Prior mean for Beta-Binomial =3D a/(a+b)
Variance of hypothetical means =3D ab/(a+b+1)(a+b)^2 =3D prior variance=
Expected value of process variance =3D ab/(a+b+1)(a+b)
Does anyone know why the prior variance for Beta-Binomial equals to VHM=
(i.e.
ab/(a+b+1)(a+b)^2) and not the sum of VHM and EPV (i.e. ab/(a+b)^2)? I =
always
thought that (total) variance equals VHM + EPV. In Conjugate Prior
distributions, it doesn't look like this formula applies. (Same for
Gamma-Poisson: VHM for Gamma-Poisson equals its variance?)
Thanks for any inputs!
=20
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