{
  localUrl: '../page/bayes_rule_odds.html',
  arbitalUrl: 'https://arbital.com/p/bayes_rule_odds',
  rawJsonUrl: '../raw/1x5.json',
  likeableId: '848',
  likeableType: 'page',
  myLikeValue: '0',
  likeCount: '8',
  dislikeCount: '0',
  likeScore: '8',
  individualLikes: [
    'AndrewMcKnight',
    'RonnyFernandez',
    'EranVax',
    'IanPitchford',
    'NateSoares',
    'CamSpiers',
    'SzymonWilczyski',
    'NadeemMohsin'
  ],
  pageId: 'bayes_rule_odds',
  edit: '27',
  editSummary: '',
  prevEdit: '26',
  currentEdit: '27',
  wasPublished: 'true',
  type: 'wiki',
  title: 'Bayes' rule: Odds form',
  clickbait: 'The simplest and most easily understandable form of Bayes' rule uses relative odds.',
  textLength: '6053',
  alias: 'bayes_rule_odds',
  externalUrl: '',
  sortChildrenBy: 'likes',
  hasVote: 'false',
  voteType: '',
  votesAnonymous: 'false',
  editCreatorId: 'EliezerYudkowsky',
  editCreatedAt: '2016-10-13 00:56:37',
  pageCreatorId: 'EliezerYudkowsky',
  pageCreatedAt: '2016-02-08 01:43:10',
  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: '33242',
  text: '[summary:  A form of [1lz Bayes' rule] that uses relative [1rb odds].\n\nSuppose we're trying to solve a mysterious murder, and we [1rm start out] thinking the odds of Professor Plum vs. Miss Scarlet committing the murder are 1 : 2, that is, Scarlet is twice as likely as Plum to have committed the murder.  We then observe that the victim was bludgeoned with a lead pipe.  If we think that Plum, *if* he commits a murder, is around 60% likely to use a lead pipe, and that Scarlet, *if* she commits a murder, would be around 6% likely to us a lead pipe, this implies [1rq relative likelihoods] of 10 : 1 for Plum vs. Scarlet using the pipe.\n\nThe [1rp posterior] odds for Plum vs. Scarlet, after observing the victim to have been murdered by a pipe, are $(1 : 2) \\times (10 : 1) = (10 : 2) = (5 : 1)$.  We now think Plum is around five times as likely as Scarlet to have committed the murder.]\n\nOne of the more convenient forms of [1lz Bayes' rule] uses [1rb relative odds]. Bayes' rule says that, when you observe a piece of evidence $e,$ your [1rp posterior] odds $\\mathbb O(\\boldsymbol H \\mid e)$ for your hypothesis [-vector] $\\boldsymbol H$ given $e$ is just your [1rm prior] odds $\\mathbb O(\\boldsymbol H)$ on $\\boldsymbol H$ times the [-56s] $\\mathcal L_e(\\boldsymbol H).$\n\nFor example, suppose we're trying to solve a mysterious murder, and we start out thinking the odds of Professor Plum vs. Miss Scarlet committing the murder are 1 : 2, that is, Scarlet is twice as likely as Plum to have committed the murder [1rm a priori].  We then observe that the victim was bludgeoned with a lead pipe.  If we think that Plum, *if* he commits a murder, is around 60% likely to use a lead pipe, and that Scarlet, *if* she commits a murder, would be around 6% likely to us a lead pipe, this implies [1rq relative likelihoods] of 10 : 1 for Plum vs. Scarlet using the pipe.  The [1rp posterior] odds for Plum vs. Scarlet, after observing the victim to have been murdered by a pipe, are $(1 : 2) \\times (10 : 1) = (10 : 2) = (5 : 1)$.  We now think Plum is around five times as likely as Scarlet to have committed the murder.\n\n# Odds functions\n\nLet $\\boldsymbol H$ denote a [-vector] of hypotheses. An odds function $\\mathbb O$ is a function that maps $\\boldsymbol H$ to a set of [-1rb]. For example, if $\\boldsymbol H = (H_1, H_2, H_3),$ then $\\mathbb O(\\boldsymbol H)$ might be $(6 : 2 : 1),$ which says that $H_1$ is 3x as likely as $H_2$ and 6x as likely as $H_3.$ An odds function captures our *relative* probabilities between the hypotheses in $\\boldsymbol H;$ for example, (6 : 2 : 1) odds are the same as (18 : 6 : 3) odds. We don't need to know the absolute probabilities of the $H_i$ in order to know the relative odds. All we require is that the relative odds are proportional to the absolute probabilities:\n$$\\mathbb O(\\boldsymbol H) \\propto \\mathbb P(\\boldsymbol H).$$\n\nIn the example with the death of Mr. Boddy, suppose $H_1$ denotes the proposition "Reverend Green murdered Mr. Boddy", $H_2$ denotes "Mrs. White did it", and $H_3$ denotes "Colonel Mustard did it". Let $\\boldsymbol H$ be the vector $(H_1, H_2, H_3).$ If these propositions respectively have [1rm prior] probabilities of 80%, 8%, and 4% (the remaining 8% being reserved for other hypotheses), then $\\mathbb O(\\boldsymbol H) = (80 : 8 : 4) = (20 : 2 : 1)$ represents our *relative* credences about the murder suspects — that Reverend Green is 10 times as likely to be the murderer as Miss White, who is twice as likely to be the murderer as Colonel Mustard.\n\n# Likelihood functions\n\nSuppose we discover that the victim was murdered by wrench.  Suppose we think that Reverend Green, Mrs. White, and Colonel Mustard, *if* they murdered someone, would respectively be 60%, 90%, and 30% likely to use a wrench.  Letting $e_w$ denote the observation "The victim was murdered by wrench," we would have $\\mathbb P(e_w\\mid \\boldsymbol H) = (0.6, 0.9, 0.3).$ This gives us a [-56s] defined as $\\mathcal L_{e_w}(\\boldsymbol H) = P(e_w \\mid \\boldsymbol H).$\n\n# Bayes' rule, odds form\n\nLet $\\mathbb O(\\boldsymbol H\\mid e)$ denote the [1rp posterior] odds of the hypotheses $\\boldsymbol H$ after observing evidence $e.$  [1xr Bayes' rule] then states:\n\n$$\\mathbb O(\\boldsymbol H) \\times \\mathcal L_{e}(\\boldsymbol H) = \\mathbb O(\\boldsymbol H\\mid e)$$\n\nThis says that we can multiply the relative prior credence $\\mathbb O(\\boldsymbol H)$ by the likelihood $\\mathcal L_{e}(\\boldsymbol H)$ to arrive at the relative posterior credence $\\mathbb O(\\boldsymbol H\\mid e).$ Because odds are invariant under multiplication by a positive constant, it wouldn't make any difference if the _likelihood_ function was scaled up or down by a constant, because that would only have the effect of multiplying the final odds by a constant, which does not affect them. Thus, only the [-1rq relative likelihoods] are necessary to perform the calculation; the absolute likelihoods are unnecessary. Therefore, when performing the calculation, we can simplify $\\mathcal L_e(\\boldsymbol H) = (0.6, 0.9, 0.3)$ to the relative likelihoods $(2 : 3 : 1).$\n\nIn our example, this makes the calculation quite easy. The prior odds for Green vs White vs Mustard were $(20 : 2 : 1).$ The relative likelihoods were $(0.6 : 0.9 : 0.3)$ = $(2 : 3 : 1).$ Thus, the relative posterior odds after observing $e_w$ = Mr. Boddy was killed by wrench are $(20 : 2 : 1) \\times (2 : 3 : 1) = (40 : 6 : 1).$ Given the evidence, Reverend Green is 40 times as likely as Colonel Mustard to be the killer, and 20/3 times as likely as Mrs. White.\n\nBayes' rule states that this *relative* proportioning of odds among these three suspects will be correct, regardless of how our remaining 8% probability mass is assigned to all other suspects and possibilities, or indeed, how much probability mass we assigned to other suspects to begin with. For a proof, see [1xr].\n\n# Visualization\n\n[560 Frequency diagrams], [1wy waterfall diagrams], and [1zm spotlight diagrams] may be helpful for explaining or visualizing the odds form of Bayes' rule.',
  metaText: '',
  isTextLoaded: 'true',
  isSubscribedToDiscussion: 'false',
  isSubscribedToUser: 'false',
  isSubscribedAsMaintainer: 'false',
  discussionSubscriberCount: '5',
  maintainerCount: '2',
  userSubscriberCount: '0',
  lastVisit: '2016-02-27 17:44:07',
  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: 'A form of [1lz Bayes' rule] that uses relative [1rb odds].\n\nSuppose we're trying to solve a mysterious murder, and we [1rm start out] thinking the odds of Professor Plum vs. Miss Scarlet committing the murder are 1 : 2, that is, Scarlet is twice as likely as Plum to have committed the murder.  We then observe that the victim was bludgeoned with a lead pipe.  If we think that Plum, *if* he commits a murder, is around 60% likely to use a lead pipe, and that Scarlet, *if* she commits a murder, would be around 6% likely to us a lead pipe, this implies [1rq relative likelihoods] of 10 : 1 for Plum vs. Scarlet using the pipe.\n\nThe [1rp posterior] odds for Plum vs. Scarlet, after observing the victim to have been murdered by a pipe, are $(1 : 2) \\times (10 : 1) = (10 : 2) = (5 : 1)$.  We now think Plum is around five times as likely as Scarlet to have committed the murder.'
