{
localUrl: '../page/bayesian_likelihood.html',
arbitalUrl: 'https://arbital.com/p/bayesian_likelihood',
rawJsonUrl: '../raw/56v.json',
likeableId: '2991',
likeableType: 'page',
myLikeValue: '0',
likeCount: '3',
dislikeCount: '0',
likeScore: '3',
individualLikes: [
'EricBruylant',
'NateSoares',
'SzymonWilczyski'
],
pageId: 'bayesian_likelihood',
edit: '4',
editSummary: '',
prevEdit: '3',
currentEdit: '4',
wasPublished: 'true',
type: 'wiki',
title: 'Likelihood',
clickbait: '',
textLength: '3425',
alias: 'bayesian_likelihood',
externalUrl: '',
sortChildrenBy: 'likes',
hasVote: 'false',
voteType: '',
votesAnonymous: 'false',
editCreatorId: 'EliezerYudkowsky',
editCreatedAt: '2016-10-08 01:58:35',
pageCreatorId: 'NateSoares',
pageCreatedAt: '2016-07-07 05:40:04',
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: '115',
text: '[summary: "Likelihood", when speaking of Bayesian reasoning, denotes *the probability of an observation, supposing some hypothesis to be correct.*\n\nSuppose our piece of evidence $e$ is that "Mr. Boddy was shot." One of our suspects is Miss Scarlett, and we denote by $H_S$ the hypothesis that Miss Scarlett shot Mr. Boddy. Suppose that if Miss Scarlett *were* the killer, we'd have predicted in advance a 20% probability she would use a gun, and an 80% chance she'd use some other weapon.\n\nThen the *likelihood* from the evidence, to Miss Scarlett being the killer, is 0.20. Using [1rj conditional probability notation], $\\mathbb P(e \\mid H_S) = 0.20.$\n\nThis doesn't mean Miss Scarlett has a 20% chance of being the killer; it means that if she is the killer, our observation had a probability of 20%.\n\nRelative likelihoods are a key ingredient for [1ly Bayesian reasoning] and one of the quantities plugged into [1lz Bayes's Rule].]\n\nConsider a piece of evidence $e,$ such as "Mr. Boddy was shot." We might have a number of different hypotheses that explain this evidence, including $H_S$ = "Miss Scarlett killed him", $H_M$ = "Colonel Mustard killed him", and so on.\n\nEach of those hypotheses assigns a different probability to the evidence. For example, imagine that _if_ Miss Scarlett _were_ the killer, there's a 20% chance she would use a gun, and an 80% chance she'd use some other weapon. In this case, the "Miss Scarlett" hypothesis assigns a *likelihood* of 20% to $e.$\n\nWhen reasoning about different hypotheses using a [-probability_distribution probability distribution] $\\mathbb P$, the likelihood of evidence $e$ given hypothesis $H_i$ is often written using the [1rj conditional probability] $\\mathbb P(e \\mid H_i).$ When reporting likelihoods of many different hypotheses at once, it is common to use a [-likelihood_function,] sometimes written [51n $\\mathcal L_e(H_i)$].\n\n[1rq Relative likelihoods] measure the degree of support that a piece of evidence $e$ provides for different hypotheses. For example, let's say that if Colonel Mustard were the killer, there's a 40% chance he would use a gun. Then the absolute likelihoods of $H_S$ and $H_M$ are 20% and 40%, for _relative_ likelihoods of (1 : 2). This says that the evidence $e$ supports $H_M$ twice as much as it supports $H_S,$ and that the amount of support would have been the same if the absolute likelihoods were 2% and 4% instead.