postmed {EbayesThresh}R Documentation

Posterior median estimator

Description

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).

Usage

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)

Arguments

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.

Details

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.

Value

If xx is a scalar, the posterior median \mboxmed(θx)\mbox{med}(\theta|x) where θ\theta is the mean of the distribution from which xx is drawn. If xx is a vector with elements x1,...,xnx_1, ... , x_n and ss is a vector with elements s1,...,sns_1, ... , s_n (s_i is 1 for Cauchy prior), then the vector returned has elements \mboxmed(θixi,si)\mbox{med}(\theta_i|x_i, s_i), where each xix_i has mean θi\theta_i and standard deviation sis_i, all with the given prior.

Note

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.

Author(s)

Bernard Silverman

References

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

See Also

postmean

Examples

postmed(c(-2,1,0,-4,8,50), w = 0.05, prior = "cauchy")
postmed(c(-2,1,0,-4,8,50), s = 1:6, w = 0.2, prior = "laplace", a = 0.3)

[Package EbayesThresh version 1.4-12 Index]