R: Posterior median estimator

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 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.

### 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]