LingvoCore.com

marginal probability

Low (specialist)
UK/ˌmɑː.dʒɪ.nəl ˌprɒb.əˈbɪl.ə.ti/US/ˌmɑːr.dʒɪ.nəl ˌprɑː.bəˈbɪl.ə.t̬i/

Technical / Academic

My Flashcards

Definition

Meaning

In probability theory and statistics, the probability of a single event occurring, independent of other variables.

The probability of a specific outcome for one variable in a set of variables, obtained by summing or integrating the joint probability distribution over the possible values of all other variables. It represents the overall likelihood of that outcome regardless of the states of other related factors.

Linguistics

Semantic Notes

The term 'marginal' derives from the practice of writing sums of joint probabilities in the margins of contingency tables. It implies a 'standalone' or 'overall' probability, ignoring the influence or presence of other variables.

Dialectal Variation

British vs American Usage

Differences

No significant lexical differences. Usage and concept are identical in statistical contexts. Spelling follows regional norms (e.g., 'marginalise' vs. 'marginalize' in related terms).

Connotations

Strictly mathematical. No variation in connotation between regions.

Frequency

Identical, low frequency outside mathematics, statistics, data science, and related academic fields.

Vocabulary

Collocations

strong
calculate the marginal probabilityjoint and marginal probabilitymarginal probability distributionmarginal probability function
medium
find the marginal probabilitythe marginal probability of Xobtain from the joint probabilitysum over the marginal probability
weak
high marginal probabilitylow marginal probabilityestimate the marginal probabilitytable of marginal probabilities

Grammar

Valency Patterns

The marginal probability of [variable/event] is...To find/get the marginal probability, [sum/integrate] over...[Calculate/Compute] the marginal probability from the joint distribution.

Vocabulary

Synonyms

Strong

unconditional probability (when not conditioned on any other event)

Neutral

univariate probabilitysingle-variable probability

Weak

overall probabilitytotal probability (context-specific)

Vocabulary

Antonyms

joint probabilityconditional probability

Phrases

Idioms & Phrases

  • “It's in the margins (informal, mnemonic for the concept's origin).”

Usage

Context Usage

Business

Used in risk analysis and decision-making models, e.g., 'The marginal probability of a market downturn informs our hedge.'

Academic

Core concept in statistics, probability theory, machine learning (e.g., naive Bayes classifiers), and quantitative social sciences.

Everyday

Virtually never used in everyday conversation.

Technical

Fundamental in data science, econometrics, engineering reliability studies, and any field using probabilistic models.

Examples

By Part of Speech

verb

British English

  • We need to marginalise over the other variables to find the probability.
  • The joint distribution was marginalised to obtain the required figures.

American English

  • We need to marginalize over the other variables to find the probability.
  • The joint distribution was marginalized to obtain the required figures.

adverb

British English

  • The probabilities were calculated marginally.

American English

  • The probabilities were calculated marginally.

adjective

British English

  • The marginal probability estimate was plotted on the graph.
  • We compared the marginal distributions.

American English

  • The marginal probability estimate was plotted on the graph.
  • We compared the marginal distributions.

Examples

By CEFR Level

B2
  • To find the chance of rain tomorrow, we look at the marginal probability, ignoring temperature.
  • The survey showed the marginal probability of a person owning a car was 75%.
C1
  • The marginal probability of a component failing, derived from the full system model, was alarmingly high.
  • In Bayesian networks, evidence is propagated to update the marginal probabilities of all unknown nodes.

Learning

Memory Aids

Mnemonic

Think of totals written in the MARGIN of a data table. MARGinal probability is the total probability for one thing, found in the 'margin' after adding up all possibilities for other things.

Conceptual Metaphor

PROBABILITY IS AREA (where marginal probability is the total area of one column in a multi-column chart, ignoring the divisions).

Watch out

Common Pitfalls

Translation Traps (for Russian speakers)

  • Avoid a direct translation implying 'insignificant' or 'minor' probability. 'Marginal' here is technical, from 'margin' of a table.
  • The Russian term 'маргинальная вероятность' is a direct calque and is correct in technical contexts but should not be interpreted with the sociological meaning of 'маргинальный'.

Common Mistakes

  • Confusing it with conditional probability ('probability of A given B').
  • Using it to mean a 'small' or 'insignificant' probability.
  • Failing to specify which variable's marginal probability is being discussed.

Practice

Quiz

Fill in the gap
To find the probability of rolling a four on a single die, you don't consider any other dice in your calculation.
Multiple Choice

What is the key operation involved in deriving a marginal probability from a joint probability table?

FAQ

Frequently Asked Questions

Marginal probability is the simple probability of an event (P(A)), ignoring others. Conditional probability is the probability of an event GIVEN another event has occurred (P(A|B)).

The term originates from contingency tables. The sums of rows and columns, which give the probabilities for single variables, were traditionally written in the table's margins.

Often yes, particularly when no conditioning event is specified. However, 'unconditional' explicitly contrasts with 'conditional,' while 'marginal' specifically refers to its derivation from a joint distribution.

Primarily in statistics, probability theory, data science, machine learning (e.g., in naive Bayes classifiers), econometrics, and quantitative research across social and physical sciences.