Given a data value or a vector of data, find the corresponding posterior mean estimate(s) of the underlying signal value(s)

1 | ```
postmean(x, w, prior = "laplace", a = 0.5)
``` |

`x` |
a data value or a vector of data |

`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 |

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.
If `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.
If `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.

Bernard Silverman

See `ebayesthresh`

and http://www.bernardsilverman.com

1 2 |

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