nisone

Provides different interval estimates of a location parameter when the sample size is one or more. These include classical methods when n=1, new Bayesian analogues of these classical methods, and extensions of these methods to larger sample sizes in the normal case. Other functions calculate Bayes factors based on t-statistics, and implement the (generalized) inverse normal distribution (and other inverse distributions). See Gerard (2026) for details of these methods.

Installation

You can install the development version of nisone from GitHub with:

# install.packages("pak")
pak::pak("dcgerard/nisone", build_vignettes = TRUE)

n=1 confidence interval

If we observe \(X = 10\) and we have prior guess that the mean is around 5, then the resulting 95% CI based on a normal model is

library(nisone)
ci1(x = 10, A = 5)
#>       x center  lower upper
#> [1,] 10    7.5 -40.76 55.76

Its full posterior distribution based on a probability matching prior can be calculated using the n1post family of functions. For example, the median and 95% credible interval is

qn1post(p = c(0.025, 0.5, 0.975), A = 5, obs = 10, nu = 1, fam = "normal")
#> [1] -40.755   8.549  55.773

Some random posterior draws and density curve is

samp <- rn1post(n = 10000, A = 5, obs = 10, nu = 1, fam = "normal")
samp <- samp[samp > -20 & samp < 40]
x <- seq(-20, 40, length.out = 500)
y <- dn1post(x = x, A = 5, obs = 10, nu = 1, fam = "normal")
graphics::hist(
  samp, 
  freq = FALSE, 
  breaks = 200, 
  border = "grey", 
  col = "grey",
  main = "Posterior Density and Histogram",
  xlab = "Mean",
  ylab = "Posterior Density"
)
graphics::lines(x, y, type = "l", col = "#E69F00")

If we just want to assume that \(X\) comes from any symmetric unimodal distribution, a 95% CI for the mode is

ci1(x = 10, A = 5, family = "uniform")
#>       x center  lower upper
#> [1,] 10    7.5 -87.43 102.4

See more functionality by running

browseVignettes("nisone")

References

• Gerard, D. (2026). Constructing and extending n = 1 Bayesian confidence intervals for location parameters in location-scale families. arXiv Preprint. doi:10.48550/arXiv.2607.25007