Posterior mean estimator
Given a data value or a vector of data, find the corresponding posterior mean estimate(s) of the underlying signal value(s)
postmean(x, w, prior = "laplace", a = 0.5)
a data value or a vector of data
the value of the prior probability that the signal is nonzero
family of the nonzero part of the prior; can be "cauchy" or "laplace"
the scale parameter of the nonzero part of the prior if the Laplace prior is used
If x is a scalar, the posterior mean E(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 E(theta_i|x_i), where each x_i has mean theta_i, all with the given prior.
If the quasicauchy prior is used, the argument
a is ignored.
prior="laplace", the routine calls
postmean.laplace, which finds the posterior
mean explicitly, as the product of the posterior probability that the parameter is nonzero and
the posterior mean conditional on not being zero.
prior="cauchy", the routine calls
postmean.cauchy; in that case
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.
ebayesthresh and http://www.bernardsilverman.com