$$ P(\beta_t|\beta_{t+1},\theta,\tilde{Y}_t)=N(E(\beta_t|\beta_{t+1},\theta,\tilde{Y}_t),Var(\beta_t|\beta_{t+1},\theta,\tilde{Y}_t)) $$
$$ E(\beta_t|\beta_{t+1},\theta,\tilde{Y}_t)=\beta_{tt}+V_{tt}(V_{tt}+Q)^{-1}(\beta_{t+1}-\beta_{tt}) $$
$$ Var(\beta_t|\beta_{t+1},\theta,\tilde{Y}_t)=V_{tt}-V_{tt}(V_{tt}+Q)^{-1} $$




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