beta.laplace: Function beta for the Laplace prior

In stephenslab/EbayesThresh: Empirical Bayes Thresholding and Related Methods

Description

Given a single value or a vector of x and s, find the value(s) of the function beta(x;s,a) = g(x;s,a)/fn(x;0,s) - 1 , where fn(x;0,s) is the normal density with mean 0 and standard deviation s, and g is the convolution of the Laplace density with inverse scale (rate) parameter a, gamma(mu; a), with the normal density fn(x;mu,s) with mean mu and standard deviation s.

Usage

beta.laplace(x, s = 1, a = 0.5)

Arguments

x	Vector of data values.
s	Value or vector of standard deviations; if vector, must have the same length as x
a	Inverse scale (i.e., rate) parameter of the Laplace distribution.

Value

A vector of the same length as x is returned, containing the value(s) beta(x).

Note

The Laplace density is given by gamma(u) = (a/2) exp(-a|u|) and is also known as the double exponential density.

Author(s)

Bernard Silverman

References

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

See Also

beta.cauchy

Examples

beta.laplace(c(-2,1,0,-4,8,50), s=1)
beta.laplace(c(-2,1,0,-4,8,50), s=1:6, a=1)

stephenslab/EbayesThresh documentation built on May 15, 2019, 4:28 p.m.