BDgraph (version 2.33)

bdgraph.ts: Search algorithm in time series graphical models

Description

This function is for Bayesian model determination in time series graphical models, based on birth-death MCMC method.

Usage

bdgraph.ts( data, Nlength = NULL, n, iter = 1000, burnin = iter / 2,
            g.start = "empty", prior.df = rep( 3, Nlength ), save.all = FALSE )

Arguments

data

The aggregate periodogram \(P_k\), which is arranged as a large \(p x (Nlength*p)\) matrix \([P_1, P_2, ... ,P_Nlength]\).

Nlength

The length of the time series. It can be NULL.

n

The number of observations.

iter

The number of iteration for the sampling algorithm.

burnin

The number of burn-in iteration for the sampling algorithm.

g.start

Corresponds to a starting point of the graph. It could be "empty" (default) and "full". Option "empty" means the initial graph is an empty graph and "full" means a full graph. It also could be an object with S3 class "bdgraph"; with this option we could run the sampling algorithm from the last objects of previous run (see examples).

prior.df

The degree of freedom for complex G-Wishart distribution, \(CW_G(b,D)\), which is a prior distribution of the precision matrix in each frequency. The default is 3.

save.all

Logical: if FALSE (default), the adjacency matrices are NOT saved. If TRUE, the adjacency matrices after burn-in are saved.

Value

An object with S3 class "bdgraph" is returned:

p_links

An upper triangular matrix which corresponds the estimated posterior probabilities of all possible links.

K_hat

The posterior estimation of the precision matrix.

For the case "save.all = TRUE" is returned:

sample_graphs

A vector of strings which includes the adjacency matrices of visited graphs after burn-in.

graph_weights

A vector which includes the waiting times of visited graphs after burn-in.

all_graphs

A vector which includes the identity of the adjacency matrices for all iterations after burn-in. It is needed for monitoring the convergence of the BD-MCMC algorithm.

all_weights

A vector which includes the waiting times for all iterations after burn-in. It is needed for monitoring the convergence of the BD-MCMC algorithm.

status

An integer to indicate the iteration where the algorithm exits, since if the sum of all rates is 0 at some iteration, the graph at this iteration is regarded as the real graph. It is 0 if the algorithm doesn't exit.

References

Tank, A., N. Foti, and E. Fox (2015) Bayesian Structure Learning for Stationary Time Series, , arXiv:1505.03131 Mohammadi, A. and E. Wit (2015). Bayesian Structure Learning in Sparse Gaussian Graphical Models, Bayesian Analysis, 10(1):109-138 Mohammadi, A. and E. Wit (2015). BDgraph: An R Package for Bayesian Structure Learning in Graphical Models, arXiv:1501.05108 Mohammadi, A., F. Abegaz Yazew, E. van den Heuvel, and E. Wit (2016). Bayesian modelling of Dupuytren disease by using Gaussian copula graphical models, Journal of the Royal Statistical Society: Series C

See Also

bdgraph bdgraph.sim, summary.bdgraph, and compare

Examples

## Not run: ------------------------------------
# # Generating time series data
# Nlength = 100; N = 150; p = 6; b = 3
#    
# I               = diag(p)
# A               = 0.5 * matrix( rbinom( p * p, 1, 0.2 ), p, p )
# A[lower.tri(A)] = 0
# diag(A)         = 0.5
#    
# G = matrix( 0, p, p )
# K = matrix( 0, p, p * Nlength )
#    
# lambda  = seq( 0, Nlength - 1, 1 ) * 2 * pi / Nlength
# K0      = matrix( 0, p, p * Nlength )
# K_times = matrix( 1, p, p )
#    
# for( k in 1:Nlength )
# { # Compute K0
# 	K0[, ( k * p - p + 1 ):( k * p )] = I + t(A) <!-- %*% A +  -->
# 	            complex( 1, cos( -lambda[k] ), sin( -lambda[k] ) ) * A + 
# 				complex( 1, cos( lambda[k] ), sin( lambda[k] ) ) * t(A)
# 	
# 	K_times = K_times * ( K0[, ( k * p - p + 1 ):( k * p )] != 0 )
# 	diag( K[, (k * p - p + 1 ):( k * p )] ) = 1
# }
#     
# G0       = K_times
# diag(G0) = 0
#    
# D = K
# # d is the Fourier coefficients of X
# d = array( 0, c( p, Nlength, N ) )
# x = array( 0, c( p, Nlength, N ) )
# 
# for( n in 1:N )
# { # Generate X
# 	e = matrix( rnorm( p * Nlength ), p, Nlength )
# 	
# 	x[, 1, n] = e[, 1]
# 	for( t in 2:Nlength ) x[,t,n] = A <!-- %*% x[,t-1,n] + e[,t] -->
# }
#    
# P = 0 * D
# for( n in 1:N )
# { # Compute Pk
# 	X = x[,,n]
# 
# 	for( i in 1:p ) d[i, , n] = fft( X[i,] )
# 
# 	for( i in 1:Nlength ) 
# 		P[, ( i * p - p + 1 ):( i * p)] = P[, ( i * p - p + 1 ):( i * p )] + 
# 		                                  d[, i, n] <!-- %*% t( Conj( d[, i, n] ) ) -->
# }
#    
# bdgraph.obj = bdgraph.ts( P, Nlength, N, iter = 1000 )
#   
# summary( bdgraph.obj )
#      
# compare( G0, bdgraph.obj )	  
## ---------------------------------------------