Table A1.

The duality of Gaussian distribution.

	Marginalization p(α) = ∫ p(α, β)dβ	Conditioning p(α|β) = p(α, β)/p(β)
Covariance Form	μ = μα	${\mathbf{\mu }}^{\prime }={\mathbf{\mu }}_{\alpha }+{\mathrm{\Sigma }}_{\alpha \beta }{\mathrm{\Sigma }}_{\beta \beta }^{-1}\left(\mathbf{\beta }-{\mathbf{\mu }}_{\beta }\right)$
	Σ = Σαα	${\mathrm{\Sigma }}^{\prime }={\mathrm{\Sigma }}_{\alpha \alpha }-{\mathrm{\Sigma }}_{\alpha \alpha }{\mathrm{\Sigma }}_{\beta \beta }^{-1}{\mathrm{\Sigma }}_{\beta \alpha }$
Information Form	$\mathbf{\eta }={\mathbf{\eta }}_{\alpha }-{\mathrm{\Lambda }}_{\alpha \beta }{\mathrm{\Lambda }}_{\beta \beta }^{-1}{\mathbf{\eta }}_{\beta }$	η′ = ηα – Λαββ
	$\mathrm{\Lambda }={\mathrm{\Lambda }}_{\alpha \alpha }{\mathrm{\Lambda }}_{\beta \beta }^{-1}{\mathrm{\Lambda }}_{\beta \alpha }$	Λ′ = Λαα