Given a vector of data and a single value or vector of sampling standard deviations, find the marginal maximum likelihood choice of both weight and scale factor under the Laplace prior.
wandafromx(x, s = 1, universalthresh = TRUE)
negloglik.laplace(xpar, xx, ss, tlo, thi)A vector of data.
A single value or a vector of standard deviations. If
vector, must have the same length as x.
If universalthresh = TRUE, the thresholds
will be upper bounded by universal threshold; otherwise, the
thresholds can take any non-negative values.
A vector of data.
Vector of two parameters: xpar[1] : a value between
0 and 1, which will be adjusted to range of w; xpar[2],
scale factor "a".
Vector of standard deviations.
Lower bound of thresholds.
Upper bound of thresholds.
A list with values:
The estimated weight.
The estimated scale factor.
The parameters are 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 \((s_1, ... , s_n)\) is the vector of sampling standard
deviation of data \((x_1, ... , x_n)\); otherwise, the search is over
\([0,1]\).
The search uses a nonlinear optimization routine (optim in
R) to minimize the negative log likelihood function
negloglik.laplace. The range over which the scale factor is
searched is (0.04, 3). For reasons of numerical stability within the
optimization, the prior is parametrized internally by the threshold and
the scale parameter.
# NOT RUN {
wandafromx(rnorm(100, c(rep(0,90),rep(5,10))), s = 1)
# }
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