# GWishart_PAS_DMH: Gaussian Non-decomposable graph determination using PAS... In NonDecompGraph: NonDecomposable Graph

## Description

MCMC algorithm for Gaussian Non-decomposable graph determination using PAS algorithm.

## Usage

 `1` ```GWishart_PAS_DMH(b_prior, D_prior, n, S, C, beta, burnin, nmc) ```

## Arguments

 `b_prior` d.f. `D_prior` location `n` `S` `C` initial partial covariance matrix `beta` `burnin` number of MCMC burnin `nmc` number of MCMC samples

## Details

Sample C from Gwishart distribution with density: p(C) \propto |C|^{(bG-2)/2} exp(-1/2 tr(C DG)) where (1) bG : d.f. (2) DG: location C: initial partial covariance matrix;

## Value

 `C ` Samples from G-Wishart distribution. The result is 3D array with `c(dim(C)[1],dim(C)[2], nmc )`. `Sig ` Inverse of C The result is 3D array with `c(dim(C)[1],dim(C)[2], nmc )`. `adj` Sampled adjacency matrix. The result is 3D array with `c(dim(C)[1],dim(C)[2], nmc )`.

## Author(s)

Hao Wang ; Sophia Zhengzi Li

## References

Wang and Li (2011) "Efficient Gaussian Graphical Model Determination without Approximating Normalizing Constant of the G-Wishart distribution " http://www.stat.sc.edu/~wang345/RESEARCH/GWishart/GWishart.html

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17``` ``` p = 6; tedge = p*(p-1)/2; beta = 0.5; indmx = matrix(1:(p^2),p,p); b_prior = 3; D_prior = diag(p); n = 3*p; b_post = b_prior+n; A = toeplitz(c(1,0.5,matrix(0,1,p-2))); A[1,p] = 0.4; A[p,1] = 0.4; S = solve(A)*n; D_post = D_prior + S; adjTrue = 1*(abs(A)>0.001); burnin = 30; nmc = 100; C = diag(p); resPAS_DMH <- GWishart_PAS_DMH(b_prior,D_prior,n,S,C,beta,burnin,nmc); C_save <- resPAS_DMH[[1]] Sig_save<- resPAS_DMH[[2]] adj_save<- resPAS_DMH[[3]] ```

NonDecompGraph documentation built on May 31, 2017, 4:56 a.m.