Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Suppose $X$ is a Gaussian random variable with mean $\mu$.

After observing realizations of $X$, say $\{x_1, \dots, x_N\}$, how do I update the p.d.f using Bayesian formula,

$$f^{t+1}=P(\mu|\{x_1, \dots, x_N\})$$

I need the derivation steps for the update. Thanks for your help!

EDIT:

I realized that $\mu$ is the underlying parameter of $X$. Instead of updating $X$ (which is not right) I should update the p.d.f of $\mu$ when predicting.

share|improve this question
    
Since mean and variance of the sample will give the maximum likelihood estimates for $\mu$ and $\sigma^2$ you need to compute running means and variances. –  Sasha Feb 6 '12 at 23:03
1  
You'd need a prior probability distributin of $\mu$ and $\sigma^2$. –  Michael Hardy Feb 7 '12 at 0:17
    
@Sasha Thanks. I would have a look. –  shuaiyuancn Feb 7 '12 at 9:41
    
@MichaelHardy I cannot give that. All I can do (and want to do) is to give a guess in the beginning then revise according to observations. –  shuaiyuancn Feb 7 '12 at 9:45
    
@MichaelHardy Thanks. I see what you mean. What are suggested to use as p.d.f for $\mu$ and $\sigma^2$ in the beginning? No clue at all. –  shuaiyuancn Feb 7 '12 at 11:20

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.