  },
  creatorIds: [
    'NateSoares',
    'EliezerYudkowsky',
    'AlexeiAndreev'
  ],
  childIds: [
    'bayes_rule_odds_intro'
  ],
  parentIds: [
    'bayes_rule'
  ],
  commentIds: [
    '2g5'
  ],
  questionIds: [],
  tagIds: [
    'b_class_meta_tag'
  ],
  relatedIds: [],
  markIds: [],
  explanations: [
    {
      id: '2066',
      parentId: 'bayes_rule_odds',
      childId: 'bayes_rule_odds',
      type: 'subject',
      creatorId: 'AlexeiAndreev',
      createdAt: '2016-06-17 21:58:56',
      level: '3',
      isStrong: 'true',
      everPublished: 'true'
    },
    {
      id: '2113',
      parentId: 'bayes_rule_odds',
      childId: 'bayes_rule_odds_intro',
      type: 'subject',
      creatorId: 'AlexeiAndreev',
      createdAt: '2016-06-17 21:58:56',
      level: '2',
      isStrong: 'true',
      everPublished: 'true'
    },
    {
      id: '5815',
      parentId: 'bayes_rule_odds',
      childId: '5f3',
      type: 'subject',
      creatorId: 'AlexeiAndreev',
      createdAt: '2016-08-02 01:05:06',
      level: '2',
      isStrong: 'true',
      everPublished: 'true'
    },
    {
      id: '6499',
      parentId: 'bayes_rule_odds',
      childId: 'bayes_rule_fast_intro',
      type: 'subject',
      creatorId: 'EliezerYudkowsky',
      createdAt: '2016-09-29 04:41:29',
      level: '2',
      isStrong: 'true',
      everPublished: 'true'
    }
  ],
  learnMore: [
    {
      id: '5116',
      parentId: 'bayes_rule_odds',
      childId: 'bayes_rule_proof_math1',
      type: 'subject',
      creatorId: 'NateSoares',
      createdAt: '2016-07-10 21:05:20',
      level: '3',
      isStrong: 'false',
      everPublished: 'true'
    },
    {
      id: '5811',
      parentId: 'bayes_rule_odds',
      childId: 'bayes_rule_multiple',
      type: 'subject',
      creatorId: 'AlexeiAndreev',
      createdAt: '2016-08-02 00:58:51',
      level: '3',
      isStrong: 'false',
      everPublished: 'true'
    },
    {
      id: '5799',
      parentId: 'bayes_rule_odds',
      childId: 'bayes_log_odds',
      type: 'subject',
      creatorId: 'AlexeiAndreev',
      createdAt: '2016-08-02 00:35:31',
      level: '2',
      isStrong: 'false',
      everPublished: 'true'
    },
    {
      id: '5802',
      parentId: 'bayes_rule_odds',
      childId: 'bayes_rule_proportional',
      type: 'subject',
      creatorId: 'AlexeiAndreev',
      createdAt: '2016-08-02 00:44:19',
      level: '2',
      isStrong: 'false',
      everPublished: 'true'
    },
    {
      id: '5162',
      parentId: 'bayes_rule_odds',
      childId: 'bayes_odds_to_probability',
      type: 'subject',
      creatorId: 'NateSoares',
      createdAt: '2016-07-10 22:10:26',
      level: '2',
      isStrong: 'false',
      everPublished: 'true'
    }
  ],
  requirements: [
    {
      id: '2061',
      parentId: 'bayes_rule',
      childId: 'bayes_rule_odds',
      type: 'requirement',
      creatorId: 'AlexeiAndreev',
      createdAt: '2016-06-17 21:58:56',
      level: '2',
      isStrong: 'true',
      everPublished: 'true'
    },
    {
      id: '2063',
      parentId: 'conditional_probability',
      childId: 'bayes_rule_odds',
      type: 'requirement',
      creatorId: 'AlexeiAndreev',
      createdAt: '2016-06-17 21:58:56',
      level: '2',
      isStrong: 'true',
      everPublished: 'true'
    },
    {
      id: '5127',
      parentId: 'odds',
      childId: 'bayes_rule_odds',
      type: 'requirement',
      creatorId: 'NateSoares',
      createdAt: '2016-07-10 21:35:48',
      level: '3',
      isStrong: 'true',
      everPublished: 'true'
    },
    {
      id: '5634',
      parentId: 'math2',
      childId: 'bayes_rule_odds',
      type: 'requirement',
      creatorId: 'AlexeiAndreev',
      createdAt: '2016-07-26 16:50:39',
      level: '2',
      isStrong: 'true',
      everPublished: 'true'
    }
  ],
  subjects: [
    {
      id: '2065',
      parentId: 'odds',
      childId: 'bayes_rule_odds',
      type: 'subject',
      creatorId: 'AlexeiAndreev',
      createdAt: '2016-06-17 21:58:56',
      level: '3',
      isStrong: 'false',
      everPublished: 'true'
    },
    {
      id: '2066',
      parentId: 'bayes_rule_odds',
      childId: 'bayes_rule_odds',
      type: 'subject',
      creatorId: 'AlexeiAndreev',
      createdAt: '2016-06-17 21:58:56',
      level: '3',
      isStrong: 'true',
      everPublished: 'true'
    },
    {
      id: '5635',
      parentId: 'bayes_rule',
      childId: 'bayes_rule_odds',
      type: 'subject',
      creatorId: 'AlexeiAndreev',
      createdAt: '2016-07-26 16:54:00',
      level: '3',
      isStrong: 'false',
      everPublished: 'true'
    },
    {
      id: '5762',
      parentId: 'likelihood_function',
      childId: 'bayes_rule_odds',
      type: 'subject',
      creatorId: 'AlexeiAndreev',
      createdAt: '2016-08-01 23:33:51',
      level: '1',
      isStrong: 'true',
      everPublished: 'true'
    }
  ],
  lenses: [
    {
      id: '10',
      pageId: 'bayes_rule_odds',
      lensId: 'bayes_rule_odds_intro',
      lensIndex: '0',
      lensName: 'Intro',
      lensSubtitle: '',
      createdBy: '1',
      createdAt: '2016-06-17 21:58:56',
      updatedBy: '32',
      updatedAt: '2016-07-08 15:42:10'
    }
  ],
  lensParentId: '',
  pathPages: [],
  learnMoreTaughtMap: {
    '1x5': [
      '1yd',
      '1zg'
    ]
  },
  learnMoreCoveredMap: {
    '1lz': [
      '1yd',
      '1zg',
      '1zj',
      '554'
    ]
  },
  learnMoreRequiredMap: {
    '1x5': [
      '1zg'
    ]
  },
  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: '20132',
      pageId: 'bayes_rule_odds',
      userId: 'EliezerYudkowsky',
      edit: '27',
      type: 'newEdit',
      createdAt: '2016-10-13 00:56:37',
      auxPageId: '',
      oldSettingsValue: '',
      newSettingsValue: ''
    },
    {
      likeableId: '0',
      likeableType: 'changeLog',
      myLikeValue: '0',
      likeCount: '0',
      dislikeCount: '0',
      likeScore: '0',
      individualLikes: [],
      id: '20084',
      pageId: 'bayes_rule_odds',
      userId: 'AlexeiAndreev',
      edit: '0',
      type: 'deleteTeacher',
