lmn_prior {LMN} | R Documentation |
Conjugate prior specification for LMN models.
Description
The conjugate prior for LMN models is the Matrix-Normal Inverse-Wishart (MNIW) distribution. This convenience function converts a partial MNIW prior specification into a full one.
Usage
lmn_prior(p, q, Lambda, Omega, Psi, nu)
Arguments
p |
Integer specifying row dimension of Beta . p = 0 corresponds to no Beta in the model, i.e., X = 0 in lmn_suff() .
|
q |
Integer specifying the dimension of Sigma .
|
Lambda |
Mean parameter for Beta . Either:
A p x q matrix.
A scalar, in which case Lambda = matrix(Lambda, p, q) .
Missing, in which case Lambda = matrix(0, p, q) .
|
Omega |
Row-wise precision parameter for Beta . Either:
A p x p matrix.
A scalar, in which case Omega = diag(rep(Omega,p)) .
Missing, in which case Omega = matrix(0, p, p) .
-
NA , which signifies that Beta is known, in which case the prior is purely Inverse-Wishart on Sigma (see Details).
|
Psi |
Scale parameter for Sigma . Either:
A q x q matrix.
A scalar, in which case Psi = diag(rep(Psi,q)) .
Missing, in which case Psi = matrix(0, q, q) .
|
nu |
Degrees-of-freedom parameter for Sigma . Either a scalar, missing (defaults to nu = 0 ), or NA , which signifies that Sigma = diag(q) is known, in which case the prior is purely Matrix-Normal on Beta (see Details).
|
Details
The Matrix-Normal Inverse-Wishart (MNIW) distribution (B,Σ)∼MNIW(Λ,Ω,Ψ,ν)
on random matrices Xp×q
and symmetric positive-definite Σq×q
is defined as
ΣB∣Σ∼∼Inverse-Wishart(Ψ,ν)Matrix-Normal(Λ,Ω−1,Σ),
where the Matrix-Normal distribution is defined in lmn_suff()
.
Value
A list with elements Lambda
, Omega
, Psi
, nu
with the proper dimensions specified above, except possibly Omega = NA
or nu = NA
(see Details).
Examples
# problem dimensions
p <- 2
q <- 4
# default noninformative prior pi(Beta, Sigma) ~ |Sigma|^(-(q+1)/2)
lmn_prior(p, q)
# pi(Sigma) ~ |Sigma|^(-(q+1)/2)
# Beta | Sigma ~ Matrix-Normal(0, I, Sigma)
lmn_prior(p, q, Lambda = 0, Omega = 1)
# Sigma = diag(q)
# Beta ~ Matrix-Normal(0, I, Sigma = diag(q))
lmn_prior(p, q, Lambda = 0, Omega = 1, nu = NA)
[Package
LMN version 1.1.3
Index]