rvalues (version 0.6.3)

PostPercentile: Posterior expected percentiles

Description

Computes posterior expected percentiles for both parametric and nonparametric models.

Usage

PostPercentile(object)

Arguments

object

An object of class "rvals"

Value

A vector of estimated posterior expected percentiles.

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.

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

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

# NOT RUN {
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)
# }