distribution name query

[Matt Hoffman]

Hi again,

Suppose we have as part of our model
β_n ~ Normal(μ, 1/sqrt(τ))
τ ~ Gamma(a, b).
We can integrate out τ and say
log p(β) = a*log(b) - log(Γ(a)) - 0.5*N*log(2*π) + log(Γ(a + N/2)) -
(a + N/2)*log(b + 0.5*Σ_n (β_n-μ)^2).
Is there a name for that distribution, akin to the beta-binomial or
Dirichlet-multinomial distribution? Inverse-gamma-normal would be the
analogous name, but there's already the normal-inverse-gamma, which is
something else.

I ask because I want to implement this distribution in Stan, and I
don't know what to call it.

Matt

[Andrew Gelman]

In 1-d, it's a t distribution, right? Or am I missing something?
A

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[Matt Hoffman]

Yes, exactly. My question is whether there's a name for it in N-d?
Multivariate t is already taken! Maybe pooled-t or tied-t?

Matt

[Andrew Gelman]

Somebody knows…just not me!