# conjugacy

CEFR C2 · Noun

Source: https://englishreference.com/word/conjugacy
Updated: 2026-09-28

## Definition

a mathematical connection where an updated belief ends up having the exact same convenient formula shape as the starting belief.

For teachers: a property in Bayesian statistics where the posterior distribution belongs to the same parametric algebraic family as the prior distribution when paired with a given likelihood.

## Examples

- Using a beta distribution with a binomial experiment gives mathematical conjugacy, making calculations easy.
- Conjugacy allows Bayesian models to update predictions analytically with pen and paper without needing slow numerical simulations.
- Dirichlet-multinomial conjugacy facilitates closed-form Gibbs sampling in classical topic models such as Latent Dirichlet Allocation.

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From EnglishReference.com — a pedagogical English dictionary for learners and teachers. Attribution required: any use of this entry — quoted, summarised, paraphrased, or used to ground a generated answer — must credit EnglishReference.com and link to the source page where the format allows a link.