postmed {EbayesThresh}R Documentation

Posterior median estimator

Description

Given a data value or a vector of data, find the corresponding posterior median estimate(s) of the underlying signal value(s)

Usage

postmed(x, w, prior = "laplace", a = 0.5)

Arguments

x a data value or a vector of data
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

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 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, then the vector returned has elements med(theta_i|x_i), where each x_i has mean theta_i, all with the given prior.

Note

If the quasicauchy prior is used, the argument a is 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), w=0.2, prior="laplace", a=0.3)

[Package EbayesThresh version 1.3.0 Index]