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.