      createdAt: '2016-10-11 18:39:26',
      auxPageId: 'odds_technical',
      oldSettingsValue: '',
      newSettingsValue: ''
    },
    {
      likeableId: '0',
      likeableType: 'changeLog',
      myLikeValue: '0',
      likeCount: '0',
      dislikeCount: '0',
      likeScore: '0',
      individualLikes: [],
      id: '20078',
      pageId: 'bayes_rule_odds',
      userId: 'AlexeiAndreev',
      edit: '0',
      type: 'newTeacher',
      createdAt: '2016-10-11 18:36:59',
      auxPageId: 'odds_technical',
      oldSettingsValue: '',
      newSettingsValue: ''
    },
    {
      likeableId: '0',
      likeableType: 'changeLog',
      myLikeValue: '0',
      likeCount: '0',
      dislikeCount: '0',
      likeScore: '0',
      individualLikes: [],
      id: '19748',
      pageId: 'bayes_rule_odds',
      userId: 'EliezerYudkowsky',
      edit: '0',
      type: 'newTeacher',
      createdAt: '2016-09-29 04:41:29',
      auxPageId: 'bayes_rule_fast_intro',
      oldSettingsValue: '',
      newSettingsValue: ''
    },
    {
      likeableId: '0',
      likeableType: 'changeLog',
      myLikeValue: '0',
      likeCount: '0',
      dislikeCount: '0',
      likeScore: '0',
      individualLikes: [],
      id: '18187',
      pageId: 'bayes_rule_odds',
      userId: 'EricBruylant',
      edit: '0',
      type: 'newTag',
      createdAt: '2016-08-02 18:30:43',
      auxPageId: 'b_class_meta_tag',
      oldSettingsValue: '',
      newSettingsValue: ''
    },
    {
      likeableId: '0',
      likeableType: 'changeLog',
      myLikeValue: '0',
      likeCount: '0',
      dislikeCount: '0',
      likeScore: '0',
      individualLikes: [],
      id: '18053',
      pageId: 'bayes_rule_odds',
      userId: 'AlexeiAndreev',
      edit: '0',
      type: 'newTeacher',
      createdAt: '2016-08-02 01:05:07',
      auxPageId: '5f3',
      oldSettingsValue: '',
      newSettingsValue: ''
    },
    {
      likeableId: '0',
      likeableType: 'changeLog',
      myLikeValue: '0',
      likeCount: '0',
      dislikeCount: '0',
      likeScore: '0',
      individualLikes: [],
      id: '18048',
      pageId: 'bayes_rule_odds',
      userId: 'AlexeiAndreev',
      edit: '0',
      type: 'newTeacher',
      createdAt: '2016-08-02 00:58:52',
      auxPageId: 'bayes_rule_multiple',
      oldSettingsValue: '',
      newSettingsValue: ''
    },
    {
      likeableId: '0',
      likeableType: 'changeLog',
      myLikeValue: '0',
      likeCount: '0',
      dislikeCount: '0',
      likeScore: '0',
      individualLikes: [],
      id: '18031',
      pageId: 'bayes_rule_odds',
      userId: 'AlexeiAndreev',
      edit: '0',
      type: 'newTeacher',
      createdAt: '2016-08-02 00:44:20',
      auxPageId: 'bayes_rule_proportional',
      oldSettingsValue: '',
      newSettingsValue: ''
    },
    {
      likeableId: '0',
      likeableType: 'changeLog',
      myLikeValue: '0',
      likeCount: '0',
      dislikeCount: '0',
      likeScore: '0',
      individualLikes: [],
      id: '18023',
      pageId: 'bayes_rule_odds',
      userId: 'AlexeiAndreev',
      edit: '0',
      type: 'newTeacher',
      createdAt: '2016-08-02 00:35:32',
      auxPageId: 'bayes_log_odds',
      oldSettingsValue: '',
      newSettingsValue: ''
    },
    {
      likeableId: '0',
      likeableType: 'changeLog',
      myLikeValue: '0',
      likeCount: '0',
      dislikeCount: '0',
      likeScore: '0',
      individualLikes: [],
      id: '18009',
      pageId: 'bayes_rule_odds',
      userId: 'AlexeiAndreev',
      edit: '0',
      type: 'deleteRequiredBy',
      createdAt: '2016-08-02 00:29:58',
      auxPageId: 'bayes_rule_functional',
      oldSettingsValue: '',
      newSettingsValue: ''
    },
    {
      likeableId: '0',
      likeableType: 'changeLog',
      myLikeValue: '0',
      likeCount: '0',
      dislikeCount: '0',
      likeScore: '0',
      individualLikes: [],
      id: '17969',
      pageId: 'bayes_rule_odds',
      userId: 'AlexeiAndreev',
      edit: '0',
      type: 'deleteTeacher',
      createdAt: '2016-08-02 00:17:17',
      auxPageId: 'bayes_rule_proof',
      oldSettingsValue: '',
      newSettingsValue: ''
    },
    {
      likeableId: '0',
      likeableType: 'changeLog',
      myLikeValue: '0',
      likeCount: '0',
      dislikeCount: '0',
      likeScore: '0',
      individualLikes: [],
      id: '17966',
      pageId: 'bayes_rule_odds',
      userId: 'AlexeiAndreev',
      edit: '0',
      type: 'deleteRequiredBy',
      createdAt: '2016-08-02 00:15:25',
      auxPageId: 'bayes_probability_notation_math1',
      oldSettingsValue: '',
      newSettingsValue: ''
    },
    {
      likeableId: '0',
      likeableType: 'changeLog',
      myLikeValue: '0',
      likeCount: '0',
      dislikeCount: '0',
      likeScore: '0',
      individualLikes: [],
      id: '17951',
      pageId: 'bayes_rule_odds',
      userId: 'AlexeiAndreev',
      edit: '0',
      type: 'newSubject',
      createdAt: '2016-08-01 23:33:52',
      auxPageId: 'likelihood_function',
      oldSettingsValue: '',
      newSettingsValue: ''
    },
    {
      likeableId: '0',
      likeableType: 'changeLog',
      myLikeValue: '0',
      likeCount: '0',
      dislikeCount: '0',
      likeScore: '0',
      individualLikes: [],
      id: '17949',
      pageId: 'bayes_rule_odds',
      userId: 'AlexeiAndreev',
      edit: '0',
      type: 'deleteRequirement',
      createdAt: '2016-08-01 23:32:53',
      auxPageId: 'reads_algebra',
      oldSettingsValue: '',
      newSettingsValue: ''
    },
    {
      likeableId: '0',
      likeableType: 'changeLog',
      myLikeValue: '0',
      likeCount: '0',
      dislikeCount: '0',
      likeScore: '0',
      individualLikes: [],
      id: '17533',
      pageId: 'bayes_rule_odds',
      userId: 'AlexeiAndreev',
      edit: '0',
      type: 'newSubject',
      createdAt: '2016-07-26 16:54:00',
      auxPageId: 'bayes_rule',
      oldSettingsValue: '',
      newSettingsValue: ''
    },
    {
      likeableId: '0',
      likeableType: 'changeLog',
      myLikeValue: '0',
      likeCount: '0',
      dislikeCount: '0',
      likeScore: '0',
