Given a single value or a vector of data and sampling standard deviations (sd equals 1 for Cauchy prior), find the corresponding posterior mean estimate(s) of the underlying signal value(s).
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A data value or a vector of data.
A single value or a vector of standard deviations if the
Laplace prior is used. If a vector, must have the same length as
The value of the prior probability that the signal is nonzero.
Family of the nonzero part of the prior; can be
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 and s is a vector with elements s_1, ... , s_n (s_i is 1 for Cauchy prior), then the vector returned has elements E(theta_i|x_i, s_i), where each x_i has mean theta_i and standard deviation s_i, all with the given prior.
If the quasicauchy prior is used, the argument
s are ignored.
prior="laplace", the routine calls
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
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.
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