\n\nAccording to [1lz Bayes' rule], relative likelihoods are the appropriate tool for measuring the [22x strength of a given piece evidence]. Relative likelihoods are one of two key constituents of belief in [bayesian_reasoning Bayesian reasoning], the other being [1rm prior probabilities].\n\nWhile absolute likelihoods aren't necessary when updating beliefs by Bayes' rule, they are useful when checking for [227 confusion]. For example, say you have a coin and only two hypotheses about how it works: $H_{0.3}$ = "the coin is random and comes up heads 30% of the time", and $H_{0.9}$ = "the coin is random and comes up heads 90% of the time." Now let's say you toss the coin 100 times, and observe the data HTHTHTHTHTHTHTHT... (alternating heads and tails). The _relative_ likelihoods strongly favor $H_{0.3},$ because it was less wrong. However, the _absolute_ likelihood of $H_{0.3}$ will be much lower than expected, and this deficit is a hint that $H_{0.3}$ isn't right. (For more on this idea, see [227].)',
metaText: '',
isTextLoaded: 'true',
isSubscribedToDiscussion: 'false',
isSubscribedToUser: 'false',
isSubscribedAsMaintainer: 'false',
discussionSubscriberCount: '1',
maintainerCount: '1',
userSubscriberCount: '0',
lastVisit: '',
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: '"Likelihood", when speaking of Bayesian reasoning, denotes *the probability of an observation, supposing some hypothesis to be correct.*\n\nSuppose our piece of evidence $e$ is that "Mr. Boddy was shot." One of our suspects is Miss Scarlett, and we denote by $H_S$ the hypothesis that Miss Scarlett shot Mr. Boddy. Suppose that if Miss Scarlett *were* the killer, we'd have predicted in advance a 20% probability she would use a gun, and an 80% chance she'd use some other weapon.\n\nThen the *likelihood* from the evidence, to Miss Scarlett being the killer, is 0.20. Using [1rj conditional probability notation], $\\mathbb P(e \\mid H_S) = 0.20.$\n\nThis doesn't mean Miss Scarlett has a 20% chance of being the killer; it means that if she is the killer, our observation had a probability of 20%.\n\nRelative likelihoods are a key ingredient for [1ly Bayesian reasoning] and one of the quantities plugged into [1lz Bayes's Rule].'
},
creatorIds: [
'NateSoares',
'EliezerYudkowsky'
],
childIds: [
'relative_likelihood',
'likelihood_notation',
'likelihood_function',
'likelihood_ratio'
],
parentIds: [
'bayes_reasoning'
],
commentIds: [],
questionIds: [],
tagIds: [
'start_meta_tag',
'needs_summary_meta_tag',
'needs_clickbait_meta_tag'
],
relatedIds: [],
markIds: [],
explanations: [
{
id: '5840',
parentId: 'bayesian_likelihood',
childId: 'bayesian_likelihood',
type: 'subject',
creatorId: 'AlexeiAndreev',
createdAt: '2016-08-02 17:11:45',
level: '1',
isStrong: 'true',
everPublished: 'true'
}
],
learnMore: [
{
id: '5844',
parentId: 'bayesian_likelihood',