      individualLikes: [],
      id: '17531',
      pageId: 'bayes_rule_odds',
      userId: 'AlexeiAndreev',
      edit: '0',
      type: 'newRequirement',
      createdAt: '2016-07-26 16:50:40',
      auxPageId: 'math2',
      oldSettingsValue: '',
      newSettingsValue: ''
    },
    {
      likeableId: '0',
      likeableType: 'changeLog',
      myLikeValue: '0',
      likeCount: '0',
      dislikeCount: '0',
      likeScore: '0',
      individualLikes: [],
      id: '16519',
      pageId: 'bayes_rule_odds',
      userId: 'NateSoares',
      edit: '0',
      type: 'deleteRequiredBy',
      createdAt: '2016-07-10 22:21:11',
      auxPageId: 'bayes_science_virtues',
      oldSettingsValue: '',
      newSettingsValue: ''
    },
    {
      likeableId: '0',
      likeableType: 'changeLog',
      myLikeValue: '0',
      likeCount: '0',
      dislikeCount: '0',
      likeScore: '0',
      individualLikes: [],
      id: '16500',
      pageId: 'bayes_rule_odds',
      userId: 'NateSoares',
      edit: '0',
      type: 'newTeacher',
      createdAt: '2016-07-10 22:10:27',
      auxPageId: 'bayes_odds_to_probability',
      oldSettingsValue: '',
      newSettingsValue: ''
    },
    {
      likeableId: '0',
      likeableType: 'changeLog',
      myLikeValue: '0',
      likeCount: '0',
      dislikeCount: '0',
      likeScore: '0',
      individualLikes: [],
      id: '16414',
      pageId: 'bayes_rule_odds',
      userId: 'NateSoares',
      edit: '0',
      type: 'newRequirement',
      createdAt: '2016-07-10 21:35:49',
      auxPageId: 'odds',
      oldSettingsValue: '',
      newSettingsValue: ''
    },
    {
      likeableId: '0',
      likeableType: 'changeLog',
      myLikeValue: '0',
      likeCount: '0',
      dislikeCount: '0',
      likeScore: '0',
      individualLikes: [],
      id: '16404',
      pageId: 'bayes_rule_odds',
      userId: 'NateSoares',
      edit: '0',
      type: 'newTeacher',
      createdAt: '2016-07-10 21:27:23',
      auxPageId: 'bayes_rule_proof',
      oldSettingsValue: '',
      newSettingsValue: ''
    },
    {
      likeableId: '0',
      likeableType: 'changeLog',
      myLikeValue: '0',
      likeCount: '0',
      dislikeCount: '0',
      likeScore: '0',
      individualLikes: [],
      id: '16384',
      pageId: 'bayes_rule_odds',
      userId: 'NateSoares',
      edit: '0',
      type: 'newTeacher',
      createdAt: '2016-07-10 21:05:21',
      auxPageId: 'bayes_rule_proof_math1',
      oldSettingsValue: '',
      newSettingsValue: ''
    },
    {
      likeableId: '0',
      likeableType: 'changeLog',
      myLikeValue: '0',
      likeCount: '0',
      dislikeCount: '0',
      likeScore: '0',
      individualLikes: [],
      id: '16310',
      pageId: 'bayes_rule_odds',
      userId: 'AlexeiAndreev',
      edit: '26',
      type: 'newEdit',
      createdAt: '2016-07-09 23:44:44',
      auxPageId: '',
      oldSettingsValue: '',
      newSettingsValue: ''
    },
    {
      likeableId: '0',
      likeableType: 'changeLog',
      myLikeValue: '0',
      likeCount: '0',
      dislikeCount: '0',
      likeScore: '0',
      individualLikes: [],
      id: '16309',
      pageId: 'bayes_rule_odds',
      userId: 'AlexeiAndreev',
      edit: '25',
      type: 'newEdit',
      createdAt: '2016-07-09 23:44:19',
      auxPageId: '',
      oldSettingsValue: '',
      newSettingsValue: ''
    },
    {
      likeableId: '0',
      likeableType: 'changeLog',
      myLikeValue: '0',
      likeCount: '0',
      dislikeCount: '0',
      likeScore: '0',
      individualLikes: [],
      id: '16222',
      pageId: 'bayes_rule_odds',
      userId: 'NateSoares',
      edit: '24',
      type: 'newEdit',
      createdAt: '2016-07-08 15:50:19',
      auxPageId: '',
      oldSettingsValue: '',
      newSettingsValue: ''
    },
    {
      likeableId: '0',
      likeableType: 'changeLog',
      myLikeValue: '0',
      likeCount: '0',
      dislikeCount: '0',
      likeScore: '0',
      individualLikes: [],
      id: '16221',
      pageId: 'bayes_rule_odds',
      userId: 'NateSoares',
      edit: '23',
      type: 'newEdit',
      createdAt: '2016-07-08 15:50:05',
      auxPageId: '',
      oldSettingsValue: '',
      newSettingsValue: ''
    },
    {
      likeableId: '0',
      likeableType: 'changeLog',
      myLikeValue: '0',
      likeCount: '0',
      dislikeCount: '0',
      likeScore: '0',
      individualLikes: [],
      id: '16215',
      pageId: 'bayes_rule_odds',
      userId: 'NateSoares',
      edit: '0',
      type: 'deleteTeacher',
      createdAt: '2016-07-08 15:44:01',
      auxPageId: '1x9',
      oldSettingsValue: '',
      newSettingsValue: ''
    },
    {
      likeableId: '0',
      likeableType: 'changeLog',
      myLikeValue: '0',
      likeCount: '0',
      dislikeCount: '0',
      likeScore: '0',
      individualLikes: [],
      id: '16211',
      pageId: 'bayes_rule_odds',
      userId: 'NateSoares',
      edit: '0',
      type: 'deleteTeacher',
      createdAt: '2016-07-08 15:43:46',
      auxPageId: '1x7',
      oldSettingsValue: '',
      newSettingsValue: ''
    },
    {
      likeableId: '0',
      likeableType: 'changeLog',
      myLikeValue: '0',
      likeCount: '0',
      dislikeCount: '0',
      likeScore: '0',
      individualLikes: [],
      id: '16205',
      pageId: 'bayes_rule_odds',
      userId: 'NateSoares',
      edit: '0',
      type: 'deleteChild',
      createdAt: '2016-07-08 15:43:36',
      auxPageId: '1x7',
      oldSettingsValue: '',
      newSettingsValue: ''
    },
    {
      likeableId: '0',
      likeableType: 'changeLog',
      myLikeValue: '0',
      likeCount: '0',
      dislikeCount: '0',
      likeScore: '0',
      individualLikes: [],
      id: '16200',
      pageId: 'bayes_rule_odds',
      userId: 'NateSoares',
      edit: '0',
      type: 'lensOrderChanged',
      createdAt: '2016-07-08 15:42:03',
      auxPageId: '',
      oldSettingsValue: '',
      newSettingsValue: ''
    },
    {
      likeableId: '0',
      likeableType: 'changeLog',
      myLikeValue: '0',
      likeCount: '0',
      dislikeCount: '0',
      likeScore: '0',
