posterior probability: meaning, definition, pronunciation and examples
C2Academic, Technical, Scientific
Quick answer
What does “posterior probability” mean?
In Bayesian statistics, the probability of a hypothesis given the observed data, calculated by updating a prior probability with new evidence using Bayes' theorem.
Audio
Pronunciation
Definition
Meaning and Definition
In Bayesian statistics, the probability of a hypothesis given the observed data, calculated by updating a prior probability with new evidence using Bayes' theorem.
A measure of belief or certainty about an uncertain event after incorporating relevant evidence. More broadly, it can refer to any updated assessment or conclusion reached after considering new information.
Dialectal Variation
British vs American Usage
Differences
No significant differences in meaning or usage. Spelling conventions follow national norms (e.g., 'analyse' vs. 'analyze' in surrounding text).
Connotations
Purely technical, carries no regional connotations.
Frequency
Equally frequent in relevant academic/technical fields in both regions.
Grammar
How to Use “posterior probability” in a Sentence
The posterior probability of [HYPOTHESIS] given [DATA] is [VALUE].We calculated the posterior probability.The posterior probability updated our prior belief.Vocabulary
Collocations
Examples
Examples of “posterior probability” in a Sentence
verb
British English
- We need to posteriorise the probability estimates. (Highly technical/neologism)
- The model posteriorises beliefs efficiently.
American English
- The algorithm will posterior-probabilize the data. (Technical/neologism)
- We posteriorized the distribution.
adverb
British English
- The parameter was estimated posterior-probabilistically.
- We inferred the result posterior-probabilistically.
American English
- The hypothesis was evaluated posterior-probability-wise.
- We updated our views posterior-probabilistically.
adjective
British English
- The posterior-probability calculation is central.
- We examined the posterior-probability density function.
American English
- The posterior-probability estimate was robust.
- Posterior-probability analysis guided the decision.
Usage
Meaning in Context
Business
Rare. Could appear in advanced risk modelling or data science contexts.
Academic
Primary context. Used in statistics, machine learning, data science, cognitive science, and philosophy of science.
Everyday
Virtually never used.
Technical
Core term in fields relying on Bayesian methods (e.g., AI, medical diagnostics, signal processing).
Vocabulary
Synonyms of “posterior probability”
Neutral
Weak
Vocabulary
Antonyms of “posterior probability”
Watch out
Common Mistakes When Using “posterior probability”
- Using 'posterior probability' to mean a probability of something happening later in time.
- Confusing it with 'prior probability'.
- Misspelling as 'posteriority probability'.
- Using it outside a Bayesian framework without explanation.
FAQ
Frequently Asked Questions
All posterior probabilities are conditional (on the data), but not all conditional probabilities are posterior. 'Posterior' specifically implies an update from a 'prior' belief within the Bayesian framework.
No. By definition, a posterior probability is derived by updating a prior probability using Bayes' theorem. The prior represents the initial state of belief.
It is fundamental in statistics (Bayesian inference), machine learning (Bayesian networks, Naive Bayes classifiers), epidemiology, psychometrics, and any field employing formal Bayesian reasoning.
In British English: /pɒˈstɪə.ri.ə ˌprɒb.əˈbɪl.ə.ti/. In American English: /pɑːˈstɪr.i.ɚ ˌprɑː.bəˈbɪl.ə.t̬i/. The stress is on 'ster' in 'posterior' and 'bil' in 'probability'.
In Bayesian statistics, the probability of a hypothesis given the observed data, calculated by updating a prior probability with new evidence using Bayes' theorem.
Posterior probability is usually academic, technical, scientific in register.
Learning
Memory Aids
Mnemonic
Think of a POSTman arriving AFTER (posterior) with new EVIDENCE (data), which updates your belief about whether a letter will arrive (probability).
Conceptual Metaphor
BELIEF IS A QUANTITY THAT CAN BE UPDATED. KNOWLEDGE EVOLUTION (from prior to posterior).
Practice
Quiz
What does a 'posterior probability' represent?