Gaussian-noise posterior for an autologistic image
= Gaussian-noise posterior for an autologistic image
{c}
{title2=$p_v^{\rm post}=\operatorname{logistic}(\alpha+\beta z_v+y_v-\tfrac12)$}
Independent unit-variance Gaussian observations with mean $x_v$ add $y_v-1/2$ to the local binary field. The <posterior distribution> <conditional probability> is $\operatorname{logistic}(\alpha+\beta z_v+y_v-1/2)$. The neighbor interaction is unchanged, so checkerboard conditional independence and the same Gibbs schemes remain valid.