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Nov 15, 2021 02:40 AM

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## What & Why

### What is a conjugate prior?

- When the posterior is in the same family as the prior distribution they are called conjugate distributions, and the prior is called a conjugate prior for the likelihood function.

- That means that if the prior distribution for x is a beta distribution, the posterior is also a beta distribution. (Tb)

### What is The beta distribution?

## How does that look like?

- frequently used in Bayesian statistics (Wiki)

- The shape of it depends on two parameters, written α and β, or alpha and beta.
- is uniform from 0 to 1 when alpha=1 and beta=1. (TB p39)
- If the
*prior is a beta distribution*with parameters and , and we see data with h heads and t tails,*the posterior is a beta distribution*with parameters and . - Or Dan Simpson called it :
- Under Uniform(0, 1) prior, if y = 8 Heads from n = 10 tosses, posterior is Beta(9, 3)
- In other words, we can do an update with two additions. (TB p39)

- It is great that we can leverage this advantage :
- ∵ many realistic priors there is a beta distribution that is at least a good approximation, and for a uniform prior there is a perfect match. (TB p39)

## How

图解教材:概率机器学习（Murphy)_哔哩哔哩_bilibili 第69 教你如何adjust prior

#### Example : Drug efficacy (Lambert p237)

## Reference

(TB) —

*The best source to get the gist*. thinkbayes.pdf (amazonaws.com)**Author:**Jason Siu**URL:**https://jason-siu.com/article/9e8a8b1f-e93e-423a-9423-175afe30e1ff**Copyright:**All articles in this blog, except for special statements, adopt BY-NC-SA agreement. Please indicate the source!

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