Confidence Functionals for SelectBoost-GAMLSS

We consider stability curves \(p_j(c0)\) for each term \(j\) across a grid of SelectBoost thresholds c0. The following functionals condense these curves into scalar confidences:

What you’ll learn

  • How to compute confidence_functionals() from a sb_gamlss_c0_grid() result.
  • How to plot ranking summaries (plot()) and raw stability trajectories (plot_stability_curves()).
  • How to customise weights, quantiles, and conservative adjustments for different decision rules.
  1. AUSC (Area Under the Stability Curve): normalized trapezoidal area over the grid.
  2. Thresholded AUSC: integrate the positive excess \((p - \pi^\star)_+\).
  3. Coverage: fraction of grid points with \(p \ge \pi^\star\).
  4. Quantiles: median and high quantiles (e.g., 80th/90th) of \(p\) across c0.
  5. Weighted AUSC: integrate \(w(c0)\,p(c0)\) normalized by \(\int w(c0)\,dc0\).
  6. Conservative AUSC: replace \(p\) by a Wilson lower bound before integrating.
library(gamlss)
library(SelectBoost.gamlss)

set.seed(1)
n <- 400
x1 <- rnorm(n); x2 <- rnorm(n); x3 <- rnorm(n)
y  <- gamlss.dist::rNO(n, mu = 1 + 1.3*x1 - 1.0*x3, sigma = 1)
dat <- data.frame(y, x1, x2, x3)

g <- sb_gamlss_c0_grid(
  y ~ 1, data = dat, family = gamlss.dist::NO(),
  mu_scope = ~ x1 + x2 + x3, sigma_scope = ~ x1 + x2,
  c0_grid = seq(0.2, 0.8, by = 0.2), B = 40, pi_thr = 0.6, pre_standardize = TRUE, trace = FALSE
)

cf <- confidence_functionals(
  g, pi_thr = 0.6, q = c(0.5, 0.8, 0.9),
  weight_fun = NULL, conservative = FALSE, method = "trapezoid"
)

plot(cf, top = 10, label_top = 6)
plot_stability_curves(g, terms = c("x1","x3"), parameter = "mu")