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BElnPrior.cpp
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BElnPrior.cpp
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#include <iostream>
#include<RcppArmadillo.h>
#include<math.h>
//Sampling Scheme from Inverse Gaussian Distribution
//[[Rcpp::export]]
Rcpp::NumericVector inversegauss(int k,Rcpp::NumericVector mu_ig_v,Rcpp::NumericVector lambda_ig_v){
//variable declaration
Rcpp::NumericVector x_ig_v(k);
Rcpp::NumericVector UniRand = Rcpp::runif(k); //sampling a vector from U(0,1)
Rcpp::NumericVector NormRand = Rcpp::rnorm(k); //sampling a vector from N(0,1)
for(int i =0; i<k ; i++){
//variable declaration
double mu_ig = mu_ig_v(i);
double lambda_ig = lambda_ig_v(i);
double y_ig;
double x_ig;
// returns 0, when we sample from inverse gauss(0.0,lambda)
if(mu_ig!=0.0) {
y_ig = pow(NormRand[i],2) ;
x_ig = mu_ig + (pow(mu_ig,2)*y_ig)/(2*lambda_ig) - (mu_ig/(2*lambda_ig))*sqrt(4*mu_ig*lambda_ig*y_ig+ pow(mu_ig,2)*pow(y_ig,2));
if (UniRand[i] >= mu_ig/(mu_ig+x_ig)) {
x_ig_v[i] = (pow(mu_ig,2))/x_ig;
} else {
x_ig_v[i] = x_ig;
}
} else {
x_ig_v[i] = 0.0;
}
}
return x_ig_v;
}
//Sampling Beta from Multivariate Normal
//[[Rcpp::depends(RcppArmadillo)]]
//[[Rcpp::export]]
Rcpp::NumericVector sampleBetainC(double sigma2, Rcpp::NumericMatrix Lambda,Rcpp::NumericMatrix XtX,Rcpp::NumericVector XtYminusYbar){
int n=XtX.nrow(), p=XtX.ncol();
arma::mat xtx(XtX.begin(),n,p,false) ;
arma::mat lambda(Lambda.begin(),p,p,false) ;
arma::vec xtyminusybar(XtYminusYbar.begin(),XtYminusYbar.size(),false);
arma::mat cov_beta = sigma2*arma::inv(xtx + lambda);
arma::vec mean_beta = (1/sigma2)*cov_beta*xtyminusybar ;
arma::mat U(p,p) ;
arma::vec s(p) ;
arma::mat V(p,p);
arma::svd(U,s,V,cov_beta);
arma::mat d(p,p);
s = arma::pow(s,.5) ;
d = arma::diagmat(s);
Rcpp::NumericVector mean = Rcpp::as<Rcpp::NumericVector>(Rcpp::wrap(mean_beta));
Rcpp::NumericMatrix cov = Rcpp::as<Rcpp::NumericMatrix>(Rcpp::wrap(cov_beta));
arma::vec beta(p);
arma::vec normrand = Rcpp::as<arma::vec>(Rcpp::rnorm(p)) ;
//arma::vec normrand(p, arma::fill::randn) ;
//beta = mean_beta + std::sqrt(sigma2)*arma::chol(cov_beta)*normrand;
beta = mean_beta +U*d*normrand;
return Rcpp::as<Rcpp::NumericVector>(Rcpp::wrap(beta));
}
//[[Rcpp::depends(RcppArmadillo)]]
//[[Rcpp::export]]
Rcpp::List BElasticNetFixed(Rcpp::NumericMatrix X,Rcpp::NumericVector Y, double lambda1, double lambda2, double asig, double bsig, int niter){
// Variable Declaration
int ncol = X.ncol();
int nrow = X.nrow();
arma::mat XX(nrow,ncol);
arma::mat XtX(ncol,ncol);
arma::colvec XtY(ncol);
arma::colvec YY(nrow);
arma::colvec XX1(ncol,ncol);
arma::colvec tausqe(ncol);
arma::colvec tauinvsqe(ncol);
arma::colvec onecol(ncol);
Rcpp::NumericMatrix dtauinv(ncol,ncol);
Rcpp::NumericMatrix xtx(ncol,ncol);
Rcpp::NumericVector xty(ncol);
Rcpp::NumericVector betae(ncol);
arma::colvec beta(ncol);
arma::colvec mu1(ncol);
arma::colvec mu2(ncol);
Rcpp::NumericVector Mu1(ncol);
Rcpp::NumericVector Mu2(ncol);
Rcpp::NumericVector Tau(ncol);
int N=niter;
arma::mat Betahist(N,ncol);
arma::mat Tausqhist(N,ncol);
Rcpp::NumericVector sigma2hist(N);
// Data Scaling
XX = Rcpp::as<arma::mat>(X);
XX = XX - arma::cumsum(XX,0)/nrow;
XX1 = XX*XX ;
XX1 = arma::cumsum(XX1,0)/(nrow-1);
XX1 = arma::pow(XX,-1/2);
XX = XX*XX1;
// Basic Variables
XtX = XX.t()*XX;
xtx = Rcpp::as<Rcpp::NumericMatrix>(Rcpp::wrap(XtX));
YY = Rcpp::as<arma::colvec>(Y);
YY = YY - arma::cumsum(YY)/nrow;
XtY = XX.t()*YY;
xty = Rcpp::as<Rcpp::NumericVector>(Rcpp::wrap(XtY));
// Starting Values
double lambda1sq = lambda1*lambda1;
double sigsqe = R::runif(.1,10);
for (int i=0;i <ncol;i++) {
tausqe[i] = R::rgamma(1,2/lambda1sq);
tauinvsqe[i] = 1/tausqe[i];
}
// MCMC Looping
for (int i =0; i <niter; i ++) {
// #beta
dtauinv = Rcpp::as<Rcpp::NumericMatrix>(Rcpp::wrap(arma::diagmat(tauinvsqe + lambda2*onecol)));
betae = sampleBetainC(sigsqe,dtauinv,xtx,xty);
// #tausq
beta = Rcpp::as<arma::colvec>(betae);
mu1 = lambda1sq*sigsqe*arma::pow(beta,-2)
mu1 = arma::pow(mu1,.5);
mu2 = lambda2*onecol;
Mu1 = Rcpp::as<Rcpp::NumericMatrix>(Rcpp::wrap(mu1));
Mu2 = Rcpp::as<Rcpp::NumericMatrix>(Rcpp::wrap(mu2));
Tau = inversegauss(ncol,Mu1,Mu2);
tauinvsqe = Rcpp::as<arma::colvec>(Tau);
tausqe = arma::pow(tauinvsqe,-1) ;
// #sigsq
double shsig = (ncol+nrow -1)/2 + asig;
double scsig = .5*( YY - XX*beta).t()*( YY - XX*beta) + 0.5*beta.t()*arma::diagmat(tauinvsqe +lambda2*onecol)*beta + bsig;
sigsqe = 1/R::rgamma(shsig,1/scsig);
Betahist.row(i) = beta.t() ;
Tausqhist.row(i) = arma::pow(tauinvsqe.t(),-1) ;
sigma2hist[i] = sisqe;
}
return Rcpp::List::create(Rcpp::Named("Betahist")=Betahist,Rcpp::Named("Tausqhist")=Tausqhist,Rcpp::Named("sigma2hist")=sigma2hist);
}