//======================================================================
Vector &impute_mvn(Vector &observation,
const Vector &mean, const SpdMatrix &variance,
const Selector &observed, RNG &rng) {
if (observed.nvars() == observed.nvars_possible()) {
return observation;
} else if (observed.nvars() == 0) {
observation = rmvn_mt(rng, mean, variance);
return observation;
}
if (observation.size() != observed.nvars_possible()) {
report_error("observation and observed must be the same size.");
}
// The distribution we want is N(mu, V), with
// V = Sig11 - Sig12 Sig22.inv Sig.21
// and
// mu = mu1 - Sig12 Sig22.inv (y2 - mu2)
// The 1's are missing, and the 2's are observed.
Selector missing = observed.complement();
Matrix cross_covariance = missing.select_rows(
observed.select_cols(variance));
SpdMatrix observed_precision = observed.select_square(variance).inv();
Vector mu = missing.select(mean) + cross_covariance * observed_precision
* (observed.select(observation) - observed.select(mean));
SpdMatrix V = missing.select_square(variance)
- sandwich(cross_covariance, observed_precision);
Vector imputed = rmvn_mt(rng, mu, V);
observed.fill_missing_elements(observation, imputed);
return observation;
}
// When dimensions are small the updates are trivial, and careful
// optimization is not necessary.
void Marginal::low_dimensional_update(
const Vector &observation,
const Selector &observed,
const SparseKalmanMatrix &transition,
const SparseKalmanMatrix &observation_coefficient_subset) {
set_prediction_error(
observed.select(observation)
- observation_coefficient_subset * state_mean());
SpdMatrix forecast_variance =
observed.select_square(model_->observation_variance(time_index())) +
observation_coefficient_subset.sandwich(state_variance());
SpdMatrix forecast_precision = forecast_variance.inv();
set_forecast_precision_log_determinant(forecast_precision.logdet());
set_scaled_prediction_error(forecast_precision * prediction_error());
set_kalman_gain(transition * state_variance() *
observation_coefficient_subset.Tmult(forecast_precision));
}