Iteration

Although $I_{\theta{\bf a}}$ is non-zero, we can ignore it and update $\theta$ independently, then update ${\bf a},\sigma^2$ as in (4.2), (4.3). The algorithm is

1. Initialize $\hat{\mbox{\boldmath $\theta$}}, \hat{{\bf a}}, \hat{\sigma}^2$. Set iteration number $n=1$.
2. Compute $\delta$$_\theta$ and $I_\theta$.
3. Update $\theta$:
   $\theta$$$_{n+1}=$$$\theta$$$_{n}+(I_\theta)^{-1}$$   $\delta$$$_\theta.$$

4. Update ${\bf a},\sigma^2$ using (4.2), (4.3).
5. Repeat.