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https://github.com/vgherard/fcci

Feldman-Cousins Confidence Intervals
https://github.com/vgherard/fcci

confidence-intervals physics r statistics

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Feldman-Cousins Confidence Intervals

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README 

        
---

output: github_document

---



```{r, include = FALSE}

knitr::opts_chunk$set(

  collapse = TRUE,

  comment = "#>",

  fig.path = "man/figures/README-",

  out.width = "100%"

)

```



# fcci



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[![CRAN status](https://www.r-pkg.org/badges/version/fcci)](https://CRAN.R-project.org/package=fcci)

[![R-universe status](https://vgherard.r-universe.dev/badges/fcci)](https://vgherard.r-universe.dev/)

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`fcci` is an R package providing support for building [Feldman-Cousins](https://doi.org/10.1103/PhysRevD.57.3873) confidence 

intervals.



## Motivation



The Feldman-Cousins construction was originally developed in the context of 

High-Energy Physics, as a consistent method for building classical (frequentist) confidence intervals for Poisson rates of rare events. In experiments which expect only few events, it is often the case that the number of observed events is actually zero or, more generally, lower than the expected number of spurious background events (if the latter is significantly larger than zero). 



In these situations, classical central intervals (such as those produced by `stats::poisson.test()`) are not satisfying, as they can lead both to significant overcoverage and to non-physical negative rates in the presence of a non-negligible background. Moreover, a naive special treatment of boundary values, which chooses to report an upper limit or a confidence interval depending on the data (the so-called ["flip-flopping" policy](https://doi.org/10.1103/PhysRevD.57.3873)), can lead to undercoverage.



Feldman and Cousins provide a unified treatment of boundary and regular values, by explicitly constructing the [Neyman confidence belt](https://en.wikipedia.org/wiki/Neyman_construction) for physical rates, using an ordering for count values based on a likelihood ratio.



## Installation



You can install the latest release of `fcci` from [CRAN](https://CRAN.R-project.org/package=fcci) using:



``` r

install.packages("fcci")

```



and the development version from [my R-universe](https://vgherard.r-universe.dev/) with:



``` r

install.packages("fcci", repos = "https://vgherard.r-universe.dev/")

```

## Example



```{r}

library(fcci)

```



To compute a confidence interval for, e.g., a Poisson rate, use:



```{r}

# 95% C.L. interval for n = 10 events and b = 2 expected background events

confint_pois(n = 10, b = 2, cl = 0.95)

```



Let us compare the 68% C.L. intervals for $n=0$ events and no background 

obtained from `fcci` and from `stats::poisson.test()` 



```{r}

confint_pois(n = 0, cl = 0.68)

stats::poisson.test(0, conf.level = 0.68, alternative = "two.sided")$conf.int

```



Notice that the latter is significantly larger, and it corresponds in fact to

an 84% C.L. *upper limit* on the rate:



```{r}

stats::poisson.test(0, conf.level = 0.84, alternative = "less")$conf.int

```



## Getting Help



For further help, you can consult the reference page of the `fcci` [website](https://vgherard.github.io/fcci/) or [open an issue](https://github.com/vgherard/fcci/issues) on the GitHub repository of `fcci`.