 'newChild',
createdAt: '2016-07-07 01:41:52',
auxPageId: 'bayes_rule_probability_proof',
oldSettingsValue: '',
newSettingsValue: ''
},
{
likeableId: '0',
likeableType: 'changeLog',
myLikeValue: '0',
likeCount: '0',
dislikeCount: '0',
likeScore: '0',
individualLikes: [],
id: '15093',
pageId: 'bayes_rule_proof',
userId: 'NateSoares',
edit: '20',
type: 'newEdit',
createdAt: '2016-07-02 00:03:29',
auxPageId: '',
oldSettingsValue: '',
newSettingsValue: ''
},
{
likeableId: '0',
likeableType: 'changeLog',
myLikeValue: '0',
likeCount: '0',
dislikeCount: '0',
likeScore: '0',
individualLikes: [],
id: '15075',
pageId: 'bayes_rule_proof',
userId: 'NateSoares',
edit: '19',
type: 'newEdit',
createdAt: '2016-07-01 19:56:08',
auxPageId: '',
oldSettingsValue: '',
newSettingsValue: ''
},
{
likeableId: '0',
likeableType: 'changeLog',
myLikeValue: '0',
likeCount: '0',
dislikeCount: '0',
likeScore: '0',
individualLikes: [],
id: '15074',
pageId: 'bayes_rule_proof',
userId: 'EliezerYudkowsky',
edit: '18',
type: 'newEdit',
createdAt: '2016-07-01 19:54:12',
auxPageId: '',
oldSettingsValue: '',
newSettingsValue: ''
},
{
likeableId: '0',
likeableType: 'changeLog',
myLikeValue: '0',
likeCount: '0',
dislikeCount: '0',
likeScore: '0',
individualLikes: [],
id: '8107',
pageId: 'bayes_rule_proof',
userId: 'NateSoares',
edit: '17',
type: 'newEdit',
createdAt: '2016-03-03 03:19:01',
auxPageId: '',
oldSettingsValue: '',
newSettingsValue: ''
},
{
likeableId: '0',
likeableType: 'changeLog',
myLikeValue: '0',
likeCount: '0',
dislikeCount: '0',
likeScore: '0',
individualLikes: [],
id: '7593',
pageId: 'bayes_rule_proof',
userId: 'EliezerYudkowsky',
edit: '16',
type: 'newEdit',
createdAt: '2016-02-22 21:23:35',
auxPageId: '',
oldSettingsValue: '',
newSettingsValue: ''
},
{
likeableId: '0',
likeableType: 'changeLog',
myLikeValue: '0',
likeCount: '0',
dislikeCount: '0',
likeScore: '0',
individualLikes: [],
id: '7154',
pageId: 'bayes_rule_proof',
userId: 'EliezerYudkowsky',
edit: '15',
type: 'newRequiredBy',
createdAt: '2016-02-16 05:35:38',
auxPageId: 'bayes_rule_details',
oldSettingsValue: '',
newSettingsValue: ''
},
{
likeableId: '0',
likeableType: 'changeLog',
myLikeValue: '0',
likeCount: '0',
dislikeCount: '0',
likeScore: '0',
individualLikes: [],
id: '6859',
pageId: 'bayes_rule_proof',
userId: 'EliezerYudkowsky',
edit: '15',
type: 'newTeacher',
createdAt: '2016-02-11 04:03:41',
auxPageId: 'bayes_rule_proof_math1',
oldSettingsValue: '',
newSettingsValue: ''
},
{
likeableId: '0',
likeableType: 'changeLog',
myLikeValue: '0',
likeCount: '0',
dislikeCount: '0',
likeScore: '0',
individualLikes: [],
id: '6853',
pageId: 'bayes_rule_proof',
userId: 'EliezerYudkowsky',
edit: '15',
type: 'newChild',
createdAt: '2016-02-11 04:02:43',
auxPageId: 'bayes_rule_proof_math1',
oldSettingsValue: '',
newSettingsValue: ''
},
{
likeableId: '0',
likeableType: 'changeLog',
myLikeValue: '0',
likeCount: '0',
