Valpha {rvalues}

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)

Author(s)

Nicholas Henderson and Michael Newton

References

Henderson, N.C. and Newton, M.A. (2016). Making the cut: improved ranking and selection for large-scale inference. J. Royal Statist. Soc. B., 78(4), 781-804. doi: 10.1111/rssb.12131 https://arxiv.org/abs/1312.5776

See Also

rvalues rvaluesMCMC

Examples

## Not run: 
data(fluEnrich)
rvobj <- rvalues(fluEnrich, family = binomial)

Vrvals <- Valpha(rvobj$aux$V, rvobj$aux$alpha.grid)

## End(Not run)