Highest Posterior Density (HPD) interval for Binomial proportion

This function calculates the Highest Posterior Density (HPD) interval for a Binomial proportion using a Bayesian approach. It is vectorized, allowing the evaluation of single values or vectors.

ci_p_hpd(x, n, conf.level = 0.95, prior = "uniform")

Arguments

x: A number or a vector with the number of successes.
n: A number or a vector with the number of trials.
conf.level: Confidence level for the returned confidence interval. By default, it is 0.95.
prior: The prior distribution to use. Options are "uniform" (default) or "jeffreys".

Value

A vector with the lower and upper limits.

Details

The HPD interval is a Bayesian credible interval for the Binomial proportion \(p\). The posterior distribution is calculated based on the Beta prior:

- "uniform": \(\text{Beta}(1, 1)\).

- "jeffreys": \(\text{Beta}(0.5, 0.5)\).

The limits of the interval are computed using the quantiles of the Beta posterior distribution:

- Lower limit: \(\text{qbeta}((1 - \text{conf.level}) / 2, \alpha + x, \beta + n - x)\).

- Upper limit: \(\text{qbeta}(1 - (1 - \text{conf.level}) / 2, \alpha + x, \beta + n - x)\).

References

Missing reference.

Author

Omar David Mercado Turizo, omercado@unal.edu.co

Examples

# Example with a single value
ci_p_hpd(x = 15, n = 50, conf.level = 0.95)
#>           [,1]
#> [1,] 0.1911040
#> [2,] 0.4382887