//----------------------------------------------------------------------
double PoissonBartPosteriorSampler::draw_mean(Bart::TreeNode *leaf) {
const Bart::PoissonSufficientStatistics &suf(
dynamic_cast<const Bart::PoissonSufficientStatistics &>(
leaf->compute_suf()));
double ivar = suf.sum_of_weights() + 1.0 / mean_prior_variance();
double posterior_mean = suf.weighted_sum_of_residuals() / ivar;
double posterior_sd = sqrt(1.0 / ivar);
return rnorm_mt(rng(), posterior_mean, posterior_sd);
}
//----------------------------------------------------------------------
double ProbitBartPosteriorSampler::draw_mean(Bart::TreeNode *leaf) {
const Bart::ProbitSufficientStatistics &suf(
dynamic_cast<const Bart::ProbitSufficientStatistics &>(
leaf->compute_suf()));
double prior_variance = mean_prior_variance();
double ivar = suf.sample_size() + (1.0 / prior_variance);
double posterior_mean = suf.sum() / ivar;
double posterior_sd = sqrt(1.0 / ivar);
return rnorm_mt(rng(), posterior_mean, posterior_sd);
}
//----------------------------------------------------------------------
// Drawing the mean at a leaf node is like drawing the intercept in
// a logistic regression model after the other linear effects have
// been subtracted out.
double LogitBartPosteriorSampler::draw_mean(Bart::TreeNode *leaf) {
const Bart::LogitSufficientStatistics &suf(
dynamic_cast<const Bart::LogitSufficientStatistics &>(
leaf->compute_suf()));
double prior_variance = mean_prior_variance();
double ivar = (1.0 / prior_variance) + suf.sum_of_information();
double posterior_mean = suf.information_weighted_residual_sum() / ivar;
double posterior_sd = sqrt(1.0 / ivar);
return rnorm_mt(rng(), posterior_mean, posterior_sd);
}
double GaussianBartPosteriorSampler::draw_mean(Bart::TreeNode *leaf) {
double sigsq = model_->sigsq();
const Bart::GaussianBartSufficientStatistics &suf(
dynamic_cast<const Bart::GaussianBartSufficientStatistics &>(
leaf->compute_suf()));
double ivar = suf.n() / sigsq + 1.0 / mean_prior_variance();
double mean = (suf.sum() / sigsq) / ivar;
double sd = sqrt(1.0 / ivar);
double value = rnorm_mt(rng(), mean, sd);
return value;
}
//----------------------------------------------------------------------
// Omits a factor of (2*pi)^{N/2} \exp{-.5 * (N - 1) * s^2 } from
// the integrated likelihood.
double ProbitBartPosteriorSampler::log_integrated_probit_likelihood(
const Bart::ProbitSufficientStatistics &suf) const {
double n = suf.sample_size();
if (n <= 0) {
return negative_infinity();
}
double ybar = suf.sum() / n; // handle n == 0;
double prior_variance = mean_prior_variance();
double ivar = n + (1.0 / prior_variance);
double posterior_variance = 1.0 / ivar;
double posterior_mean = suf.sum() / ivar;
double ans = log(posterior_variance / prior_variance)
- n * square(ybar)
+ square(posterior_mean) / posterior_variance;
return .5 * ans;
}
//----------------------------------------------------------------------
double PoissonBartPosteriorSampler::log_integrated_likelihood(
const Bart::SufficientStatisticsBase &abstract_suf) const {
const Bart::PoissonSufficientStatistics &suf(
dynamic_cast<const Bart::PoissonSufficientStatistics &>(
abstract_suf));
double prior_variance = mean_prior_variance();
double ivar = suf.sum_of_weights() + (1.0 / prior_variance);
double posterior_mean = suf.weighted_sum_of_residuals() / ivar;
double posterior_variance = 1.0 / ivar;
// We omit facors in the integrated likelihood that will cancel in
// the MH ratio for splitting nodes in the same tree. The omitted
// is the log of (2 * pi)^(-n/2) * \prod(w[i] ^.5)
double ans =
.5 * (log(posterior_variance / prior_variance)
+(square(posterior_mean) / posterior_variance));
return ans;
}
double GaussianBartPosteriorSampler::log_integrated_gaussian_likelihood(
const Bart::GaussianBartSufficientStatistics &suf) const {
double n = suf.n();
if (n < 5) {
return negative_infinity();
}
double prior_variance = mean_prior_variance();
double sigsq = model_->sigsq();
double ybar = suf.ybar();
double sample_variance = suf.sample_var();
double ivar = (n / sigsq) + (1.0 / prior_variance);
double posterior_variance = 1.0 / ivar;
double posterior_mean = (n * ybar / sigsq) / ivar;
double ans = -n * (log_2_pi + log(sigsq)) +
log(posterior_variance / prior_variance) -
(n - 1) * sample_variance / sigsq - n * square(ybar) / sigsq +
square(posterior_mean) / posterior_variance;
return .5 * ans;
}
// As documented above, this function returns the log integrated
// likelihood, with the following factor omitted from the
// likelihood.
//
// (2 * pi)^{-n/2} \prod_i w[i]^{1/2} exp(-.5 \sum_i w[i]y[i]^2)
double LogitBartPosteriorSampler::log_integrated_logit_likelihood(
const Bart::LogitSufficientStatistics &suf) const {
double information = suf.sum_of_information();
if (information <= 0) {
// The node is empty. Note that information can never be
// negative. The <= comparison is used because it is not safe
// to ask information == 0 on a double.
return 0;
}
double prior_variance = mean_prior_variance();
double ivar = information + (1.0 / prior_variance);
double posterior_variance = 1.0 / ivar;
double posterior_mean = suf.information_weighted_sum() / ivar;
// This function omits a factor of (2 * pi)^(-n/2) * \prod_i
// w[i]^{-.5} from the integrated likelihood, because it will
// cancel in the relevant MH acceptance ratios.
double ans = .5 * (
log(posterior_variance / prior_variance)
+ (square(posterior_mean) / posterior_variance));
return ans;
}
