# [R] Questions about EM algorithm

From: Hung-Hsuan Chen (Sean) <sandwichc_at_gmail.com>
Date: Fri, 15 Feb 2008 09:12:22 +0800

Dear all:
Assume I have 3 distributions, x1, x2, and x3.

```x1 ~ normal(mu1, sd1)
x2 ~ normal(mu2, sd2)
x3 ~ normal(mu3, sd3)
```

y1 = x1 + x2
y2 = x1 + x3

Now that the data I can observed is only y1 and y2. It is easy to estimate (mu1+m2), (mu1+mu3), (sd1^2+sd2^2) and (sd1^2+sd3^2) by EM algorithm since
y1 ~ normal(mu1+mu2, sqrt(sd1^2+sd2^2)) and y2 ~ normal(mu1+mu3, sqrt(sd1^2+sd3^2))

However, I want to estimate mu1, mu2, mu3, sd1, sd2, and sd3. Is it possible to do so by EM algorithm (or any other estimation methods like gibbs sampling or MLE) ?

Anyone can give me some sample code or suggestions? Thanks a lot in advance.

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