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# Sample C from Gwishart distribution with density:
# p(C) \propto |C|^{(bG-2)/2} exp(-1/2 tr(C DG))
# where
# (1) bG : d.f.
# (2) DG: location
# (3) adj: adjacency matrix
# C: initial partial covariance matrix;
# burnin, nmc : number of MCMC burnins and saved samples
GWishart_BIPS_maximumClique <- function( bG, DG, adj, C, burnin, nmc )
{
adj0 <- adj - diag( diag( adj ) ) # Create adjacency matrix with diagonal elements zero
p <- dim( DG )[1]
cliqueList <- maximal.cliques( graph.adjacency( adj0 ) )
numcliques <- length( cliqueList )
C_save <- array( 0, c( p, p, nmc ) )
Sig_save <- C_save
C <- C * adj
if( !is.null( numcliques ) ){
if( ( burnin + nmc ) > 0 ){
for( iter in 1:( burnin + nmc ) ){
for( i in 1:numcliques ){
cliqueid <- cliqueList[[i]] + 1 #which(cliqueMatrix[[i]]==1);
cliquesize <- length( cliqueid )
A <- rwish( bG + cliquesize - 1, solve( DG[cliqueid,cliqueid,drop=FALSE] ) )
C_12 <- C[ cliqueid,-cliqueid,drop = FALSE]
C_22 <- C[-cliqueid,-cliqueid,drop = FALSE]
C121 <- C_12 %*% solve( C_22 ) %*% t( C_12 )
C121 <- ( C121 + t( C121 ) ) / 2
K_c <- A + C121
C[cliqueid,cliqueid] = ( K_c + t( K_c ) ) / 2
} #end for
if( iter > burnin ){
Sig_save[,,( iter - burnin )] = solve( C )
C_save[,,( iter - burnin )] = C
} #end if
} #end for
} #end if
} #end if
return( list( C= C_save, Sig = Sig_save ) )
}
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