dream13rxs

2022-07-08

Estimating the parameters of gaussians to fit a lot of samples can be do with Exceptation Maximization, for instance if we want to fit two gaussian on points, to have the clusters $a$ and $b$. (1)
${b}_{i}=P\left(b|{x}_{i}\right)=\frac{P\left({x}_{i}|b\right)P\left(b\right)}{P\left({x}_{i}|b\right)P\left(b\right)+P\left({x}_{i}|b\right)P\left(a\right)}$
Here $P\left(b\right)$ is the prior that depicts the overall importance of the $b$ cluster.
This prior is then updated for the next step, according on how many the points belongs to the $b$ cluster:
$P\left(b\right)=\frac{1}{n}\sum _{i}{b}_{i}$
However, what is the value of the prior $P\left(b\right)$ on the first iteration of the algorithm?

Sophia Mcdowell

Expert