      individualLikes: [],
      id: '16199',
      pageId: 'bayes_rule_odds',
      userId: 'NateSoares',
      edit: '0',
      type: 'lensOrderChanged',
      createdAt: '2016-07-08 15:42:01',
      auxPageId: '',
      oldSettingsValue: '',
      newSettingsValue: ''
    },
    {
      likeableId: '0',
      likeableType: 'changeLog',
      myLikeValue: '0',
      likeCount: '0',
      dislikeCount: '0',
      likeScore: '0',
      individualLikes: [],
      id: '16192',
      pageId: 'bayes_rule_odds',
      userId: 'NateSoares',
      edit: '0',
      type: 'deleteChild',
      createdAt: '2016-07-08 15:40:36',
      auxPageId: '1x9',
      oldSettingsValue: '',
      newSettingsValue: ''
    },
    {
      likeableId: '0',
      likeableType: 'changeLog',
      myLikeValue: '0',
      likeCount: '0',
      dislikeCount: '0',
      likeScore: '0',
      individualLikes: [],
      id: '16161',
      pageId: 'bayes_rule_odds',
      userId: 'NateSoares',
      edit: '22',
      type: 'newEdit',
      createdAt: '2016-07-08 15:07:10',
      auxPageId: '',
      oldSettingsValue: '',
      newSettingsValue: ''
    },
    {
      likeableId: '0',
      likeableType: 'changeLog',
      myLikeValue: '0',
      likeCount: '0',
      dislikeCount: '0',
      likeScore: '0',
      individualLikes: [],
      id: '16160',
      pageId: 'bayes_rule_odds',
      userId: 'NateSoares',
      edit: '21',
      type: 'newEdit',
      createdAt: '2016-07-08 15:04:47',
      auxPageId: '',
      oldSettingsValue: '',
      newSettingsValue: ''
    },
    {
      likeableId: '0',
      likeableType: 'changeLog',
      myLikeValue: '0',
      likeCount: '0',
      dislikeCount: '0',
      likeScore: '0',
      individualLikes: [],
      id: '15981',
      pageId: 'bayes_rule_odds',
      userId: 'NateSoares',
      edit: '20',
      type: 'newEdit',
      createdAt: '2016-07-07 15:22:16',
      auxPageId: '',
      oldSettingsValue: '',
      newSettingsValue: ''
    },
    {
      likeableId: '0',
      likeableType: 'changeLog',
      myLikeValue: '0',
      likeCount: '0',
      dislikeCount: '0',
      likeScore: '0',
      individualLikes: [],
      id: '15980',
      pageId: 'bayes_rule_odds',
      userId: 'NateSoares',
      edit: '19',
      type: 'newEdit',
      createdAt: '2016-07-07 15:21:40',
      auxPageId: '',
      oldSettingsValue: '',
      newSettingsValue: ''
    },
    {
      likeableId: '0',
      likeableType: 'changeLog',
      myLikeValue: '0',
      likeCount: '0',
      dislikeCount: '0',
      likeScore: '0',
      individualLikes: [],
      id: '15979',
      pageId: 'bayes_rule_odds',
      userId: 'NateSoares',
      edit: '18',
      type: 'newEdit',
      createdAt: '2016-07-07 15:20:54',
      auxPageId: '',
      oldSettingsValue: '',
      newSettingsValue: ''
    },
    {
      likeableId: '0',
      likeableType: 'changeLog',
      myLikeValue: '0',
      likeCount: '0',
      dislikeCount: '0',
      likeScore: '0',
      individualLikes: [],
      id: '15955',
      pageId: 'bayes_rule_odds',
      userId: 'NateSoares',
      edit: '17',
      type: 'newEdit',
      createdAt: '2016-07-07 06:37:56',
      auxPageId: '',
      oldSettingsValue: '',
      newSettingsValue: ''
    },
    {
      likeableId: '0',
      likeableType: 'changeLog',
      myLikeValue: '0',
      likeCount: '0',
      dislikeCount: '0',
      likeScore: '0',
      individualLikes: [],
      id: '15645',
      pageId: 'bayes_rule_odds',
      userId: 'NateSoares',
      edit: '16',
      type: 'newEdit',
      createdAt: '2016-07-06 07:26:48',
      auxPageId: '',
      oldSettingsValue: '',
      newSettingsValue: ''
    },
    {
      likeableId: '0',
      likeableType: 'changeLog',
      myLikeValue: '0',
      likeCount: '0',
      dislikeCount: '0',
      likeScore: '0',
      individualLikes: [],
      id: '15644',
      pageId: 'bayes_rule_odds',
      userId: 'NateSoares',
      edit: '15',
      type: 'newEdit',
      createdAt: '2016-07-06 07:26:18',
      auxPageId: '',
      oldSettingsValue: '',
      newSettingsValue: ''
    },
    {
      likeableId: '0',
      likeableType: 'changeLog',
      myLikeValue: '0',
      likeCount: '0',
      dislikeCount: '0',
      likeScore: '0',
      individualLikes: [],
      id: '15600',
      pageId: 'bayes_rule_odds',
      userId: 'NateSoares',
      edit: '14',
      type: 'newEdit',
      createdAt: '2016-07-06 06:40:27',
      auxPageId: '',
      oldSettingsValue: '',
      newSettingsValue: ''
    },
    {
      likeableId: '0',
      likeableType: 'changeLog',
      myLikeValue: '0',
      likeCount: '0',
      dislikeCount: '0',
      likeScore: '0',
      individualLikes: [],
      id: '15599',
      pageId: 'bayes_rule_odds',
      userId: 'NateSoares',
      edit: '13',
      type: 'newEdit',
      createdAt: '2016-07-06 06:40:06',
      auxPageId: '',
      oldSettingsValue: '',
      newSettingsValue: ''
    },
    {
      likeableId: '0',
      likeableType: 'changeLog',
      myLikeValue: '0',
      likeCount: '0',
      dislikeCount: '0',
      likeScore: '0',
      individualLikes: [],
      id: '8105',
      pageId: 'bayes_rule_odds',
      userId: 'NateSoares',
      edit: '10',
      type: 'newEdit',
      createdAt: '2016-03-03 03:14:12',
      auxPageId: '',
      oldSettingsValue: '',
      newSettingsValue: ''
    },
    {
      likeableId: '0',
      likeableType: 'changeLog',
      myLikeValue: '0',
      likeCount: '0',
      dislikeCount: '0',
      likeScore: '0',
      individualLikes: [],
      id: '8104',
      pageId: 'bayes_rule_odds',
      userId: 'NateSoares',
      edit: '9',
      type: 'newEdit',
      createdAt: '2016-03-03 03:12:45',
      auxPageId: '',
      oldSettingsValue: '',
      newSettingsValue: ''
    },
    {
      likeableId: '0',
      likeableType: 'changeLog',
      myLikeValue: '0',
      likeCount: '0',
      dislikeCount: '0',
      likeScore: '0',
      individualLikes: [],
      id: '7436',
      pageId: 'bayes_rule_odds',
      userId: 'EliezerYudkowsky',
      edit: '8',
      type: 'newRequiredBy',
