Description Usage Arguments Details Value Note Author(s) References See Also
Suppose a sequence of data has underlying mean vector with elements
θ_i. Given the sequence of data, and a vector of scale
factors cs
and a lower limit pilo
, this routine finds the
marginal maximum likelihood estimate of the parameter zeta
such
that the prior probability of θ_i being nonzero is of the
form median(pilo, zeta*cs, 1)
.
1 |
xd |
A vector of data. |
cs |
A vector of scale factors, of the same length as |
pilo |
The lower limit for the estimated weights. If
|
prior |
Specification of prior to be used conditional on the mean
being nonzero; can be |
a |
Inverse scale (i.e., rate) parameter if Laplace prior
is used. Ignored if Cauchy prior is used. If, on entry, |
An exact algorithm is used, based on splitting the range up for
zeta
into subintervals over which no element of zeta*cs
crosses either pilo
or 1.
Within each of these subintervals, the log likelihood is concave and its maximum can be found to arbitrary accuracy; first the derivatives at each end of the interval are checked to see if there is an internal maximum at all, and if there is this can be found by a binary search for a zero of the derivative.
Finally, the maximum of all the local maxima over these subintervals is found.
A list with the following elements:
zeta |
The value of |
w |
The weights (prior probabilities of nonzero) yielded by this
value of |
cs |
The factors as supplied to the program. |
pilo |
The lower bound on the weight, either as supplied or as calculated internally. |
Once the maximizing zeta
and corresponding weights have
been found, the thresholds can be found using the program
tfromw
, and these can be used to process the original
data using the routine threshld
.
Bernard Silverman
See ebayesthresh
and
http://www.bernardsilverman.com
tfromw
, threshld
,
wmonfromx
, wfromx
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