horseshoe (version 0.2.0)

HS.var.select: Variable selection using the horseshoe prior

Description

The function implements two methods to perform variable selection. The first checks whether 0 is contained in the credible set (see Van der Pas et al. (2016)). The second is only intended for the sparse normal means problem (regression with identity matrix). It is described in Carvalho et al. (2010). The horseshoe posterior mean can be written as \(c_i y_i\), with \(y_i\) the observation. A variable is selected if \(c_i \geq c\), where \(c\) is a user-specified threshold.

Usage

HS.var.select(hsobject, y, method = c("intervals", "threshold"),
  threshold = 0.5)

Arguments

hsobject

The outcome from one of the horseshoe functions horseshoe or HS.normal.means.

y

The data.

method

Use "intervals" to perform variable selection using the credible sets (at the level specified when creating the hsobject), "threshold" to perform variable selection using the thresholding procedure (only for the sparse normal means problem).

threshold

Threshold for the thresholding procedure. Default is 0.5.

Value

A vector of zeroes and ones. The ones correspond to the selected variables.

References

van der Pas, S.L., Szabo, B., and van der Vaart, A. (2017), Uncertainty quantification for the horseshoe (with discussion). Bayesian Analysis 12(4), 1221-1274.

van der Pas, S.L., Szabo, B., and van der Vaart A. (2017), Adaptive posterior contraction rates for the horseshoe. Electronic Journal of Statistics 10(1), 3196-3225.

Carvalho, C. M., Polson, N. G., and Scott, J. G. (2010), The Horseshoe Estimator for Sparse Signals. Biometrika 97(2), 465<U+2013>480.

See Also

horseshoe and HS.normal.means to obtain the required hsobject.

Examples

# NOT RUN {
#Example with 20 signals (last 20 entries), rest is noise
truth <- c(rep(0, 80), rep(8, 20))
data <-  truth + rnorm(100)
horseshoe.results <- HS.normal.means(data, method.tau = "truncatedCauchy",
 method.sigma = "fixed")
#Using credible sets. Ideally, the first 80 entries are equal to 0,
#and the last 20 entries equal to 1.
HS.var.select(horseshoe.results, data, method = "intervals")
#Using thresholding. Ideally, the first 80 entries are equal to 0,
#and the last 20 entries equal to 1.
HS.var.select(horseshoe.results, data, method = "threshold")

# }