What is a conjugate prior?
hardAnswer
- A prior p(θ) is conjugate to a likelihood if the posterior belongs to the same family.
- Examples: Beta prior + Bernoulli likelihood → Beta posterior; Gamma prior + Poisson → Gamma; Normal prior + Normal (known σ) → Normal; Dirichlet + categorical → Dirichlet.
- Enables closed-form Bayesian updates — cornerstone of Thompson sampling, online Bayesian inference, contextual bandits.
Check yourself — multiple choice
- Random
- Prior + likelihood → posterior in same family; Beta-Bernoulli / Gamma-Poisson / Normal-Normal / Dirichlet-Categorical — enables closed-form updates + Thompson sampling
- Not real
- Only frequentist
Conjugate priors: posterior in same family; closed-form updates.
#bayesian#estimation
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