      createdAt: '2016-02-19 06:56:13',
      auxPageId: 'bayes_science_virtues',
      oldSettingsValue: '',
      newSettingsValue: ''
    },
    {
      likeableId: '0',
      likeableType: 'changeLog',
      myLikeValue: '0',
      likeCount: '0',
      dislikeCount: '0',
      likeScore: '0',
      individualLikes: [],
      id: '7430',
      pageId: 'bayes_rule_odds',
      userId: 'EliezerYudkowsky',
      edit: '0',
      type: 'deleteUsedAsTag',
      createdAt: '2016-02-19 06:55:57',
      auxPageId: 'bayes_science_virtues',
      oldSettingsValue: '',
      newSettingsValue: ''
    },
    {
      likeableId: '0',
      likeableType: 'changeLog',
      myLikeValue: '0',
      likeCount: '0',
      dislikeCount: '0',
      likeScore: '0',
      individualLikes: [],
      id: '7424',
      pageId: 'bayes_rule_odds',
      userId: 'EliezerYudkowsky',
      edit: '8',
      type: 'newUsedAsTag',
      createdAt: '2016-02-19 06:55:35',
      auxPageId: 'bayes_science_virtues',
      oldSettingsValue: '',
      newSettingsValue: ''
    },
    {
      likeableId: '0',
      likeableType: 'changeLog',
      myLikeValue: '0',
      likeCount: '0',
      dislikeCount: '0',
      likeScore: '0',
      individualLikes: [],
      id: '7397',
      pageId: 'bayes_rule_odds',
      userId: 'EliezerYudkowsky',
      edit: '8',
      type: 'newRequiredBy',
      createdAt: '2016-02-18 20:44:51',
      auxPageId: 'bayes_extraordinary_claims',
      oldSettingsValue: '',
      newSettingsValue: ''
    },
    {
      likeableId: '0',
      likeableType: 'changeLog',
      myLikeValue: '0',
      likeCount: '0',
      dislikeCount: '0',
      likeScore: '0',
      individualLikes: [],
      id: '7208',
      pageId: 'bayes_rule_odds',
      userId: 'EliezerYudkowsky',
      edit: '8',
      type: 'newTeacher',
      createdAt: '2016-02-16 06:14:40',
      auxPageId: '1x7',
      oldSettingsValue: '',
      newSettingsValue: ''
    },
    {
      likeableId: '0',
      likeableType: 'changeLog',
      myLikeValue: '0',
      likeCount: '0',
      dislikeCount: '0',
      likeScore: '0',
      individualLikes: [],
      id: '7158',
      pageId: 'bayes_rule_odds',
      userId: 'EliezerYudkowsky',
      edit: '8',
      type: 'newRequiredBy',
      createdAt: '2016-02-16 05:35:49',
      auxPageId: 'bayes_rule_details',
      oldSettingsValue: '',
      newSettingsValue: ''
    },
    {
      likeableId: '0',
      likeableType: 'changeLog',
      myLikeValue: '0',
      likeCount: '0',
      dislikeCount: '0',
      likeScore: '0',
      individualLikes: [],
      id: '7104',
      pageId: 'bayes_rule_odds',
      userId: 'EliezerYudkowsky',
      edit: '8',
      type: 'newEdit',
      createdAt: '2016-02-14 00:08:03',
      auxPageId: '',
      oldSettingsValue: '',
      newSettingsValue: ''
    },
    {
      likeableId: '0',
      likeableType: 'changeLog',
      myLikeValue: '0',
      likeCount: '0',
      dislikeCount: '0',
      likeScore: '0',
      individualLikes: [],
      id: '7103',
      pageId: 'bayes_rule_odds',
      userId: 'EliezerYudkowsky',
      edit: '7',
      type: 'newEdit',
      createdAt: '2016-02-14 00:06:39',
      auxPageId: '',
      oldSettingsValue: '',
      newSettingsValue: ''
    },
    {
      likeableId: '0',
      likeableType: 'changeLog',
      myLikeValue: '0',
      likeCount: '0',
      dislikeCount: '0',
      likeScore: '0',
      individualLikes: [],
      id: '7096',
      pageId: 'bayes_rule_odds',
      userId: 'EliezerYudkowsky',
      edit: '6',
      type: 'newTeacher',
      createdAt: '2016-02-13 23:02:24',
      auxPageId: 'bayes_rule_guide',
      oldSettingsValue: '',
      newSettingsValue: ''
    },
    {
      likeableId: '0',
      likeableType: 'changeLog',
      myLikeValue: '0',
      likeCount: '0',
      dislikeCount: '0',
      likeScore: '0',
      individualLikes: [],
      id: '7059',
      pageId: 'bayes_rule_odds',
      userId: 'EliezerYudkowsky',
      edit: '6',
      type: 'newRequiredBy',
      createdAt: '2016-02-13 21:26:40',
      auxPageId: 'bayes_rule_proportional',
      oldSettingsValue: '',
      newSettingsValue: ''
    },
    {
      likeableId: '0',
      likeableType: 'changeLog',
      myLikeValue: '0',
      likeCount: '0',
      dislikeCount: '0',
      likeScore: '0',
      individualLikes: [],
      id: '7029',
      pageId: 'bayes_rule_odds',
      userId: 'EliezerYudkowsky',
      edit: '6',
      type: 'newRequiredBy',
      createdAt: '2016-02-13 20:50:00',
      auxPageId: 'bayes_rule_functional',
      oldSettingsValue: '',
      newSettingsValue: ''
    },
    {
      likeableId: '0',
      likeableType: 'changeLog',
      myLikeValue: '0',
      likeCount: '0',
      dislikeCount: '0',
      likeScore: '0',
      individualLikes: [],
      id: '6996',
      pageId: 'bayes_rule_odds',
      userId: 'EliezerYudkowsky',
      edit: '6',
      type: 'newRequiredBy',
      createdAt: '2016-02-13 20:01:39',
      auxPageId: 'bayes_log_odds',
      oldSettingsValue: '',
      newSettingsValue: ''
    },
    {
      likeableId: '0',
      likeableType: 'changeLog',
      myLikeValue: '0',
      likeCount: '0',
      dislikeCount: '0',
      likeScore: '0',
      individualLikes: [],
      id: '6971',
      pageId: 'bayes_rule_odds',
      userId: 'EliezerYudkowsky',
      edit: '6',
      type: 'newRequiredBy',
      createdAt: '2016-02-13 19:03:12',
      auxPageId: 'bayes_rule_multiple',
      oldSettingsValue: '',
      newSettingsValue: ''
    },
    {
      likeableId: '0',
      likeableType: 'changeLog',
      myLikeValue: '0',
      likeCount: '0',
      dislikeCount: '0',
      likeScore: '0',
      individualLikes: [],
      id: '6849',
      pageId: 'bayes_rule_odds',
      userId: 'EliezerYudkowsky',
      edit: '0',
      type: 'deleteRequiredBy',
      createdAt: '2016-02-11 04:00:13',
      auxPageId: 'bayes_probability_notation',
      oldSettingsValue: '',
      newSettingsValue: ''
    },
    {
      likeableId: '0',
      likeableType: 'changeLog',
      myLikeValue: '0',
      likeCount: '0',
