Valpha: R-values from a matrix of posterior tail probabilities.
Description
Computes r-values directly from a "Valpha" matrix V where each
column of Valpha contains posterior tail probabilities relative
to a threshold indexed by alpha.
Usage
Valpha(V, alpha.grid, smooth = "none")
Arguments
V
a numeric vector with (i,j) entry: V[i,j] = P(theta_i >= theta[alpha_j]|data)
alpha.grid
grid of values in (0,1); used for the discrete approximation
approach for computing r-values.
smooth
either smooth="none" or smooth takes
a value between 0 and 10; this determines the level of smoothing applied to the
estimate of \(\lambda(\alpha)\); if smooth is given a number, the
number is used as the bass argument in supsmu.
Value
A list with the following components
rvalues
a vector of computed r-values
Vmarginals
The estimated V-marginals along the alpha grid points
Vmarginals.smooth
a function obtained through interpolation
and smoothing (if desired) the Vmarginals; i.e., an estimate of
\(\lambda(\alpha)\) (see rvalues)
References
Henderson, N.C. and Newton, M.A. (2015) Making the Cut: Improved Ranking and Selection
for Large-Scale Inference.http://arxiv.org/abs/1312.5776