conjugate-prior-same-parametric-family
IN premise — summaries/2026/08/24/wiki-Bayesian_inference-chunk-2.md
Created 2026-08-25T02:58:43+00:00
A conjugate prior is a prior family chosen so that the resulting posterior belongs to the same parametric family, enabling closed-form Bayesian updates.
Summary
When you pick a starting distribution that's mathematically "friendly" to the model you're fitting, updating it with new data produces a result in the same family of shapes, so you can do the update with simple algebra instead of expensive numerical approximation. In practice, this means the system can incorporate new evidence quickly and exactly, trading some flexibility in the prior's shape for computational tractability at every update step.