PostPercentile {rvalues}

Posterior expected percentiles

Description

Computes posterior expected percentiles for both parametric and nonparametric models.

Usage

PostPercentile(object)

Arguments

object

An object of class "rvals"

Details

With parameters of interest \theta_1,...,\theta_n the rank of the ith parameter (when we set the ranking so that the largest \theta_i gets rank 1) is defined as rank(\theta_i) = sum_j(\theta_j \ge \theta_i) and the associated percentile is perc(\theta_i) = rank(\theta_i)/(n+1). The posterior expected percentile for the ith unit (see e.g., Lin et. al. (2006)) is simply the expected value of perc(\theta_i) given the data.

The function PostPercentile computes an asymptotic version of the posterior expected percentile, which is defined as

P(\theta_i \le \theta|data),

where \theta has the same distribution as \theta_i and is independent of both \theta_i and the data. See Henderson and Newton (2014) for additional details.

Value

A vector of estimated posterior expected percentiles.

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

Lin, R., Louis, T.A., Paddock, S.M., and Ridgeway, G. (2006). Loss function based ranking in two-stage, hierarchical models. Bayesian Analysis, 1, 915–946.

See Also

rvalues

Examples

n <- 3000
theta <- rnorm(n, sd = 3)
ses <- sqrt(rgamma(n, shape = 1, scale = 1))
XX <- theta + ses*rnorm(n)
dd <- cbind(XX,ses)

rv <- rvalues(dd, family = gaussian)

perc <- PostPercentile(rv)
plot(rv$rvalues, perc)