# Posterior mean estimator

### Description

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

### Usage

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

### Arguments

`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 |

### Value

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.

### Note

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.

### Author(s)

Bernard Silverman

### References

See `ebayesthresh`

and http://www.bernardsilverman.com

### See Also

`postmed`

### Examples

1 2 |