dislikeCount: '0',
likeScore: '0',
individualLikes: [],
id: '6788',
pageId: 'bayes_rule_proof',
userId: 'EliezerYudkowsky',
edit: '15',
type: 'newEdit',
createdAt: '2016-02-11 03:23:35',
auxPageId: '',
oldSettingsValue: '',
newSettingsValue: ''
},
{
likeableId: '0',
likeableType: 'changeLog',
myLikeValue: '0',
likeCount: '0',
dislikeCount: '0',
likeScore: '0',
individualLikes: [],
id: '6772',
pageId: 'bayes_rule_proof',
userId: 'EliezerYudkowsky',
edit: '14',
type: 'newTeacher',
createdAt: '2016-02-11 03:08:49',
auxPageId: 'bayes_rule_odds_intro',
oldSettingsValue: '',
newSettingsValue: ''
},
{
likeableId: '0',
likeableType: 'changeLog',
myLikeValue: '0',
likeCount: '0',
dislikeCount: '0',
likeScore: '0',
individualLikes: [],
id: '6683',
pageId: 'bayes_rule_proof',
userId: 'EliezerYudkowsky',
edit: '14',
type: 'newEdit',
createdAt: '2016-02-10 04:57:45',
auxPageId: '',
oldSettingsValue: '',
newSettingsValue: ''
},
{
likeableId: '0',
likeableType: 'changeLog',
myLikeValue: '0',
likeCount: '0',
dislikeCount: '0',
likeScore: '0',
individualLikes: [],
id: '6682',
pageId: 'bayes_rule_proof',
userId: 'EliezerYudkowsky',
edit: '13',
type: 'newEdit',
createdAt: '2016-02-10 04:56:50',
auxPageId: '',
oldSettingsValue: '',
newSettingsValue: ''
},
{
likeableId: '0',
likeableType: 'changeLog',
myLikeValue: '0',
likeCount: '0',
dislikeCount: '0',
likeScore: '0',
individualLikes: [],
id: '6681',
pageId: 'bayes_rule_proof',
userId: 'EliezerYudkowsky',
edit: '12',
type: 'newEdit',
createdAt: '2016-02-10 04:56:23',
auxPageId: '',
oldSettingsValue: '',
newSettingsValue: ''
},
{
likeableId: '0',
likeableType: 'changeLog',
myLikeValue: '0',
likeCount: '0',
dislikeCount: '0',
likeScore: '0',
individualLikes: [],
id: '6680',
pageId: 'bayes_rule_proof',
userId: 'EliezerYudkowsky',
edit: '11',
type: 'newEdit',
createdAt: '2016-02-10 04:52:37',
auxPageId: '',
oldSettingsValue: '',
newSettingsValue: ''
},
{
likeableId: '0',
likeableType: 'changeLog',
myLikeValue: '0',
likeCount: '0',
dislikeCount: '0',
likeScore: '0',
individualLikes: [],
id: '6679',
pageId: 'bayes_rule_proof',
userId: 'EliezerYudkowsky',
edit: '10',
type: 'newEdit',
createdAt: '2016-02-10 04:51:29',
auxPageId: '',
oldSettingsValue: '',
newSettingsValue: ''
},
{
likeableId: '0',
likeableType: 'changeLog',
myLikeValue: '0',
likeCount: '0',
dislikeCount: '0',
likeScore: '0',
individualLikes: [],
id: '6678',
pageId: 'bayes_rule_proof',
userId: 'EliezerYudkowsky',
edit: '9',
type: 'newEdit',
createdAt: '2016-02-10 04:50:15',
auxPageId: '',
oldSettingsValue: '',
newSettingsValue: ''
},
{
likeableId: '0',
likeableType: 'changeLog',
myLikeValue: '0',
likeCount: '0',
dislikeCount: '0',
likeScore: '0',
individualLikes: [],
id: '6677',
pageId: 'bayes_rule_proof',
userId: 'EliezerYudkowsky',
edit: '8',
type: 'newEdit',
createdAt: '2016-02-10 04:48:26',
auxPageId: '',
oldSettingsValue: '',
newSettingsValue: ''
},