      dislikeCount: '0',
      likeScore: '0',
      individualLikes: [],
      id: '6802',
      pageId: 'bayes_rule_odds',
      userId: 'EliezerYudkowsky',
      edit: '6',
      type: 'newRequiredBy',
      createdAt: '2016-02-11 03:36:23',
      auxPageId: 'bayes_probability_notation_math1',
      oldSettingsValue: '',
      newSettingsValue: ''
    },
    {
      likeableId: '0',
      likeableType: 'changeLog',
      myLikeValue: '0',
      likeCount: '0',
      dislikeCount: '0',
      likeScore: '0',
      individualLikes: [],
      id: '6770',
      pageId: 'bayes_rule_odds',
      userId: 'EliezerYudkowsky',
      edit: '6',
      type: 'newTeacher',
      createdAt: '2016-02-11 03:08:45',
      auxPageId: 'bayes_rule_odds_intro',
      oldSettingsValue: '',
      newSettingsValue: ''
    },
    {
      likeableId: '0',
      likeableType: 'changeLog',
      myLikeValue: '0',
      likeCount: '0',
      dislikeCount: '0',
      likeScore: '0',
      individualLikes: [],
      id: '6710',
      pageId: 'bayes_rule_odds',
      userId: 'EliezerYudkowsky',
      edit: '6',
      type: 'newRequiredBy',
      createdAt: '2016-02-10 20:55:57',
      auxPageId: 'bayes_probability_notation',
      oldSettingsValue: '',
      newSettingsValue: ''
    },
    {
      likeableId: '0',
      likeableType: 'changeLog',
      myLikeValue: '0',
      likeCount: '0',
      dislikeCount: '0',
      likeScore: '0',
      individualLikes: [],
      id: '6688',
      pageId: 'bayes_rule_odds',
      userId: 'EliezerYudkowsky',
      edit: '0',
      type: 'deleteRequiredBy',
      createdAt: '2016-02-10 05:00:42',
      auxPageId: 'bayes_rule_elimination',
      oldSettingsValue: '',
      newSettingsValue: ''
    },
    {
      likeableId: '0',
      likeableType: 'changeLog',
      myLikeValue: '0',
      likeCount: '0',
      dislikeCount: '0',
      likeScore: '0',
      individualLikes: [],
      id: '6686',
      pageId: 'bayes_rule_odds',
      userId: 'EliezerYudkowsky',
      edit: '6',
      type: 'newRequiredBy',
      createdAt: '2016-02-10 05:00:35',
      auxPageId: 'bayes_rule_elimination',
      oldSettingsValue: '',
      newSettingsValue: ''
    },
    {
      likeableId: '0',
      likeableType: 'changeLog',
      myLikeValue: '0',
      likeCount: '0',
      dislikeCount: '0',
      likeScore: '0',
      individualLikes: [],
      id: '6612',
      pageId: 'bayes_rule_odds',
      userId: 'EliezerYudkowsky',
      edit: '6',
      type: 'newTeacher',
      createdAt: '2016-02-09 20:46:24',
      auxPageId: '1x9',
      oldSettingsValue: '',
      newSettingsValue: ''
    },
    {
      likeableId: '0',
      likeableType: 'changeLog',
      myLikeValue: '0',
      likeCount: '0',
      dislikeCount: '0',
      likeScore: '0',
      individualLikes: [],
      id: '6585',
      pageId: 'bayes_rule_odds',
      userId: 'EliezerYudkowsky',
      edit: '6',
      type: 'newChild',
      createdAt: '2016-02-08 05:16:44',
      auxPageId: '1x9',
      oldSettingsValue: '',
      newSettingsValue: ''
    },
    {
      likeableId: '0',
      likeableType: 'changeLog',
      myLikeValue: '0',
      likeCount: '0',
      dislikeCount: '0',
      likeScore: '0',
      individualLikes: [],
      id: '6575',
      pageId: 'bayes_rule_odds',
      userId: 'EliezerYudkowsky',
      edit: '6',
      type: 'newTeacher',
      createdAt: '2016-02-08 04:54:11',
      auxPageId: 'bayes_rule_odds_intro',
      oldSettingsValue: '',
      newSettingsValue: ''
    },
    {
      likeableId: '0',
      likeableType: 'changeLog',
      myLikeValue: '0',
      likeCount: '0',
      dislikeCount: '0',
      likeScore: '0',
      individualLikes: [],
      id: '6565',
      pageId: 'bayes_rule_odds',
      userId: 'EliezerYudkowsky',
      edit: '6',
      type: 'newChild',
      createdAt: '2016-02-08 04:52:51',
      auxPageId: 'bayes_rule_odds_intro',
      oldSettingsValue: '',
      newSettingsValue: ''
    },
    {
      likeableId: '0',
      likeableType: 'changeLog',
      myLikeValue: '0',
      likeCount: '0',
      dislikeCount: '0',
      likeScore: '0',
      individualLikes: [],
      id: '6550',
      pageId: 'bayes_rule_odds',
      userId: 'EliezerYudkowsky',
      edit: '6',
      type: 'newChild',
      createdAt: '2016-02-08 02:08:51',
      auxPageId: '1x7',
      oldSettingsValue: '',
      newSettingsValue: ''
    },
    {
      likeableId: '0',
      likeableType: 'changeLog',
      myLikeValue: '0',
      likeCount: '0',
      dislikeCount: '0',
      likeScore: '0',
      individualLikes: [],
      id: '6549',
      pageId: 'bayes_rule_odds',
      userId: 'EliezerYudkowsky',
      edit: '6',
      type: 'newEdit',
      createdAt: '2016-02-08 02:08:22',
      auxPageId: '',
      oldSettingsValue: '',
      newSettingsValue: ''
    },
    {
      likeableId: '0',
      likeableType: 'changeLog',
      myLikeValue: '0',
      likeCount: '0',
      dislikeCount: '0',
      likeScore: '0',
      individualLikes: [],
      id: '6548',
      pageId: 'bayes_rule_odds',
      userId: 'EliezerYudkowsky',
      edit: '5',
      type: 'newEdit',
      createdAt: '2016-02-08 02:06:18',
      auxPageId: '',
      oldSettingsValue: '',
      newSettingsValue: ''
    },
    {
      likeableId: '0',
      likeableType: 'changeLog',
      myLikeValue: '0',
      likeCount: '0',
      dislikeCount: '0',
      likeScore: '0',
      individualLikes: [],
      id: '6547',
      pageId: 'bayes_rule_odds',
      userId: 'EliezerYudkowsky',
      edit: '4',
      type: 'newEdit',
      createdAt: '2016-02-08 02:03:32',
      auxPageId: '',
      oldSettingsValue: '',
      newSettingsValue: ''
    },
    {
      likeableId: '0',
      likeableType: 'changeLog',
      myLikeValue: '0',
      likeCount: '0',
      dislikeCount: '0',
      likeScore: '0',
      individualLikes: [],
      id: '6546',
      pageId: 'bayes_rule_odds',
      userId: 'EliezerYudkowsky',
      edit: '3',
      type: 'newEdit',
      createdAt: '2016-02-08 02:01:07',
      auxPageId: '',
      oldSettingsValue: '',
      newSettingsValue: ''
    },
    {
