Calibrated Gibbs Posteriors for Tolerance Intervals

Provides tools for constructing one-sided and two-sided nonparametric tolerance intervals using calibrated Gibbs posteriors. The methods target population quantiles and content levels while achieving nominal frequentist coverage through data-driven calibration. The methodology is described in Pourmohamad, Richardson, and Sansó (2026) .

gibbsTI

R Package: Calibrated Gibbs Posteriors for Tolerance Intervals

gibbsTI provides tools for constructing one-sided and two-sided nonparametric tolerance intervals using calibrated Gibbs posteriors.

⚠️ Note: This package is currently under active development. The API is subject to change, and you may encounter bugs. Please report any issues or feedback via the GitHub Issue Tracker.

Installation

You can install the development version of gibbsTI from GitHub.

1. Prerequisites

Since you are installing from source, ensure you have a functional build environment:

• Windows: Rtools
• macOS: Xcode command line tools

2. Install via remotes

Run the following commands in your R console:

# Install the remotes package if you don't have it
if (!requireNamespace("remotes", quietly = TRUE)) {
  install.packages("remotes")
}

# Install gibbsTI
remotes::install_github("tpourmohamad/gibbsTI")

Usage

library(gibbsTI)

set.seed(1)
x <- rnorm(50)

# One-sided upper 95% content / 90% confidence tolerance interval,
# with the Gibbs learning rate chosen by GPC calibration (the default).
fit <- gibbsTI(x, side = "one", type = "upper",
               content = 0.95, confidence = 0.90)
print(fit)
summary(fit)
plot(fit)

# Two-sided interval
fit2 <- gibbsTI(x, side = "two", content = 0.95, confidence = 0.90)
summary(fit2)

# Skip calibration and use a fixed learning rate
fit3 <- gibbsTI(x, side = "one", type = "upper",
                eta_method = "fixed", eta = 1)

Citation

If you use gibbsTI, please cite:

Pourmohamad, T., Richardson, R., & Sansó, B. (2026). "Calibrated Bayesian Nonparametric Tolerance Intervals." Technometrics, 1–27. https://doi.org/10.1080/00401706.2026.2699103

You can also run citation("gibbsTI") in R.