bayes' theorem: meaning, definition, pronunciation and examples
C2Technical / Academic
Quick answer
What does “bayes' theorem” mean?
A theorem in probability theory that describes how to update the probability of a hypothesis based on new evidence.
Audio
Pronunciation
Definition
Meaning and Definition
A theorem in probability theory that describes how to update the probability of a hypothesis based on new evidence.
A mathematical formula expressing the conditional probability of an event, given prior knowledge of conditions that might be related to the event. It provides a principled way to incorporate new data to revise prior beliefs, forming a cornerstone of Bayesian statistics, machine learning, and decision theory.
Dialectal Variation
British vs American Usage
Differences
No significant difference in meaning or usage. The possessive apostrophe (Bayes') is standard in both varieties.
Connotations
Identical technical connotations in statistics, data science, and philosophy of science.
Frequency
Equally low frequency in general discourse but equally high frequency in specialised academic and technical contexts.
Grammar
How to Use “bayes' theorem” in a Sentence
apply Bayes' theorem to + [a problem/data]update + [probability/belief] using Bayes' theoremcalculate + [posterior probability] with Bayes' theoremVocabulary
Collocations
Examples
Examples of “bayes' theorem” in a Sentence
adjective
British English
- The Bayesian approach is derived from Bayes' theorem.
- She offered a Bayesian analysis of the results.
American English
- The Bayesian framework relies on Bayes' theorem.
- He is known for his Bayesian models in machine learning.
Usage
Meaning in Context
Business
Used in risk analysis, forecasting, and machine learning applications for marketing or fraud detection.
Academic
Central to statistics, data science, machine learning, philosophy of science, and psychology (e.g., modelling cognition).
Everyday
Virtually never used in casual conversation, except in a pedagogical or popular science context.
Technical
The foundational tool for Bayesian inference, used in algorithms from spam filtering to medical diagnostics.
Vocabulary
Synonyms of “bayes' theorem”
Neutral
Weak
Watch out
Common Mistakes When Using “bayes' theorem”
- Misspelling as 'Baye's theorem', 'Bayse theorem', or 'Bayesian theorem' (which is related but not the same).
- Incorrectly using it as a verb, e.g., 'We need to bayes this data.'
- Omitting the required apostrophe.
FAQ
Frequently Asked Questions
The Reverend Thomas Bayes (c. 1701–1761), an English statistician, philosopher, and Presbyterian minister.
Bayesian statistics uses Bayes' theorem to incorporate prior beliefs with evidence, treating probability as a degree of belief. Frequentist statistics interprets probability solely as the long-run frequency of events, without incorporating prior probabilities.
Yes. A medical test for a rare disease: Bayes' theorem is used to calculate the actual probability a patient has the disease, given a positive test result, by considering the test's accuracy and the disease's rarity (prior probability).
No. While mathematical, its principles of updating beliefs are applied in fields like machine learning (spam filters), psychology (models of learning), law (probabilistic evidence), and economics (decision-making).
A theorem in probability theory that describes how to update the probability of a hypothesis based on new evidence.
Bayes' theorem is usually technical / academic in register.
Bayes' theorem: in British English it is pronounced /ˈbeɪz ˈθɪərəm/, and in American English it is pronounced /ˈbeɪz ˈθiːrəm/. Tap the audio buttons above to hear it.
Learning
Memory Aids
Mnemonic
Bayes' theorem updates your belief (prior) with new evidence to get a revised belief (posterior). Think: 'Before Evidence' -> 'After Evidence, Updated'.
Conceptual Metaphor
UPDATING A MAP (Prior belief is an old map, new evidence is fresh survey data, posterior is the updated, more accurate map).
Practice
Quiz
Bayes' theorem is fundamentally used to: