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Flat Intensity Prior

$\displaystyle p(T\vert Y,S,\beta) \propto p(T) \, C_1^N \, \vert\det(G_{in}^{\m...
..._w R_{pv} R_w Y}{2} \right) \; \left( \prod_{j=1}^{D_{pv}} q_j^{-1} w_j \right)$ (11)

where

$\displaystyle w_j = \frac{1}{2} \ensuremath{\mathrm{erfc}}\left( - \left(\frac{...
...rac{\beta}{2}\right)^{1/2} \left( q_j \, C_1^{-1} - (R_w Y)_j \right) \right);
$

$ q_j^2$ is the $ j$th diagonal element of $ (G_{pv}^{\mathrm{\textsf{T}}}R_w G_{pv})$; $ N_{eff} = N - D_{in} - D_{un} - D_{pv}$; $ R_{pv} = I - R_w G_{pv}
(G_{pv}^{\mathrm{\textsf{T}}}R_w G_{pv})^{-1} G_{pv}^{\mathrm{\textsf{T}}}R_w$; and $ R_w = I - G_{in}(
G_{in}^{\mathrm{\textsf{T}}}G_{in})^{-1} G_{in}^{\mathrm{\te...
... G_{un} ( G_{un}^{\mathrm{\textsf{T}}}G_{un})^{-1}
G_{un}^{\mathrm{\textsf{T}}}$.