childId: 'relative_likelihood',
type: 'subject',
creatorId: 'AlexeiAndreev',
createdAt: '2016-08-02 17:12:58',
level: '2',
isStrong: 'false',
everPublished: 'true'
},
{
id: '5839',
parentId: 'bayesian_likelihood',
childId: 'likelihood_function',
type: 'subject',
creatorId: 'AlexeiAndreev',
createdAt: '2016-08-02 17:10:40',
level: '2',
isStrong: 'false',
everPublished: 'true'
},
{
id: '5845',
parentId: 'bayesian_likelihood',
childId: 'likelihood_ratio',
type: 'subject',
creatorId: 'AlexeiAndreev',
createdAt: '2016-08-02 17:13:21',
level: '1',
isStrong: 'false',
everPublished: 'true'
}
],
requirements: [
{
id: '5841',
parentId: 'conditional_probability',
childId: 'bayesian_likelihood',
type: 'requirement',
creatorId: 'AlexeiAndreev',
createdAt: '2016-08-02 17:12:13',
level: '2',
isStrong: 'false',
everPublished: 'true'
},
{
id: '5842',
parentId: 'probability',
childId: 'bayesian_likelihood',
type: 'requirement',
creatorId: 'AlexeiAndreev',
createdAt: '2016-08-02 17:12:26',
level: '2',
isStrong: 'true',
everPublished: 'true'
},
{
id: '5843',
parentId: 'odds',
childId: 'bayesian_likelihood',
type: 'requirement',
creatorId: 'AlexeiAndreev',
createdAt: '2016-08-02 17:12:38',
level: '2',
isStrong: 'false',
everPublished: 'true'
}
],
subjects: [
{
id: '5840',
parentId: 'bayesian_likelihood',
childId: 'bayesian_likelihood',
type: 'subject',
creatorId: 'AlexeiAndreev',
createdAt: '2016-08-02 17:11:45',
level: '1',
isStrong: 'true',
everPublished: 'true'
}
],
lenses: [],
lensParentId: '',
pathPages: [],
learnMoreTaughtMap: {
'56v': [
'56t'
]
},
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: '19925',
pageId: 'bayesian_likelihood',
userId: 'EliezerYudkowsky',
edit: '4',
type: 'newEdit',
createdAt: '2016-10-08 01:58:35',
auxPageId: '',
oldSettingsValue: '',
newSettingsValue: ''
},
{
likeableId: '0',
likeableType: 'changeLog',
myLikeValue: '0',
likeCount: '0',
dislikeCount: '0',
likeScore: '0',
individualLikes: [],
id: '18343',
pageId: 'bayesian_likelihood',
userId: 'EricBruylant',
edit: '0',
type: 'newTag',
createdAt: '2016-08-04 14:05:21',
auxPageId: 'needs_summary_meta_tag',
oldSettingsValue: '',
newSettingsValue: ''
},
{
likeableId: '0',
likeableType: 'changeLog',
myLikeValue: '0',
likeCount: '0',
dislikeCount: '0',
likeScore: '0',
individualLikes: [],
id: '18342',
pageId: 'bayesian_likelihood',
userId: 'EricBruylant',
edit: '0',
type: 'deleteTag',
createdAt: '2016-08-04 14:04:54',
auxPageId: 'stub_meta_tag',
oldSettingsValue: '',
newSettingsValue: ''
},
{
likeableId: '0',
likeableType: 'changeLog',
myLikeValue: '0',
likeCount: '0',
dislikeCount: '0',
likeScore: '0',
individualLikes: [],
id: '18340',
pageId: 'bayesian_likelihood',
userId: 'EricBruylant',
edit: '0',
type: 'newTag',
createdAt: '2016-08-04 14:04:53',
auxPageId: 'start_meta_tag',
oldSettingsValue: '',
newSettingsValue: ''
},
{
likeableId: '0',
likeableType: 'changeLog',
myLikeValue: '0',
likeCount: '0',
dislikeCount: '0',
likeScore: '0',
individualLikes: [],
id: '18128',
pageId: 'bayesian_likelihood',
userId: 'AlexeiAndreev',
edit: '0',
type: 'newTeacher',
createdAt: '2016-08-02 17:13:22',
