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Samples variances of the Normal-Gamma prior distribution by Brown & Griffin (2010).

Source: R/sample_variances_normal_gamma.R
sample_variances_normal_gamma.Rd

This function samples variances from a Normal-Gamma prior distribution. The prior distribution has a hierarchical structure where each element \(x_i\) of a \(k\)-vector \(X\) follows: $$x_i \sim N(0,\vartheta_i \zeta_j), \vartheta_i \sim G(a_j, a_j / 2) \text{, and } \zeta_j^{-1} \sim G(b,c)$$ for \(i=j=1,\dots,k\). The hyperparameter \(a_j\) follows an i.i.d. discrete hyperprior with \(Pr(a_j = \tilde{a}_r) = p_r\), where \(\tilde{a} = (\tilde{a}_1, \dots, \tilde{a}_R)'\) is the vector of strictly positive support points. See Brown & Griffin (2010) and Gruber & Kastner (2025) for further details.

Usage

sample_variances_normal_gamma(
  x,
  theta_tilde,
  zeta,
  a,
  a_vec,
  varrho0,
  varrho1,
  hyper,
  tol = 1e-06
)

Arguments

x

A starting values vector of the variances. C++: an arma::vec vector object.

theta_tilde

A starting values vector of \(\vartheta_i\). C++:an arma::vec vector object.

zeta

A starting value of \(\zeta_j\). C++: an double object.

a

Prior shape parameter of the Gamma distribution for \(\vartheta_i\). C++: an double object.

a_vec

Multinomial grid for updating shape parameter of the Gamma distribution.C++: an arma::vec vector object.

varrho0

Prior shape parameter of the Gamma distribution for \(\zeta_j\). C++: an double object.

varrho1

Prior scale parameter of the Gamma distribution for \(\zeta_j\). C++: an double object.

hyper

A logical value. TRUE or FALSE. C++: an bool object

tol

The numerical tolerance, default is '1e-06'. C++: an double object.

Value

A vector of variances of the Normal-Gamma prior distribution. C++: an arma::vec object.

Details

This function is based on C++ code from the R package bayesianVARs by Gruber (2025) and is using objects and commands from the armadillo library by Sanderson & Curtin (2025) thanks to the RcppArmadillo package by Eddelbuettel, Francois, Bates, Ni, & Sanderson (2025).

References

Gruber, L. (2025). bayesianVARs: MCMC Estimation of Bayesian Vectorautoregressions. R package version 0.1.5.9000, <doi: 10.32614/CRAN.package.bayesianVARs>.

Gruber, L., & Kastner, G. (2025). Forecasting macroeconomic data with Bayesian VARs: Sparse or dense? It depends!. International Journal of Forecasting, 41(4), 1589-1619, <doi:org/10.1016/j.ijforecast.2025.02.001>.

Philip J. Brown., Jim E. Griffin (2010). Inference with normal-gamma prior distributions in regression problems. Bayesian Analysis, 5(1), 171-188, <doi:org/10.1214/10-BA507>.

Eddelbuettel D., Francois R., Bates D., Ni B., Sanderson C. (2025). RcppArmadillo: 'Rcpp' Integration for the 'Armadillo' Templated Linear Algebra Library. R package version 15.0.2-2. <doi:10.32614/CRAN.package.RcppArmadillo>

Sanderson C., Curtin R. (2025). Armadillo: An Efficient Framework for Numerical Linear Algebra. International Conference on Computer and Automation Engineering, 303-307, <doi:10.1109/ICCAE64891.2025.10980539>

Author

Jianying Shelly Xie shellyyinggxie@gmail.com

Examples

sample_variances_normal_gamma(rep(0,2), rep(1,2), 1, 1, rep(1,2), 1, 1, TRUE, 1e-6)
#>            [,1]
#> [1,] 0.00437863
#> [2,] 0.23291054