Bayes’ theorem
E139495
Bayes’ theorem is a fundamental result in probability theory that describes how to update the probability of a hypothesis based on new evidence.
All labels observed (6)
| Label | Occurrences |
|---|---|
| Bayes' theorem | 6 |
| Bayes theorem | 2 |
| Bayes’ law | 1 |
| Bayes’ rule | 1 |
| Bayes’ theorem canonical | 1 |
| Bayes’ theorem for continuous distributions | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T1221712 — resolving that mention is where its identity was fixed. The disambiguator weighed these candidate entities and picked the highlighted one (or “None”, minting a new entity). This is how homonymy is resolved: the same surface form can point to different entities.
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Bayes’ theorem Context triple: [Pierre-Simon Laplace, contributedTo, Bayes’ theorem]
-
A.
Bayesian inference
Bayesian inference is a statistical framework that updates the probability of hypotheses as more evidence or data becomes available, using Bayes’ theorem to combine prior beliefs with observed information.
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B.
A Treatise on Probability
A Treatise on Probability is John Maynard Keynes’s influential 1921 work that develops a logical and philosophical theory of probability, challenging classical and frequency-based interpretations.
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C.
Logical Foundations of Probability
Logical Foundations of Probability is a seminal philosophical work by Rudolf Carnap that develops a rigorous logical and formal account of probability and inductive reasoning.
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D.
Occam's razor
Occam's razor is a philosophical and scientific principle that advises preferring the simplest explanation that adequately accounts for all observed facts.
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E.
Gaussian law of error
The Gaussian law of error is a fundamental statistical principle stating that measurement errors tend to follow a normal (bell-shaped) distribution, forming the basis of much of probability theory and statistical inference.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Bayes’ theorem Target entity description: Bayes’ theorem is a fundamental result in probability theory that describes how to update the probability of a hypothesis based on new evidence.
-
A.
Bayesian inference
Bayesian inference is a statistical framework that updates the probability of hypotheses as more evidence or data becomes available, using Bayes’ theorem to combine prior beliefs with observed information.
-
B.
A Treatise on Probability
A Treatise on Probability is John Maynard Keynes’s influential 1921 work that develops a logical and philosophical theory of probability, challenging classical and frequency-based interpretations.
-
C.
Logical Foundations of Probability
Logical Foundations of Probability is a seminal philosophical work by Rudolf Carnap that develops a rigorous logical and formal account of probability and inductive reasoning.
-
D.
Occam's razor
Occam's razor is a philosophical and scientific principle that advises preferring the simplest explanation that adequately accounts for all observed facts.
-
E.
Gaussian law of error
The Gaussian law of error is a fundamental statistical principle stating that measurement errors tend to follow a normal (bell-shaped) distribution, forming the basis of much of probability theory and statistical inference.
- F. None of above. chosen
Statements (49)
| Predicate | Object |
|---|---|
| instanceOf |
probability theorem
ⓘ
result in probability theory ⓘ |
| alsoCalled |
Bayes’ law
ⓘ
linked to:
Bayes’ theorem
Bayes’ rule ⓘ
linked to:
Bayes’ theorem
|
| appliesTo |
continuous random variables
ⓘ
discrete random variables ⓘ |
| assumes |
P(B) > 0 for conditioning event B
ⓘ
well-defined probability space ⓘ |
| component |
evidence probability
ⓘ
likelihood ⓘ posterior probability ⓘ prior probability ⓘ |
| contrastsWith | frequentist interpretation of probability ⓘ |
| coreFormula |
P(A|B) = P(B|A) P(A) / P(B)
ⓘ
P(H|E) = P(E|H) P(H) / P(E) ⓘ |
| derivedFrom |
definition of conditional probability
ⓘ
product rule of probability ⓘ |
| describes | updating probabilities of hypotheses given evidence ⓘ |
| field |
Bayesian inference
ⓘ
probability theory ⓘ statistics ⓘ |
| foundationOf | Bayesian inference ⓘ |
| generalForm | P(A_i|B) = P(B|A_i) P(A_i) / Σ_j P(B|A_j) P(A_j) ⓘ |
| generalizedBy |
Bayes’ theorem for continuous distributions
ⓘ
linked to:
Bayes’ theorem
|
| hasNotation | P(H|E) ∝ P(E|H) P(H) ⓘ |
| historicalAttribution | first published posthumously by Richard Price ⓘ |
| implies | posterior is proportional to likelihood times prior ⓘ |
| mathematicalDomain | measure-theoretic probability ⓘ |
| namedAfter | Thomas Bayes ⓘ |
| relates | posterior probability to prior probability and likelihood ⓘ |
| timePeriod | 18th century ⓘ |
| usedFor |
computing diagnostic test accuracy
ⓘ
inverting conditional probabilities ⓘ learning from data ⓘ sequential updating of beliefs ⓘ |
| usedIn |
A/B testing
ⓘ
Bayesian networks ⓘ Bayesian statistics ⓘ Bayesian updating ⓘ Naive Bayes classifier ⓘ decision theory ⓘ machine learning ⓘ medical diagnosis ⓘ pattern recognition ⓘ signal processing ⓘ spam filtering ⓘ |
| usesConcept |
conditional probability
ⓘ
joint probability ⓘ marginal probability ⓘ |
How these facts were elicited
The pipeline generated the facts above by prompting gpt-5.1 with this entity's name + description and the instruction below.
Instruction
You are a knowledge base construction expert. Given a subject entity and a description of it, return factual statements that you know for the subject as a JSON list of dictionaries(triples), where keys must be "subject", "predicate" and "object". The number of facts may be very high, between 25 to 50 or more, for very popular subjects. For less popular subjects, the number of facts can be very low, like 5 or 10. # Requirements - If you don't know the subject at all, return an empty list. - If the subject is not a named entity, return an empty list. - Include at least one triple where predicate is "instanceOf". - Do not get too wordy. - Separate several objects into multiple triples with one object.
Input
Subject: Bayes’ theorem Description of subject: Bayes’ theorem is a fundamental result in probability theory that describes how to update the probability of a hypothesis based on new evidence.
Referenced by (12)
Full triples — surface form annotated when it differs from this entity's canonical label.
linked to: Bayes’ theorem
linked to: Bayes’ theorem
linked to: Bayes’ theorem
linked to: Bayes’ theorem
linked to: Bayes’ theorem
subject linked to:
Probability Theory
linked to: Bayes’ theorem
linked to: Bayes’ theorem
linked to: Bayes’ theorem
linked to: Bayes’ theorem
linked to: Bayes’ theorem
subject linked to:
1926 paper "Truth and Probability"
linked to: Bayes’ theorem