Autoregressive parameter updates

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Here we give the update equation for the parameters of the autoregressive parameter distribution $q(a_p\vert y)=N(\mu_{a_p},\Lambda_{a_p})$ :

$\displaystyle \mu_{a_p}$	$\displaystyle =$	$\displaystyle F_{a_p}^{-1}E_{a_p}$
$\displaystyle \Lambda_{a_p}$	$\displaystyle =$	$\displaystyle F_{a_p}^{-1}$	(41)

where:

$\displaystyle F_{a_p}$	$\displaystyle =$	$\displaystyle \sum_t (w_{tp}^TS_\epsilon w_{tp}) + \gamma_{a_p}D$
$\displaystyle E_{a_p}$	$\displaystyle =$	$\displaystyle \sum_t w_{tp}^TS_\epsilon (y_{t}-\sum_{q\neq p} w_{tq}\mu_{a_q} - x_t Q\mu_{B})$	(42)

where $S_\epsilon=$ Diag $(\gamma_{{\epsilon_i}})$ and $w_{tp} = y_{t-p}-x_{t-p}Q\mu_{B}$