Prior Distribution
Updated 2026-08-10
INTRODUCTION
English translation pending.
CORE DEFINITION
A central object in Bayesian statistics, formalized through Bayes' theorem. The prior expresses what is believed about a parameter before seeing data, and it is combined with the likelihood of the observed sample to produce the posterior distribution. The core proposition is that beliefs can be represented as distributions and revised by evidence in a principled way. The key qualification is that the prior is a modeling choice, so sensitivity to it must be examined rather than assumed away.
SCAFFOLDING EFFECT
Reduce cognitive load
- Belief encoding: write down what you currently believe about the parameter and how strongly. - Update rule: combine the prior with the observed data to get the posterior. - Sensitivity check: test whether the conclusion changes under a different reasonable prior.
Anchor fast decisions
The prior supplies the information available before observation, and the likelihood supplies what the data says. Multiplying them weights each source by how much it constrains the parameter, so a strong prior requires strong evidence to overturn and weak data leaves the prior largely intact. The posterior then becomes the prior for the next observation, which makes updating cumulative.
MINIMUM ACTION
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Source support: Explicit
- zh.wikipedia.orghttps://zh.wikipedia.org/wiki/%E5%85%88%E9%AA%8C%E6%A6%82%E7%8E%87verified
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