// [[Rcpp::export]]
double alphapost(colvec& y,mat& X, int k, colvec t, colvec& betadraw,
mat& Rdraw, mat& S, double gammadraw, double alpha,
double delta, double eta){
int n = X.n_rows, l = n/k;
mat invR = inv(Rdraw);
mat invS = inv(S);
mat invSig = invS*invR*invS;
double empSS = 0;
for (int j=0; j<n; j+=k){
colvec res = y.rows(j,j+k-1)-X.rows(j,j+k-1)*betadraw;
empSS += as_scalar(trans(res)*invSig*res);
}
//colvec alphat = -alpha*t, gammat = - gammadraw/t;
//double maxalphat = max(alphat), maxgammat = max(gammat);
double zalpha = max(-alpha*t)/delta,
zgamma = max(-gammadraw/t)/eta;
double dalpha = R::dnorm(zalpha,0.0,1.0,0);
double dgamma = R::dnorm(zgamma,0.0,1.0,0);
double logval = -0.5*l*log(det(S*Rdraw*S))-0.5*empSS-0.5*pow((alpha/eta),2)-log(1-dalpha)-log(1-dgamma);
return logval;
}
// [[Rcpp::export]]
double Rpost(colvec& y, mat& X, int k, colvec& betadraw,
mat& Sdraw, mat& R){
int n = X.n_rows, l = n/k;
mat invR = inv(R);
mat invS = inv(Sdraw);
mat invSig = invS*invR*invS;
double empSS = 0;
for (int j=0; j<n; j+=k){
colvec res = y.rows(j,j+k-1)-X.rows(j,j+k-1)*betadraw;
empSS += as_scalar(trans(res)*invSig*res);
}
return (-0.5*l*log(det(R))-0.5*empSS);
}
// [[Rcpp::export]]
colvec betaUpdate(colvec& y, mat& X, int k, mat& Sdraw,
mat& Rdraw, colvec& B0, mat& sigB){
int n = X.n_rows, p = X.n_cols;
mat VB = zeros<mat>(p,p);
colvec muB = zeros<colvec>(p);
mat invR = inv(Rdraw);
mat invS = inv(Sdraw);
mat invSig = invS*invR*invS;
for(int j=0; j<n; j+=k){
VB += trans(X.rows(j,j+k-1))*invSig*X.rows(j,j+k-1);
muB += trans(X.rows(j,j+k-1))*invSig*y.rows(j,j+k-1);
}
mat V1 = inv(inv(sigB)+VB);
colvec mu1 = V1*(inv(sigB)*B0+muB);
colvec betadraw = vectorise(mvrnorm(1, mu1,V1));
return betadraw;
}
// [[Rcpp::export]]
double logLik(colvec& y, mat& X, int k, int nblock, List t,
colvec& betadraw, mat& Sdraw, mat& Rdraw,
colvec& B0, mat& sigB, double delta, double eta,
colvec& gammadraw, colvec& alphadraw){
int n = X.n_rows, p = X.n_cols, l = n/k;
double logy, logbeta, logprior,logfull;
int tlen = k/nblock;
double alphaj, gammaj, maxalphat, maxgammat;
colvec alphat = zeros<colvec>(tlen),
gammat = zeros<colvec>(tlen);
colvec loggamma(nblock), logalpha(nblock);
colvec valpha(nblock), vgamma(nblock),
dalpha(nblock), dgamma(nblock);
NumericVector tj(tlen);
mat invR = inv(Rdraw);
mat invS = inv(Sdraw);
mat invSig = invS*invR*invS;
double empSS = 0;
for (int j=0; j<n; j+=k){
colvec res = y.rows(j,j+k-1)-X.rows(j,j+k-1)*betadraw;
empSS += as_scalar(trans(res)*invSig*res);
}
// log likelihood of data y, pi = M_PI
logy = as_scalar(-0.5*k*l*log(2*M_PI)-0.5*l*log(det(Sdraw*Rdraw*Sdraw))-0.5*empSS);
// log prior for beta
logbeta = as_scalar(-0.5*p*log(2*M_PI)-0.5*log(det(sigB))-0.5*(trans(betadraw-B0)*inv(sigB)*(betadraw-B0)));
//RNGScope scope;
for(int j=0; j<nblock; j++){
tj = t[j];
alphaj = alphadraw(j);
alphat = -alphaj*tj;
maxalphat = max(alphat);
gammaj = gammadraw(j);
gammat = - gammaj/tj;
maxgammat = max(gammat);
valpha(j) = maxalphat/delta;
vgamma(j) = maxgammat/eta;
dalpha(j) = R::dnorm(valpha(j),0.0,1.0,0);
dgamma(j) = R::dnorm(vgamma(j),0.0,1.0,0);
loggamma(j) = -0.5*log(2*M_PI)-log(delta)-0.5*pow(gammadraw(j)/delta,2)-log(1-dalpha(j));
logalpha(j) = -0.5*log(2*M_PI)-log(eta)-0.5*pow(alphadraw(j)/eta,2)-log(1-dgamma(j));
}
logprior = logbeta + sum(loggamma) + sum(logalpha);
logfull = logy + logprior;
return logfull;
}