      likeableId: '0',
      likeableType: 'changeLog',
      myLikeValue: '0',
      likeCount: '0',
      dislikeCount: '0',
      likeScore: '0',
      individualLikes: [],
      id: '6545',
      pageId: 'bayes_rule_odds',
      userId: 'EliezerYudkowsky',
      edit: '2',
      type: 'newEdit',
      createdAt: '2016-02-08 01:59:07',
      auxPageId: '',
      oldSettingsValue: '',
      newSettingsValue: ''
    },
    {
      likeableId: '0',
      likeableType: 'changeLog',
      myLikeValue: '0',
      likeCount: '0',
      dislikeCount: '0',
      likeScore: '0',
      individualLikes: [],
      id: '6542',
      pageId: 'bayes_rule_odds',
      userId: 'EliezerYudkowsky',
      edit: '1',
      type: 'newTeacher',
      createdAt: '2016-02-08 01:44:06',
      auxPageId: 'bayes_rule_odds',
      oldSettingsValue: '',
      newSettingsValue: ''
    },
    {
      likeableId: '0',
      likeableType: 'changeLog',
      myLikeValue: '0',
      likeCount: '0',
      dislikeCount: '0',
      likeScore: '0',
      individualLikes: [],
      id: '6543',
      pageId: 'bayes_rule_odds',
      userId: 'EliezerYudkowsky',
      edit: '1',
      type: 'newSubject',
      createdAt: '2016-02-08 01:44:06',
      auxPageId: 'bayes_rule_odds',
      oldSettingsValue: '',
      newSettingsValue: ''
    },
    {
      likeableId: '0',
      likeableType: 'changeLog',
      myLikeValue: '0',
      likeCount: '0',
      dislikeCount: '0',
      likeScore: '0',
      individualLikes: [],
      id: '6541',
      pageId: 'bayes_rule_odds',
      userId: 'EliezerYudkowsky',
      edit: '1',
      type: 'newEdit',
      createdAt: '2016-02-08 01:43:10',
      auxPageId: '',
      oldSettingsValue: '',
      newSettingsValue: ''
    },
    {
      likeableId: '0',
      likeableType: 'changeLog',
      myLikeValue: '0',
      likeCount: '0',
      dislikeCount: '0',
      likeScore: '0',
      individualLikes: [],
      id: '6540',
      pageId: 'bayes_rule_odds',
      userId: 'EliezerYudkowsky',
      edit: '0',
      type: 'newSubject',
      createdAt: '2016-02-08 01:30:47',
      auxPageId: 'odds',
      oldSettingsValue: '',
      newSettingsValue: ''
    },
    {
      likeableId: '0',
      likeableType: 'changeLog',
      myLikeValue: '0',
      likeCount: '0',
      dislikeCount: '0',
      likeScore: '0',
      individualLikes: [],
      id: '6538',
      pageId: 'bayes_rule_odds',
      userId: 'EliezerYudkowsky',
      edit: '0',
      type: 'deleteRequirement',
      createdAt: '2016-02-08 01:30:43',
      auxPageId: 'odds',
      oldSettingsValue: '',
      newSettingsValue: ''
    },
    {
      likeableId: '0',
      likeableType: 'changeLog',
      myLikeValue: '0',
      likeCount: '0',
      dislikeCount: '0',
      likeScore: '0',
      individualLikes: [],
      id: '6536',
      pageId: 'bayes_rule_odds',
      userId: 'EliezerYudkowsky',
      edit: '0',
      type: 'newRequirement',
      createdAt: '2016-02-08 01:22:04',
      auxPageId: 'reads_algebra',
      oldSettingsValue: '',
      newSettingsValue: ''
    },
    {
      likeableId: '0',
      likeableType: 'changeLog',
      myLikeValue: '0',
      likeCount: '0',
      dislikeCount: '0',
      likeScore: '0',
      individualLikes: [],
      id: '6534',
      pageId: 'bayes_rule_odds',
      userId: 'EliezerYudkowsky',
      edit: '0',
      type: 'newRequirement',
      createdAt: '2016-02-08 01:18:31',
      auxPageId: 'conditional_probability',
      oldSettingsValue: '',
      newSettingsValue: ''
    },
    {
      likeableId: '0',
      likeableType: 'changeLog',
      myLikeValue: '0',
      likeCount: '0',
      dislikeCount: '0',
      likeScore: '0',
      individualLikes: [],
      id: '6532',
      pageId: 'bayes_rule_odds',
      userId: 'EliezerYudkowsky',
      edit: '0',
      type: 'newRequirement',
      createdAt: '2016-02-08 01:18:28',
      auxPageId: 'odds',
      oldSettingsValue: '',
      newSettingsValue: ''
    },
    {
      likeableId: '0',
      likeableType: 'changeLog',
      myLikeValue: '0',
      likeCount: '0',
      dislikeCount: '0',
      likeScore: '0',
      individualLikes: [],
      id: '6530',
      pageId: 'bayes_rule_odds',
      userId: 'EliezerYudkowsky',
      edit: '0',
      type: 'newRequirement',
      createdAt: '2016-02-08 01:18:24',
      auxPageId: 'bayes_rule',
      oldSettingsValue: '',
      newSettingsValue: ''
    },
    {
      likeableId: '0',
      likeableType: 'changeLog',
      myLikeValue: '0',
      likeCount: '0',
      dislikeCount: '0',
      likeScore: '0',
      individualLikes: [],
      id: '6528',
      pageId: 'bayes_rule_odds',
      userId: 'EliezerYudkowsky',
      edit: '0',
      type: 'newParent',
      createdAt: '2016-02-08 01:17:20',
      auxPageId: 'bayes_rule',
      oldSettingsValue: '',
      newSettingsValue: ''
    }
  ],
  feedSubmissions: [],
  searchStrings: {},
  hasChildren: 'true',
  hasParents: 'true',
  redAliases: {},
  improvementTagIds: [],
  nonMetaTagIds: [],
  todos: [],
  slowDownMap: 'null',
  speedUpMap: 'null',
  arcPageIds: 'null',
  contentRequests: {
    lessTechnical: {
      likeableId: '4020',
      likeableType: 'contentRequest',
      myLikeValue: '0',
      likeCount: '1',
      dislikeCount: '0',
      likeScore: '1',
      individualLikes: [],
      id: '179',
      pageId: 'bayes_rule_odds',
      requestType: 'lessTechnical',
      createdAt: '2017-03-26 19:06:33'
    },
    moreWords: {
      likeableId: '4109',
      likeableType: 'contentRequest',
      myLikeValue: '0',
      likeCount: '1',
      dislikeCount: '0',
      likeScore: '1',
      individualLikes: [],
      id: '201',
      pageId: 'bayes_rule_odds',
      requestType: 'moreWords',
      createdAt: '2018-01-29 06:41:20'
    },
    slowDown: {
      likeableId: '3311',
      likeableType: 'contentRequest',
      myLikeValue: '0',
      likeCount: '1',
      dislikeCount: '0',
      likeScore: '1',
      individualLikes: [],
      id: '25',
      pageId: 'bayes_rule_odds',
      requestType: 'slowDown',
      createdAt: '2016-08-03 20:44:58'
    }
  }
}