| Title: | Graphical Horseshoe MCMC Sampler Using Data Augmented Block Gibbs Sampler |
|---|---|
| Description: | Draw posterior samples to estimate the precision matrix for multivariate Gaussian data. Posterior means of the samples is the graphical horseshoe estimate by Li, Bhadra and Craig(2017) <arXiv:1707.06661>. The function uses matrix decomposition and variable change from the Bayesian graphical lasso by Wang(2012) <doi:10.1214/12-BA729>, and the variable augmentation for sampling under the horseshoe prior by Makalic and Schmidt(2016) <arXiv:1508.03884>. Structure of the graphical horseshoe function was inspired by the Bayesian graphical lasso function using blocked sampling, authored by Wang(2012) <doi:10.1214/12-BA729>. |
| Authors: | Ashutosh Srivastava<[email protected]>, Anindya Bhadra<[email protected]> |
| Maintainer: | Ashutosh Srivastava<[email protected]> |
| License: | GPL-2 |
| Version: | 0.1 |
| Built: | 2024-06-28 06:10:21 UTC |
| Source: | CRAN |
GHS_est returns a tuple whose first element is a p by p by nmc matrices of saved posterior samples of precision matrix, second element is the p*(p-1)/2 by nmc vector of saved samples of the local tuning parameter and the third element is the 1 by nmc vector of saved samples of the global tuning parameter
GHS_est(S, n, burnin, nmc)GHS_est(S, n, burnin, nmc)
S |
sample covariance matrix |
n |
sample size |
burnin |
number of MCMC burnins |
nmc |
number of saved samples |
# This function generates positive definite matrices for testing purposes # with specificied eigenvalues Posdef <- function (n,ev) { Z <- matrix(ncol=n, rnorm(n^2)) decomp <- qr(Z) Q <- qr.Q(decomp) R <- qr.R(decomp) d <- diag(R) ph <- d / abs(d) O <- Q %*% diag(ph) Z <- t(O) %*% diag(ev) %*% O return(Z) } eig1 <- rep(1,2) eig2 <- rep(0.75,3) #eig3 <- rep(0.25,3) eig_val <- c(eig1,eig2) z <- Posdef(5,eig_val) Mu <- rep(0,5) Sigma <- solve(z) Y <- mvrnorm(n=5,mu=Mu,Sigma=Sigma) S <- t(Y)%*%Y out <- GHS_est(S,50,100,5000) est_matrix <- apply(out[[1]],c(1,2),mean) image(est_matrix)# This function generates positive definite matrices for testing purposes # with specificied eigenvalues Posdef <- function (n,ev) { Z <- matrix(ncol=n, rnorm(n^2)) decomp <- qr(Z) Q <- qr.Q(decomp) R <- qr.R(decomp) d <- diag(R) ph <- d / abs(d) O <- Q %*% diag(ph) Z <- t(O) %*% diag(ev) %*% O return(Z) } eig1 <- rep(1,2) eig2 <- rep(0.75,3) #eig3 <- rep(0.25,3) eig_val <- c(eig1,eig2) z <- Posdef(5,eig_val) Mu <- rep(0,5) Sigma <- solve(z) Y <- mvrnorm(n=5,mu=Mu,Sigma=Sigma) S <- t(Y)%*%Y out <- GHS_est(S,50,100,5000) est_matrix <- apply(out[[1]],c(1,2),mean) image(est_matrix)