auxPageId: 'likelihood_ratio',
oldSettingsValue: '',
newSettingsValue: ''
},
{
likeableId: '0',
likeableType: 'changeLog',
myLikeValue: '0',
likeCount: '0',
dislikeCount: '0',
likeScore: '0',
individualLikes: [],
id: '18126',
pageId: 'bayesian_likelihood',
userId: 'AlexeiAndreev',
edit: '0',
type: 'newTeacher',
createdAt: '2016-08-02 17:12:59',
auxPageId: 'relative_likelihood',
oldSettingsValue: '',
newSettingsValue: ''
},
{
likeableId: '0',
likeableType: 'changeLog',
myLikeValue: '0',
likeCount: '0',
dislikeCount: '0',
likeScore: '0',
individualLikes: [],
id: '18124',
pageId: 'bayesian_likelihood',
userId: 'AlexeiAndreev',
edit: '0',
type: 'newRequirement',
createdAt: '2016-08-02 17:12:39',
auxPageId: 'odds',
oldSettingsValue: '',
newSettingsValue: ''
},
{
likeableId: '0',
likeableType: 'changeLog',
myLikeValue: '0',
likeCount: '0',
dislikeCount: '0',
likeScore: '0',
individualLikes: [],
id: '18123',
pageId: 'bayesian_likelihood',
userId: 'AlexeiAndreev',
edit: '0',
type: 'newRequirement',
createdAt: '2016-08-02 17:12:26',
auxPageId: 'probability',
oldSettingsValue: '',
newSettingsValue: ''
},
{
likeableId: '0',
likeableType: 'changeLog',
myLikeValue: '0',
likeCount: '0',
dislikeCount: '0',
likeScore: '0',
individualLikes: [],
id: '18122',
pageId: 'bayesian_likelihood',
userId: 'AlexeiAndreev',
edit: '0',
type: 'newRequirement',
createdAt: '2016-08-02 17:12:13',
auxPageId: 'conditional_probability',
oldSettingsValue: '',
newSettingsValue: ''
},
{
likeableId: '0',
likeableType: 'changeLog',
myLikeValue: '0',
likeCount: '0',
dislikeCount: '0',
likeScore: '0',
individualLikes: [],
id: '18120',
pageId: 'bayesian_likelihood',
userId: 'AlexeiAndreev',
edit: '0',
type: 'newTeacher',
createdAt: '2016-08-02 17:11:45',
auxPageId: 'bayesian_likelihood',
oldSettingsValue: '',
newSettingsValue: ''
},
{
likeableId: '0',
likeableType: 'changeLog',
myLikeValue: '0',
likeCount: '0',
dislikeCount: '0',
likeScore: '0',
individualLikes: [],
id: '18121',
pageId: 'bayesian_likelihood',
userId: 'AlexeiAndreev',
edit: '0',
type: 'newSubject',
createdAt: '2016-08-02 17:11:45',
auxPageId: 'bayesian_likelihood',
oldSettingsValue: '',
newSettingsValue: ''
},
{
likeableId: '0',
likeableType: 'changeLog',
myLikeValue: '0',
likeCount: '0',
dislikeCount: '0',
likeScore: '0',
individualLikes: [],
id: '18118',
pageId: 'bayesian_likelihood',
userId: 'AlexeiAndreev',
edit: '0',
type: 'newTeacher',
createdAt: '2016-08-02 17:10:41',
auxPageId: 'likelihood_function',
oldSettingsValue: '',
newSettingsValue: ''
},
{
likeableId: '0',
likeableType: 'changeLog',
myLikeValue: '0',
likeCount: '0',
dislikeCount: '0',
likeScore: '0',
individualLikes: [],
id: '18098',
pageId: 'bayesian_likelihood',
userId: 'AlexeiAndreev',
edit: '0',
type: 'newChild',
createdAt: '2016-08-02 17:05:28',
auxPageId: 'likelihood_notation',
oldSettingsValue: '',
newSettingsValue: ''
},
{
likeableId: '0',
likeableType: 'changeLog',
myLikeValue: '0',
likeCount: '0',
dislikeCount: '0',
likeScore: '0',
individualLikes: [],
id: '16923',
pageId: 'bayesian_likelihood',
userId: 'EricBruylant',
