EMSHS: EM Estimator for Bayesian Shrinkage approach with Structural...

In EMSHS: EM Algorithm for Bayesian Shrinkage Approach with Structural Information Incorporated

Description

EMSHS implements the EM algorithm for Bayesian shrinkage approach that incorporates structural information. Users are referred to Chang et al (2018).

Usage

EMSHS(y, X, mus, nu, E = NULL, a_sigma = 1, b_sigma = 1, a_omega = 2,
  b_omega = 1, w = 1, eps = 1e-05)

Arguments

y	An n by 1 response vector
X	An n by p design matrix
mus	A vector of shrinkage parameters
nu	The adaptivity parameter
E	An e by 2 matrix with edges. Edges must be sorted by the first column and then the second column. A single edge (j,k) must be duplicated with (k,j) in E. NULL if no edge.
a_sigma	The shape parameter of the prior for residual variance.
b_sigma	The rate parameter of the prior for residual variance.
a_omega	The shape parameter of the prior for nonzero omega values.
b_omega	The rate parameter of the prior for nonzero omega values.
w	A weight vector for samples.
eps	The algorithm stops if relative improvement goes below eps.

Value

A list that contains the number of EM iterations (niter), the estimated coefficients (beta), the estimated residual variance (sigma), the estimated shrinkage parameter (lambda), and the imputed correlations for the shrinkage parameter (omega) is returned.

References

\insertRef

chang2018EMSHS

Examples

 # Example with no edges for a high-dimensional data
 # with n = 25 observations and p = 50 predictors

 set.seed(100)

 X <- matrix(rnorm(25*50), ncol = 50)
 B <- matrix(c(1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
               0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
               0,0,0,0,0,0,0,0,0,0), ncol = 1)
 e <- matrix(rnorm(25*1), ncol = 1)
 y <- matrix(X %*% B + e, ncol = 1)
 mus <- 2.3
 nu <- 0.3


 em_no_edge <- EMSHS(y, X, mus, nu, E = NULL,
                     a_sigma = 1, b_sigma = 1, a_omega = 2, b_omega = 1,
                     w = 1, eps = 1e-5)


 # Example with user-defined set of sorted, undirected
 # edges (E) for a high-dimensional data with n = 25
 # and p = 50

 X <- matrix(rnorm(25*50), ncol = 50)
 B <- matrix(c(1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
               0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
               0,0,0,0,0,0,0,0,0,0), ncol = 1)
 e <- matrix(rnorm(25*1), ncol = 1)
 y <- matrix(X %*% B + e, ncol = 1)
 mus <- 2.3
 nu <- 0.3
EE <- matrix(c(1,4,
              4,1,
              1,2,
              2,1,
              1,5,
              5,1,
              2,3,
              3,2,
              3,5,
              5,3,
              10,11,
              11,10,
              19,11,
              11,19,
              36,35,
              35,36,
              31,35,
              35,31,
              31,22,
              22,31,
              22,45,
              45,22,
              45,32,
              32,45,
              22,21,
              21,22,
              31,21,
              21,31,
              21,25,
              25,21,
              21,18,
              18,21,
              18,49,
              49,18,
              49,47,
              47,49,
              47,37,
              37,47,
              37,21,
              21,37,
              18,25,
              25,18), nrow = 42, ncol = 2, byrow = TRUE)

 # Sort edges by first column then second column

 E <- EE[do.call(order, lapply(1:ncol(EE), function(i) EE[,i])),]

 em_edge <- EMSHS(y, X, mus, nu, E,
                  a_sigma = 1, b_sigma = 1, a_omega = 2, b_omega = 1,
                  w = 1, eps = 1e-5)

EMSHS documentation built on May 1, 2019, 9:23 p.m.