| 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
|
w |
The value of the prior probability that the signal is nonzero. |
prior |
Family of the nonzero part of the prior; can be
|
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
|
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
\mbox{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 \mbox{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
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)