edit: '0',
type: 'newTag',
createdAt: '2016-07-16 20:29:35',
auxPageId: 'needs_clickbait_meta_tag',
oldSettingsValue: '',
newSettingsValue: ''
},
{
likeableId: '0',
likeableType: 'changeLog',
myLikeValue: '0',
likeCount: '0',
dislikeCount: '0',
likeScore: '0',
individualLikes: [],
id: '15976',
pageId: 'bayesian_likelihood',
userId: 'NateSoares',
edit: '3',
type: 'newEdit',
createdAt: '2016-07-07 14:46:35',
auxPageId: '',
oldSettingsValue: '',
newSettingsValue: ''
},
{
likeableId: '0',
likeableType: 'changeLog',
myLikeValue: '0',
likeCount: '0',
dislikeCount: '0',
likeScore: '0',
individualLikes: [],
id: '15973',
pageId: 'bayesian_likelihood',
userId: 'NateSoares',
edit: '2',
type: 'newEdit',
createdAt: '2016-07-07 14:35:16',
auxPageId: '',
oldSettingsValue: '',
newSettingsValue: ''
},
{
likeableId: '0',
likeableType: 'changeLog',
myLikeValue: '0',
likeCount: '0',
dislikeCount: '0',
likeScore: '0',
individualLikes: [],
id: '15945',
pageId: 'bayesian_likelihood',
userId: 'NateSoares',
edit: '0',
type: 'newChild',
createdAt: '2016-07-07 06:09:24',
auxPageId: 'likelihood_function',
oldSettingsValue: '',
newSettingsValue: ''
},
{
likeableId: '0',
likeableType: 'changeLog',
myLikeValue: '0',
likeCount: '0',
dislikeCount: '0',
likeScore: '0',
individualLikes: [],
id: '15941',
pageId: 'bayesian_likelihood',
userId: 'NateSoares',
edit: '0',
type: 'newChild',
createdAt: '2016-07-07 05:51:35',
auxPageId: 'likelihood_ratio',
oldSettingsValue: '',
newSettingsValue: ''
},
{
likeableId: '0',
likeableType: 'changeLog',
myLikeValue: '0',
likeCount: '0',
dislikeCount: '0',
likeScore: '0',
individualLikes: [],
id: '15936',
pageId: 'bayesian_likelihood',
userId: 'NateSoares',
edit: '0',
type: 'newChild',
createdAt: '2016-07-07 05:40:39',
auxPageId: 'relative_likelihood',
oldSettingsValue: '',
newSettingsValue: ''
},
{
likeableId: '0',
likeableType: 'changeLog',
myLikeValue: '0',
likeCount: '0',
dislikeCount: '0',
likeScore: '0',
individualLikes: [],
id: '15934',
pageId: 'bayesian_likelihood',
userId: 'NateSoares',
edit: '0',
type: 'newParent',
createdAt: '2016-07-07 05:40:05',
auxPageId: 'bayes_reasoning',
oldSettingsValue: '',
newSettingsValue: ''
},
{
likeableId: '0',
likeableType: 'changeLog',
myLikeValue: '0',
likeCount: '0',
dislikeCount: '0',
likeScore: '0',
individualLikes: [],
id: '15935',
pageId: 'bayesian_likelihood',
userId: 'NateSoares',
edit: '0',
type: 'newTag',
createdAt: '2016-07-07 05:40:05',
auxPageId: 'stub_meta_tag',
oldSettingsValue: '',
newSettingsValue: ''
},
{
likeableId: '0',
likeableType: 'changeLog',
myLikeValue: '0',
likeCount: '0',
dislikeCount: '0',
likeScore: '0',
individualLikes: [],
id: '15932',
pageId: 'bayesian_likelihood',
userId: 'NateSoares',
edit: '1',
type: 'newEdit',
createdAt: '2016-07-07 05:40:04',
auxPageId: '',
oldSettingsValue: '',
newSettingsValue: ''
}
],
feedSubmissions: [],
searchStrings: {},
hasChildren: 'true',
hasParents: 'true',
redAliases: {},
improvementTagIds: [],
nonMetaTagIds: [],
todos: [],
slowDownMap: 'null',
speedUpMap: 'null',
arcPageIds: 'null',
contentRequests: {}
}