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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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    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?2011-12-14

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