postmean: Posterior mean estimator

Description

Given a single value or a vector of data and sampling standard deviations (sd equals 1 for Cauchy prior), find the corresponding posterior mean estimate(s) of the underlying signal value(s).

Usage

postmean(x, s, w = 0.5, prior = "laplace", a = 0.5)
postmean.laplace(x, s = 1, w = 0.5, a = 0.5)
postmean.cauchy(x, w)

Arguments

A data value or a vector of data.

A single value or a vector of standard deviations if the Laplace prior is used. If a vector, must have the same length as x. Ignored if Cauchy prior is used.

The value of the prior probability that the signal is nonzero.

prior

Family of the nonzero part of the prior; can be "cauchy" or "laplace".

The scale parameter of the nonzero part of the prior if the Laplace prior is used.

Value

If \(x\) is a scalar, the posterior mean \(E(\theta|x)\) where \(\theta\) is the mean of the distribution from which \(x\) is drawn. If \(x\) is a vector with elements \(x_1, ... , x_n\) and \(s\) is a vector with elements \(s_1, ... , s_n\) (s_i is 1 for Cauchy prior), then the vector returned has elements \(E(\theta_i|x_i, s_i)\), where each \(x_i\) has mean \(\theta_i\) and standard deviation \(s_i\), all with the given prior.

References

See ebayesthresh and http://www.bernardsilverman.com

Examples

Run this code

# NOT RUN {
postmean(c(-2,1,0,-4,8,50), w = 0.05, prior = "cauchy")
postmean(c(-2,1,0,-4,8,50), s = 1:6, w = 0.2, prior = "laplace", a = 0.3)
# }