A Base R, simple implementation of the No-Underrun Sampler. This package aims to mostly directly implement the algorithm as described by the paper, with at most small changes for code aesthetics and performance. This version uses the memory saving technique described in section 2.2.

This code doesn’t parallelize the density calculation for orbit extensions but doing so is trivial.

You can install the development version of R.NURS from GitHub with:

# install.packages("pak")
pak::pak("VisruthSK/R.NURS")

library(R.NURS)
library(ggplot2)

set.seed(0)
logpdf_funnel <- function(theta) {
  y <- theta[1]
  dnorm(y, 0, 3, log = TRUE) + sum(dnorm(theta[-1], 0, exp(y / 2), log = TRUE))
}

samples <- NURS(
  logpdf_funnel,
  theta_init = rep(0, 15),
  n = 5000,
  epsilon = 0.1,
  h = 0.5,
  M = 5
)

data.frame(y = samples[, 1], x1 = samples[, 2]) |>
  ggplot(aes(x = y, y = x1)) +
  geom_point(alpha = 0.3) +
  theme_minimal()

• Nawaf Bou-Rabee, Bob Carpenter, Sifan Liu, Stefan Oberdörster. 2025. The No-Underrun Sampler: A locally adaptive, gradient free, MCMC method. arXiv 2501.18548 v2.

• Art B. Owen. 2013. Monte Carlo theory, methods and examples. artowen.su.domains.