postmed: Posterior median estimator
In EbayesThresh: Empirical Bayes Thresholding and Related Methods

Description Usage Arguments Details Value Note Author(s) References See Also Examples

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

postmed(x, s, w = 0.5, prior = "laplace", a = 0.5)
postmed.laplace(x, s = 1, w = 0.5, a = 0.5)
postmed.cauchy(x, w)
cauchy.medzero(x, z, w)

`x`	A data value or a vector of data.
`s`	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.
`w`	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"`.
`a`	The scale parameter of the nonzero part of the prior if the Laplace prior is used.
`z`	The data vector (or scalar) provided as input to `cauchy.medzero`.

The routine calls the relevant one of the routines postmed.laplace or postmed.cauchy. In the Laplace case, the posterior median is found explicitly, without any need for the numerical solution of an equation. In the quasi-Cauchy case, the posterior median is found by finding the zero, component by component, of the vector function cauchy.medzero.

If x is a scalar, the posterior median med(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 med(theta_i|x_i, s_i), where each x_i has mean theta_i and standard deviation s_i, all with the given prior.

If the quasicauchy prior is used, the argument a and s are ignored. The routine calls the approprate one of postmed.laplace or postmed.cauchy.

Bernard Silverman

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

postmean