//----------------------------------------------------------------------
// log posterior if R(i_,j_) is replaced by r. performs work needed
// for slice sampling in draw_R(i,j)
double SepStratSampler::logp_slice_R(double r){
set_R(r);
fill_siginv(false); // false means we need to compute Rinv
const Spd & Siginv(cand_);
double ans = .5 * n_ * logdet(Siginv); // positive .5
ans += -.5 * traceAB(Siginv, sumsq_);
ans += Rpri_->logp(R_);
// skip the jacobian because it only has products of sigma^2's in it
return ans;
}
double ZMMM::loglike()const{
const double log2pi = 1.83787706641;
double dim = mu_.size();
double n = suf()->n();
const Vec ybar = suf()->ybar();
const Spd sumsq = suf()->center_sumsq();
double qform = n*(siginv().Mdist(ybar));
qform+= traceAB(siginv(), sumsq);
double nc = 0.5*n*( -dim*log2pi + ldsi());
double ans = nc - .5*qform;
return ans;
}
double WeightedMvnModel::loglike(const Vector &mu_siginv_triangle)const{
const double log2pi = 1.83787706641;
const ConstVectorView mu(mu_siginv_triangle, 0, dim());
SpdMatrix siginv(dim());
Vector::const_iterator it = mu_siginv_triangle.begin() + dim();
siginv.unvectorize(it, true);
double ldsi = siginv.logdet();
double sumlogw = suf()->sumlogw();
const SpdMatrix sumsq = suf()->center_sumsq();
double n = suf()->n();
double ans = n*.5*(log2pi + ldsi) + dim() * .5 *sumlogw;
ans -= -.5*traceAB(siginv, suf()->center_sumsq(mu));
return ans;
}
//----------------------------------------------------------------------
// returns the log posterior distribution if element i_ of 1/sd_^2
// is replaced by ivar. supports slice sampler in draw_sigsq(i_);
double SepStratSampler::logp_slice_ivar(double ivar){
double ans = sinv_pri_[i_]->logp(ivar); // prior on ivar
ans += .5 * n_ * log(ivar); // determinant
sd_[i_] = 1.0/sqrt(ivar);
fill_siginv(true);
const Spd & Siginv(cand_);
ans += -.5 * traceAB(Siginv, sumsq_); // exponential
double logsd = log(sd_[i_]); // jacobian Sigma -> S
int dim = sd_.size();
ans += dim * logsd; // see notes in "logprior" member function
ans += -3 * logsd; // jacobian S -> ivar
return ans;
}
double WishartModel::Loglike(const Vector &sumsq_triangle_nu,
Vector &g, uint nd)const{
const double log2 = 0.69314718055994529;
const double logpi = 1.1447298858494002;
int k=dim();
SpdParams Sumsq_arg(dim());
Vector::const_iterator it = Sumsq_arg.unvectorize(sumsq_triangle_nu, true);
double nu = *it;
const SpdMatrix &SS(Sumsq_arg.var());
if(nu <k) return negative_infinity();
double ldSS = 0;
bool ok=true;
ldSS = SS.logdet(ok);
if(!ok) return negative_infinity();
double n = suf()->n();
double sumldw = suf()->sumldw();
const SpdMatrix &sumW(suf()->sumW());
double tab = traceAB(SS, sumW);
double tmp1(0), tmp2(0);
for(int i = 1; i<=k; ++i){
double tmp = .5*(nu-i+1);
tmp1+= lgamma(tmp);
if(nd>0) tmp2+= digamma(tmp);
}
double ans = .5*( n*(-nu*k*log2 - .5*k*(k-1)*logpi -2*tmp1 + nu*ldSS)
+(nu-k-1)*sumldw - tab);
if(nd>0){
double dnu = .5*( n*(-k*log2 - tmp2+ldSS) + sumldw);
SpdMatrix SSinv(SS.inv());
int m=0;
for(int i=0; i<k; ++i){
for(int j=0; j<=i; ++j){
g[m] = .5*n*nu * (i==j? SSinv(i,i) : 2*SSinv(i,j));
g[m] -= .5*(i==j ? sumW(i,i) : 2* sumW(i,j));
++m; }}
g[m] = dnu;
}
return ans;
}