{
likeableId: '0',
likeableType: 'changeLog',
myLikeValue: '0',
likeCount: '0',
dislikeCount: '0',
likeScore: '0',
individualLikes: [],
id: '6669',
pageId: 'bayes_rule_proof',
userId: 'EliezerYudkowsky',
edit: '7',
type: 'newEdit',
createdAt: '2016-02-10 02:27:18',
auxPageId: '',
oldSettingsValue: '',
newSettingsValue: ''
},
{
likeableId: '0',
likeableType: 'changeLog',
myLikeValue: '0',
likeCount: '0',
dislikeCount: '0',
likeScore: '0',
individualLikes: [],
id: '6668',
pageId: 'bayes_rule_proof',
userId: 'EliezerYudkowsky',
edit: '6',
type: 'newEdit',
createdAt: '2016-02-10 02:26:30',
auxPageId: '',
oldSettingsValue: '',
newSettingsValue: ''
},
{
likeableId: '0',
likeableType: 'changeLog',
myLikeValue: '0',
likeCount: '0',
dislikeCount: '0',
likeScore: '0',
individualLikes: [],
id: '6665',
pageId: 'bayes_rule_proof',
userId: 'EliezerYudkowsky',
edit: '5',
type: 'newEdit',
createdAt: '2016-02-10 02:19:46',
auxPageId: '',
oldSettingsValue: '',
newSettingsValue: ''
},
{
likeableId: '0',
likeableType: 'changeLog',
myLikeValue: '0',
likeCount: '0',
dislikeCount: '0',
likeScore: '0',
individualLikes: [],
id: '6664',
pageId: 'bayes_rule_proof',
userId: 'EliezerYudkowsky',
edit: '4',
type: 'newEdit',
createdAt: '2016-02-10 02:17:35',
auxPageId: '',
oldSettingsValue: '',
newSettingsValue: ''
},
{
likeableId: '0',
likeableType: 'changeLog',
myLikeValue: '0',
likeCount: '0',
dislikeCount: '0',
likeScore: '0',
individualLikes: [],
id: '6663',
pageId: 'bayes_rule_proof',
userId: 'EliezerYudkowsky',
edit: '3',
type: 'newEdit',
createdAt: '2016-02-10 02:08:04',
auxPageId: '',
oldSettingsValue: '',
newSettingsValue: ''
},
{
likeableId: '0',
likeableType: 'changeLog',
myLikeValue: '0',
likeCount: '0',
dislikeCount: '0',
likeScore: '0',
individualLikes: [],
id: '6662',
pageId: 'bayes_rule_proof',
userId: 'EliezerYudkowsky',
edit: '2',
type: 'newEdit',
createdAt: '2016-02-10 02:07:43',
auxPageId: '',
oldSettingsValue: '',
newSettingsValue: ''
},
{
likeableId: '0',
likeableType: 'changeLog',
myLikeValue: '0',
likeCount: '0',
dislikeCount: '0',
likeScore: '0',
individualLikes: [],
id: '6658',
pageId: 'bayes_rule_proof',
userId: 'EliezerYudkowsky',
edit: '0',
type: 'deleteTag',
createdAt: '2016-02-10 01:56:09',
auxPageId: 'stub_meta_tag',
oldSettingsValue: '',
newSettingsValue: ''
},
{
likeableId: '0',
likeableType: 'changeLog',
myLikeValue: '0',
likeCount: '0',
dislikeCount: '0',
likeScore: '0',
individualLikes: [],
id: '6656',
pageId: 'bayes_rule_proof',
userId: 'EliezerYudkowsky',
edit: '1',
type: 'newSubject',
createdAt: '2016-02-10 01:56:06',
auxPageId: 'bayes_rule_proof',
oldSettingsValue: '',
newSettingsValue: ''
},
{
likeableId: '0',
likeableType: 'changeLog',
myLikeValue: '0',
likeCount: '0',
dislikeCount: '0',
likeScore: '0',
individualLikes: [],
id: '6655',
pageId: 'bayes_rule_proof',
userId: 'EliezerYudkowsky',
edit: '1',
type: 'newTeacher',
