Theoretical Study on the Evidential Learning-based Variational Autoencoder

A normal--inverse-gamma (NIG) latent hierarchy has four parameters, but its induced latent law does not identify all four. For $σ^2\sim\mathrm{InvGamma}(α,β)$, $μ\midσ^2\sim\mathcal{N}(γ,σ^2/ν)$, and $z\midμ,σ^2\sim\mathcal{N}(μ,σ^2)$, the marginal law of $z$ depends on $(ν,β)$ only through $c=β(1+1