postmean.cauchy {ebayesthresh}R Documentation

Posterior mean estimator using quasi-Cauchy prior

Description

Given a data value or a vector of data, find the posterior mean estimate(s) of the underlying signal value(s). The quasi-Cauchy distribution is used for the nonzero component of the prior

Usage

postmean.cauchy(x, w)

Arguments

x data value or vector of data
w prior probability that signal is nonzero

Value

A value or vector of values of the estimate(s) of the mean(s) of the distribution(s) from which the x are drawn.

Note

The posterior mean is found by expressing the quasi-Cauchy prior as a mixture. The mean conditional on the mixing parameter is found and is then averaged over the posterior distribution of the mixing parameter, including the atom of probability at zero variance.

Author(s)

Bernard Silverman

References

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

See Also

postmean, postmean.laplace, postmed.cauchy

Examples

postmean.cauchy(c(-2,1,0,-4,8,50), w=0.05)

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