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Fast Approximation Point Estimates

Here we describe how we obtain the point estimates of $ \sigma _g^2$ and $ \beta _g$ for use in the fast approximation approach described in section 3.5.

We start by rewriting equation 14 as:

$\displaystyle p(\beta_g,\sigma_g^2,\vec{\tau_K}\vert Y)$ $\displaystyle =$ $\displaystyle N(\vec{\mu_{\beta_K}};X_{G} \beta_g, U) 1/\sigma_g^2$  
$\displaystyle U$ $\displaystyle =$ $\displaystyle \left[\! \begin{array}{cccc} S_1 & 0 & \cdots & 0 \\ 0 & S_2 & & 0 \\ \vdots & & \ddots & \vdots \\ 0 & \cdots & 0 & S_N \end{array}\! \right]$  
$\displaystyle S_k$ $\displaystyle =$ $\displaystyle (\sigma_{\beta_k}^2\Sigma_{\beta_k} / \tau_k)+\sigma_g^2I$ (42)


Subsections