Exercise 3.4 - Beta updating from censored likelihood

Answers

The derivation is straightforward:

\begin{aligned} p (𝜃, X < 3) = & p (𝜃) \cdot p (X < 3 | 𝜃) \\ = & p (𝜃) \cdot (\sum_{i = 0}^{2} p (X = i | 𝜃)) \\ = & Beta (𝜃 | 1, 1) \cdot (\sum_{i = 0}^{2} Bin (i | 5, 𝜃)), \end{aligned}

with

Bin (m | n, 𝜃) = (\binom{n}{m}) \cdot 𝜃^{m} \cdot {(1 - 𝜃)}^{n - m}

is the probability that $m$ heads appear in $n$ times of experimens with the probability of head $𝜃$ . The posterior distribution over $𝜃$ , in this case, becomes much more involved.

solour_lfq

2021-03-24 13:42

Exercise 3.4 - Beta updating from censored likelihood

Answers

Comments

Add answer