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# Copyright (C) 2012 - 2021 Reza Mohammadi |
# |
# This file is part of BDgraph package. |
# |
# BDgraph is free software: you can redistribute it and/or modify it under |
# the terms of the GNU General Public License as published by the Free |
# Software Foundation; see <https://cran.r-project.org/web/licenses/GPL-3>.|
# |
# Maintainer: Reza Mohammadi <a.mohammadi@uva.nl> |
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# To compute the normalizing constant of G-Wishart distribution based on |
# Monte Carlo algorithm according to below paper |
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# Atay-Kayis & Massam (2005). A monte carlo method for computing the |
# marginal likelihood in nondecomposable Gaussian graphical models, Biometrika|
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gnorm = function( adj, b = 3, D = diag( ncol( adj ) ), iter = 100 )
{
if ( b < 3 ) stop( "'b' must be more than 2" )
if( is.null( adj ) ) stop( "'adj' must be determined" )
G <- unclass( adj )
G <- as.matrix( G )
p <- nrow( G )
if( p != ncol( G ) ) stop( "'adj' must be a square matrix" )
if( ( sum( G == 0 ) + sum( G == 1 ) ) != ( nrow( G ) ^ 2 ) ) stop( "Elements of matrix 'adj' must be 0 or 1" )
G[ lower.tri( G, diag = TRUE ) ] <- 0
Ti = chol( solve( D ) )
H = Ti / t( matrix( rep( diag( Ti ), p ), p, p ) )
check_H = identical( H, diag( p ) ) * 1
nu = rowSums( G )
size_graph = sum( G )
# For the case, G is a full graph
if( size_graph == ( p * ( p - 1 ) / 2 ) )
{
logIg = ( size_graph / 2 ) * log( pi ) + ( p * ( b + p - 1 ) / 2 ) * log( 2 ) +
sum( lgamma( ( b + nu ) / 2 ) ) - ( ( b + p - 1 ) / 2 ) * log( det( D ) )
}
# For the case, G is an empty graph
if( size_graph == 0 )
logIg = ( p * b / 2 ) * log( 2 ) + p * lgamma( b / 2 ) - ( b / 2 ) * sum( log( diag( D ) ) )
if( ( size_graph != ( p * ( p - 1 ) / 2 ) ) & ( size_graph != 0 ) )
{ # For the case G is NOT full graph
# - - Monte Carlo glorithm which is implemented in C++ - - - - - - - -|
f_T = c( rep( 0, iter ) )
result = .C( "log_exp_mc", as.integer( G ), as.integer( nu ), as.integer( b ), as.double( H ), as.integer( check_H ),
as.integer( iter ), as.integer( p ), f_T = as.double( f_T ), PACKAGE = "BDgraph" )
f_T = c( result $ f_T )
log_Ef_T = log( mean( exp( - f_T / 2 ) ) )
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c_dT = ( size_graph / 2 ) * log( pi ) + ( p * b / 2 + size_graph ) * log( 2 ) +
sum( lgamma( ( b + nu ) / 2 ) ) + sum( ( b + nu + colSums( G ) ) * log( diag( Ti ) ) )
logIg = c_dT + log_Ef_T
}
return( logIg )
}
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