I'm writing an MCMC algorithm in R and I'm wondering about the following: say we have two parameters, theta_1 and thera_2. I want to update each one at a time from the corresponding posterior conditional distributions. Say theta_1^{(0)} and theta_2^{(0)}, are the initial values, the at iteration 1 I update first theta_1 from

theta_1^{(1)} ~ f(theta_1 | theta_2^{(0)}, Data)

Now when updating theta_2, I should use

theta_2^{(1)} ~ f(theta_2 | theta_1^{(1)}, Data)

Is there a theoretical problem if when updating theta_2 I use theta_1^{(0)} I instead of theta_1^{(1)}? That is

theta_2^{(1)} ~ f(theta_2 | theta_1^{(0)}, Data)?

Thanks in advance for any hints.

Dimitris

I'm writing an MCMC algorithm in R and I'm wondering about the following: say we have two parameters, $\theta_1$ and $\theta_2$. I want to update each one at a time from the corresponding posterior conditional distributions. Say $\theta_1^{(0)}$ and $\theta_2^{(0)}$ are the initial values. Then at iteration 1 I update first $\theta_1$ from

$\theta_1^{(1)} \sim f(\theta_1 | \theta_2^{(0)}, \text{Data})$

Now when updating $\theta_2$, I should use

$\theta_2^{(1)} \sim f(\theta_2 | \theta_1^{(1)}, \text{Data})$

Is there a theoretical problem if when updating $\theta_2$ I use $\theta_1^{(0)}$ I instead of $\theta_1^{(1)}$? That is

$\theta_2^{(1)} \sim f(\theta_2 | \theta_1^{(0)}, \text{Data})$?