createdAt: '2016-02-10 01:56:06',
auxPageId: 'bayes_rule_proof',
oldSettingsValue: '',
newSettingsValue: ''
},
{
likeableId: '0',
likeableType: 'changeLog',
myLikeValue: '0',
likeCount: '0',
dislikeCount: '0',
likeScore: '0',
individualLikes: [],
id: '6654',
pageId: 'bayes_rule_proof',
userId: 'EliezerYudkowsky',
edit: '1',
type: 'newRequirement',
createdAt: '2016-02-10 01:56:00',
auxPageId: 'conditional_probability',
oldSettingsValue: '',
newSettingsValue: ''
},
{
likeableId: '0',
likeableType: 'changeLog',
myLikeValue: '0',
likeCount: '0',
dislikeCount: '0',
likeScore: '0',
individualLikes: [],
id: '6652',
pageId: 'bayes_rule_proof',
userId: 'EliezerYudkowsky',
edit: '1',
type: 'newRequirement',
createdAt: '2016-02-10 01:55:57',
auxPageId: 'math3',
oldSettingsValue: '',
newSettingsValue: ''
},
{
likeableId: '0',
likeableType: 'changeLog',
myLikeValue: '0',
likeCount: '0',
dislikeCount: '0',
likeScore: '0',
individualLikes: [],
id: '6619',
pageId: 'bayes_rule_proof',
userId: 'EliezerYudkowsky',
edit: '1',
type: 'newTeacher',
createdAt: '2016-02-09 20:59:45',
auxPageId: '1x9',
oldSettingsValue: '',
newSettingsValue: ''
},
{
likeableId: '0',
likeableType: 'changeLog',
myLikeValue: '0',
likeCount: '0',
dislikeCount: '0',
likeScore: '0',
individualLikes: [],
id: '6618',
pageId: 'bayes_rule_proof',
userId: 'EliezerYudkowsky',
edit: '1',
type: 'newEdit',
createdAt: '2016-02-09 20:59:26',
auxPageId: '',
oldSettingsValue: '',
newSettingsValue: ''
},
{
likeableId: '0',
likeableType: 'changeLog',
myLikeValue: '0',
likeCount: '0',
dislikeCount: '0',
likeScore: '0',
individualLikes: [],
id: '6617',
pageId: 'bayes_rule_proof',
userId: 'EliezerYudkowsky',
edit: '0',
type: 'newTag',
createdAt: '2016-02-09 20:59:16',
auxPageId: 'stub_meta_tag',
oldSettingsValue: '',
newSettingsValue: ''
},
{
likeableId: '0',
likeableType: 'changeLog',
myLikeValue: '0',
likeCount: '0',
dislikeCount: '0',
likeScore: '0',
individualLikes: [],
id: '6615',
pageId: 'bayes_rule_proof',
userId: 'EliezerYudkowsky',
edit: '0',
type: 'newParent',
createdAt: '2016-02-09 20:59:12',
auxPageId: 'bayes_rule',
oldSettingsValue: '',
newSettingsValue: ''
}
],
feedSubmissions: [],
searchStrings: {},
hasChildren: 'true',
hasParents: 'true',
redAliases: {},
improvementTagIds: [],
nonMetaTagIds: [],
todos: [],
slowDownMap: 'null',
speedUpMap: 'null',
arcPageIds: 'null',
contentRequests: {
lessTechnical: {
likeableId: '4111',
likeableType: 'contentRequest',
myLikeValue: '0',
likeCount: '1',
dislikeCount: '0',
likeScore: '1',
individualLikes: [],
id: '203',
pageId: 'bayes_rule_proof',
requestType: 'lessTechnical',
createdAt: '2018-02-11 13:33:19'
},
moreTechnical: {
likeableId: '4074',
likeableType: 'contentRequest',
myLikeValue: '0',
likeCount: '1',
dislikeCount: '0',
likeScore: '1',
individualLikes: [],
id: '197',
pageId: 'bayes_rule_proof',
requestType: 'moreTechnical',
createdAt: '2017-09-30 20:02:08'
}
}
}