CovTools (version 0.5.4)

PreEst.2014Banerjee: Bayesian Estimation of a Banded Precision Matrix (Banerjee 2014)

Description

PreEst.2014Banerjee returns a Bayes estimator of the banded precision matrix using G-Wishart prior. Stein<U+2019>s loss or squared error loss function is used depending on the <U+201C>loss<U+201D> argument in the function. The bandwidth is set at the mode of marginal posterior for the bandwidth parameter.

Usage

PreEst.2014Banerjee(
  X,
  upperK = floor(ncol(X)/2),
  delta = 10,
  logpi = function(k) {     -k^4 },
  loss = c("Stein", "Squared")
)

Arguments

X

an $(n\times p)$ data matrix where each row is an observation.

upperK

upper bound of bandwidth $k$.

delta

hyperparameter for G-Wishart prior. Default value is 10. It has to be larger than 2.

logpi

log of prior distribution for bandwidth $k$. Default is a function proportional to $-k^4$.

loss

type of loss; either "Stein" or "Squared".

Value

a named list containing:

C

a $(p\times p)$ MAP estimate for precision matrix.

References

banerjee_posterior_2014CovTools

Examples

# NOT RUN {
## generate data from multivariate normal with Identity precision.
pdim = 10
data = matrix(rnorm(50*pdim), ncol=pdim)

## compare different K
out1 <- PreEst.2014Banerjee(data, upperK=1)
out2 <- PreEst.2014Banerjee(data, upperK=3)
out3 <- PreEst.2014Banerjee(data, upperK=5)

## visualize
opar <- par(no.readonly=TRUE)
par(mfrow=c(2,2), pty="s")
image(diag(pdim)[,pdim:1],main="Original Precision")
image(out1$C[,pdim:1], main="banded1::upperK=1")
image(out2$C[,pdim:1], main="banded1::upperK=3")
image(out3$C[,pdim:1], main="banded1::upperK=5")
par(opar)

# }