// Method of MultiNormalProposal class to generate a multivariate
// normally-distributed proposal, centered at starting value.
arma::vec MultiNormalProposal::Draw(arma::vec starting_value) {
return starting_value + RandGen.normal(covar_);
}
int main(int argc, const char * argv[])
{
double cmean = 2.0;
double bmean = 1.0;
double logssqr_mean = log(0.3);
double logssqr_var = 0.1;
double cvar = 0.3 * 0.3;
double bvar = 0.05 * 0.05;
int ndata0 = 300;
int nobjects = 200;
int mfeat = 6;
std::vector<vec2d> Xmats;
std::vector<vec1d> Yvecs;
std::vector<arma::vec> betas;
std::vector<double> sigsqrs;
for (int i=0; i<nobjects; i++) {
int ndata = 0;
if (i == nobjects - 1) {
ndata = 200;
} else {
ndata = ndata0;
}
arma::mat thisX = arma::zeros(ndata, mfeat);
thisX.col(0) = arma::ones(ndata);
for (int k=0; k<mfeat-1; k++) {
thisX.col(k+1) = 3.0 * 2.0 * arma::randn(ndata);
}
vec2d stdX;
for (int j=0; j<ndata; j++) {
vec1d Xrow = arma::conv_to<vec1d>::from(thisX.row(j));
stdX.push_back(Xrow);
}
Xmats.push_back(stdX);
arma::vec this_beta(mfeat);
this_beta.zeros();
this_beta(0) = RandGen.normal(cmean, sqrt(cvar));
this_beta(1) = RandGen.normal(bmean, sqrt(bvar));
betas.push_back(this_beta);
double this_ssqr = exp(RandGen.normal(logssqr_mean, sqrt(logssqr_var)));
sigsqrs.push_back(this_ssqr);
arma::vec unifs = arma::randu(ndata) - 0.5;
arma::vec thisY = thisX * this_beta - sqrt(this_ssqr) * unifs / arma::abs(unifs) % arma::log(1.0 - 2.0 * arma::abs(unifs));
vec1d stdY = arma::conv_to<vec1d>::from(thisY);
Yvecs.push_back(stdY);
}
int tdof = 8;
MaeGibbs Model(tdof, Yvecs, Xmats);
int nsamples = 10000;
int nburn = 20000;
int nthin = 5;
////// RUN THE GIBBS SAMPLER ///////
Model.RunMCMC(nsamples, nburn, nthin);
// make sure each value of betas are within 3-sigma of true values
arma::running_stat_vec<double> mcmc_samples(true);
boost::math::chi_squared_distribution<> chisqr_dist(mfeat);
double lower_bound = boost::math::quantile(chisqr_dist, 0.01);
double upper_bound = boost::math::quantile(chisqr_dist, 0.99);
for (int i=0; i<nobjects; i++) {
mcmc_samples.reset();
vec2d bsamples = Model.GetCoefs(i); // bsamples is of dimension [nsamples][mfeat]
for (int k=0; k<nsamples; k++) {
mcmc_samples(arma::conv_to<arma::vec>::from(bsamples[k]));
}
arma::vec post_mean = mcmc_samples.mean();
arma::mat post_cov = mcmc_samples.cov();
arma::vec post_cent = post_mean - betas[i];
double zsqr = arma::as_scalar(post_cent.t() * arma::inv(arma::sympd(post_cov)) * post_cent);
if ((zsqr > upper_bound) || (zsqr < lower_bound)) {
std::cout << "Coefficient test failed for object " << i << std::endl;
std::cout << "Reduced chis-square: " << zsqr / mfeat << std::endl;
post_mean.print("posterior mean: ");
betas[i].print("true value: ");
mcmc_samples.stddev().print("posterior stdev: ");
}
// now test sigsqr
arma::vec ssqr_samples(Model.GetSigSqr(i));
ssqr_samples = arma::log(ssqr_samples);
double post_smean = arma::mean(ssqr_samples);
double post_stdev = arma::stddev(ssqr_samples);
double zscore = (post_smean - log(sigsqrs[i])) / post_stdev;
if (std::abs(zscore) > 3.0) {
std::cout << "Noise Variance test failed for object " << i << std::endl;
std::cout << "Z-score: " << zscore << std::endl;
std::cout << "log true value: " << log(sigsqrs[i]) << std::endl;
std::cout << "posterior mean: " << post_smean << std::endl;
std::cout << "posterior stdev: " << post_stdev << std::endl;
}
}
mcmc_samples.reset();
vec2d musamples = Model.GetCoefsMean(); // musamples is of dimension [nsamples][mfeat]
for (int k=0; k<nsamples; k++) {
mcmc_samples(arma::conv_to<arma::vec>::from(musamples[k]));
}
arma::vec post_mean = mcmc_samples.mean();
arma::mat post_cov = mcmc_samples.cov();
arma::vec true_mean(mfeat);
true_mean.zeros();
true_mean(0) = cmean;
true_mean(1) = bmean;
arma::vec post_cent = post_mean - true_mean;
double zsqr = arma::as_scalar(post_cent.t() * arma::inv(arma::sympd(post_cov)) * post_cent);
if ((zsqr > upper_bound) || (zsqr < lower_bound)) {
std::cout << "Coefficient test failed for mean of coefficients." << std::endl;
std::cout << "Reduced chi-square: " << zsqr / mfeat << std::endl;
post_mean.print("posterior mean: ");
true_mean.print("true value: ");
mcmc_samples.stddev().print("posterior stdev: ");
}
// now test sigsqr
arma::vec ssqr_sample(Model.GetNoiseMean());
ssqr_sample = arma::log(ssqr_sample);
double post_smean = arma::mean(ssqr_sample);
double post_stdev = arma::stddev(ssqr_sample);
double zscore = (post_smean - logssqr_mean) / post_stdev;
if (std::abs(zscore) > 3.0) {
std::cout << "Noise Variance test failed geometric mean of noise variance." << std::endl;
std::cout << "Z-score: " << zscore << std::endl;
std::cout << "true value: " << logssqr_mean << std::endl;
std::cout << "posterior mean: " << post_smean << std::endl;
std::cout << "posterior stdev: " << post_stdev << std::endl;
}
}
// Method of NormalProposal class to generate a normally-distributed
// proposal, centered at starting_value.
double NormalProposal::Draw(double starting_value) {
return RandGen.normal(starting_value, standard_deviation_);
}
