//----------------------------------------------------------------------
// draws Sigma one element at a time using regular slice sampling
// based on the separation strategy in Barnard, McCulloch, and Meng
// (2000 statistica sinica).
void SepStratSampler::stable_draw(){
int dim = nrow(sumsq_);
cand_ = mod_->Sigma();
sd_ = sqrt(diag(cand_));
R_ = var2cor(cand_);
Rinv_ = R_.inv();
for(int i = 0; i < dim; ++i){
draw_sigsq(i);
}
for(int i = 0; i < dim; ++i){
for(int j = 0; j < i; ++j){
draw_R(i,j);}}
fill_sigma();
mod_->set_Sigma(cand_);
}
//----------------------------------------------------------------------
// log of the prior distribution at an arbitrary value of Sigma
double SepStratSampler::logprior(const Spd & Sigma)const{
// Prior is with respect to Sigma
int d = Sigma.nrow();
R_ = var2cor(Sigma);
sd_ = sqrt(diag(Sigma));
double ans = Rpri_->logp(R_);
if(ans == BOOM::negative_infinity()) return ans;
for(int i = 0; i < sd_.size(); ++i){
double sd = sd_[i];
if(sd <=0 ) return BOOM::negative_infinity();
ans += sinv_pri_[i]->logp(1.0/square(sd));
ans += (d-3) * log(sd);
// d-3 comes from the Jacobian of two transformations:
// Sigma -> (S,R) gives s^d
// s -> 1/s^2 gives s^-3
}
return(ans);
}
//----------------------------------------------------------------------
void CS::draw() {
const Vector &mu(mod_->mu());
int n = mu.size();
Sumsq_ = mod_->suf()->center_sumsq(mu);
df_ = mod_->suf()->n();
Vector sigma = sqrt(diag(mod_->Sigma()));
R_ = var2cor(mod_->Sigma());
for (int i = 0; i < n; ++i) {
Sumsq_.row(i) /= sigma[i];
Sumsq_.col(i) /= sigma[i];
}
for (int i = 1; i < n; ++i) {
i_ = i;
for (int j = 0; j < i; ++j) {
j_ = j;
draw_one();
}
}
for (int i = 0; i < sigma.size(); ++i) {
R_.row(i) *= sigma[i];
R_.col(i) *= sigma[i];
}
mod_->set_Sigma(R_);
}
