GaussianSBR: Smoothing by Roughening, Gaussian

In gregridgeway/hhsim: Hierarchical model simulation functions

Description

Implements the smoothing by roughening (SBR) estimate of g(theta).

Usage

GaussianSBR(Y, sigma2 = rep(1, length(Y)), n.iters = round(2 * log(length(Y))), n.masspoints = 200, verbose = FALSE)

Arguments

Y	vector of data points
sigma2	vector of known variances
n.iters	number of SBR iterations
n.masspoints	number of mass points for discrete SBR approximation
verbose	indicator of whether to print progress information

Details

See Shen and Louis (1999) for complete details.

Assumes a model of the form Y[k]~N(theta[k],sigma[k]) where theta[k]~g(theta). This function gets posterior means for theta using an empirical Bayes estimate for g. It sets up n.masspoints equally spaced points on the range of Y. Using the EM algorithm, it iteratively refines the estimate of g stopping after n.iters iterations. After many 1000s of iterations this will converge to the NPML for g.

Value

theta	empirical Bayes posterior mean estimates of theta
sigma2	estimates of sigma2 (currently not estimated, assumed known)
mu	mass points for the discrete approximation to SBR
alpha	probability mass for each mu

Author(s)

Greg Ridgeway [e-mail]

References

Laird NM, Louis TA (1991). Smoothing the non-parametric estimate of a prior distribution by roughening: An empirical study. Comput. Statist. and Data Analysis, 12:27-38.

Shen W, Louis TA (1999). Empirical Bayes Estimation via the Smoothing by Roughening Approach. J. Computational and Graphical Statistics, 8: 800-823.

See Also

GaussianNPML

Examples

k <- 100
theta <- rnorm(k,0,1)
sigma <- rep(1,k)
Y <- rnorm(k,theta,sigma)

out.sbr  <- GaussianSBR(Y,sigma^2,
                        n.iters=round(3*log(k)))
x <- with(out.sbr, sample(mu,size=100000,replace=TRUE,prob=alpha))
hist(x,main="SBR",prob=TRUE,xlab="theta",ylab="g(theta)")

plot(out.sbr$theta,theta)

gregridgeway/hhsim documentation built on May 17, 2019, 8:36 a.m.