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Suppose $f_x,_y$ is bivariate normal distribution. I was given the parameters $(μ_1, μ_2, σ_1^2, σ_2^2)$ and $ρ=0.95$ the correlation coefficient. I want to generate $(x_1,y_1), (x_2,y_2)...,(x_n,y_n)$, applying:

1) Gibbs algorithm

2) Metropolis algorithm.

3) Gibbs algoritm in the first dimension and Metropolis in the other.

4) Metropolis algorithm in one dimension.

My problem is , how to use in practise these methods.

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1  
So what is your question? –  Henning Makholm Dec 14 '11 at 13:41
    
I dont know how to use both of these methods.I would appreciate any help. –  Mike Fragkoulakis Dec 14 '11 at 14:43
    
For this sort of question, it generally makes sense to tell us what it is specifically that you don't understand in the corresponding Wikipedia articles. Otherwise all we can do is rewrite them for you from scratch. (Note that the article you want is en.wikipedia.org/wiki/Gibbs_sampling, not en.wikipedia.org/wiki/Gibbs_algorithm, which is something different.) –  joriki Dec 14 '11 at 15:48
    
@joriki I have read also a few papers about gibbs sampling and metropolis.I understand a little bit the theory , but my main problem is how to use them in practise and especially in my exaple with the bivariate normal distribution. –  Mike Fragkoulakis Dec 14 '11 at 20:57
3  
I don't quite understand what you mean by "in practice". As far as I can tell, the Wikipedia articles describe how to use the algorithms in practice. They have sections entitled "Step-by-step instructions" and "Implementation", respectively. Wouldn't you agree that it would be more efficient if you try to apply those instructions and then tell us where you get stuck rather than us either guessing what the problem is or explaining the entire thing from scratch? –  joriki Dec 14 '11 at 21:18

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