Description Usage Arguments Details Value Author(s) References See Also Examples
Suppose the vector (x_1, …, x_n) is such that x_i is drawn independently from a normal distribution with mean θ_i and standard deviation s_i (s_i equals 1 for Cauchy prior). The prior distribution of the theta_i is a mixture with probability 1-w of zero and probability w of a given symmetric heavy-tailed distribution. This routine finds the marginal maximum likelihood estimate of the parameter w.
1 |
x |
Vector of data. |
s |
A single value or a vector of standard deviations if the
Laplace prior is used. If a vector, must have the same length as
|
prior |
Specification of prior to be used; can be
|
a |
Inverse scale (i.e., rate) parameter if Laplace prior is used. Ignored if Cauchy prior is used. |
universalthresh |
If |
The weight is found by marginal maximum likelihood.
The search is over weights corresponding to threshold t_i in the
range [0, s_i sqrt(2 log n)] if
universalthresh=TRUE
, where n is the length of the data
vector and (s_1, ... , s_n) (s_i is 1 for Cauchy prior) is the
vector of sampling standard deviation of data (x_1, ... , x_n);
otherwise, the search is over [0, 1].
The search is by binary search for a solution to the equation S(w)=0, where S is the derivative of the log likelihood. The binary search is on a logarithmic scale in w.
If the Laplace prior is used, the inverse scale parameter is fixed at
the value given for a
, and defaults to 0.5 if no value is
provided. To estimate a
as well as w
by marginal maximum
likelihood, use the routine wandafromx
.
The numerical value of the estimated weight.
Bernard Silverman
See ebayesthresh
and
http://www.bernardsilverman.com
wandafromx
, tfromx
,
tfromw
, wfromt
1 |
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