skewtprior: Prior parameters for mixture of multivariate skew-t's.

In twopiece: The family of two piece distributions

Description

skewtprior creates a list with prior parameters required by mixskewtGibbs. The prior is given by

(mu,Sigma) ~ N(mu; m,g*Sigma) * IWishart(Sigma; Q, q)

0.5*(alpha+1) ~ Beta(a,b)

nu is discrete with P(nu=j)=nuprobs[j]

probs ~ Symmetric Dirichlet(r), where r is a scalar

Usage

skewtprior(p,G,m=rep(0,p),g=1,Q=diag(p),q=p+1,a=2,b=2,r=1/G,nuprobs=priornuJS(1:30,k=2.78,numax=30))

Arguments

p	Number of variables in the observed data
G	Number of mixture components
m	Location parameter for prior on mu given Sigma
g	Scale parameter for prior on mu given Sigma
Q	Scale matrix for Inverse Wishart prior on Sigma
q	Degrees of freedom of Inverse Wishart prior on Sigma
a	Prior on (alpha+1)/2 is Beta(a,b)
b	Prior on (alpha+1)/2 is Beta(a,b)
r	Prior on mixture component weights is Dirichlet(r)
nuprobs	vector where P(nu=j)=nuprobs[j]. Names can be provided, else it is assumed that support of nu ranges from 1 to length(nuprobs)

Details

The Juarez-Steel prior is proportional to k*nu/(nu+k)^3.

The Villa-Walker prior is proportional to

(log(nu+1)-log(nu))/2 + lbeta(0.5,(nu+1)/2) - lbeta(0.5,nu/2) - 0.5*(nu+1)*int1 + 0.5*(nu+2)*int2

where f1= E(log(1+x^2/nu)), f2= E(log(1+x^2/(nu+1))) and x follows a standard t with nu degrees of freedom.

Value

List with elements mu, Sigma, alpha, nu and probs containing the prior parameters.

References

Rossell D., Steel M.F.J. Continuous non-Gassian mixtures. In Handbook of Cluster Analysis, CRC Press.

Examples

##See help(mixskewtGibbs)

twopiece documentation built on May 2, 2019, 5:32 p.m.