First derivatives

$\displaystyle \mbox{\boldmath$\delta$}$ $\displaystyle _{\bf a}=\frac{\partial}{\partial {\bf a}} \log p({\bf x};$ $\displaystyle \mbox{\boldmath$\theta$}$ $\displaystyle ,{\bf a},\sigma^2)= \frac{1}{\sigma^2}({\bf x}-{\bf H}_\theta {\bf a})^\prime {\bf H}_\theta.$

(4.4)

$\displaystyle \mbox{\boldmath$\delta$}$ $\displaystyle _\theta=\frac{\partial}{\partial \theta} \log p({\bf x};$ $\displaystyle \mbox{\boldmath$\theta$}$ $\displaystyle ,{\bf a},\sigma^2)= \frac{1}{\sigma^2}({\bf x}-{\bf H}_\theta {\bf a})^\prime {\bf H}^\theta_\theta {\bf a},$

(4.5)

$\displaystyle \mbox{\boldmath$\delta$}$ $\displaystyle _{\sigma^2}=\frac{\partial}{\partial \sigma^2} \log p({\bf x};$ $\displaystyle \mbox{\boldmath$\theta$}$ $\displaystyle ,{\bf a},\sigma^2)= -\frac{N}{2\sigma^2}+ \frac{1}{2\sigma^4}({\bf x}-{\bf H}_\theta {\bf a})^\prime ({\bf x}-{\bf H}_\theta {\bf a})$

(4.6)