An R package for calculating and plotting binomial credible intervals. It was written for educational purposes and not necessarily for serious use.

Installation

devtools::install_github("tmalsburg/binomialCRIs")

Usage examples

Note: When plotting to PDF, use the function cairo_pdf() instead of pdf() to get Greek characters in the results.

50% credible intervals after seeing 6 successes out of 9 trials, with flat prior:

library(binomialCRIs)

binomial_hpdi(n_successes=6, n_trials=9, prob=0.5, prior_shape1=1, prior_shape2=1)

     |0.5      0.5| 
0.5643603 0.7593849

plot_binomial_hpdi(6, 9, 0.5)

binomial_pi(6, 9, 0.5)

     |0.5      0.5| 
0.5423038 0.7391494

plot_binomial_pi(6, 9, 0.5)

50% credible intervals after seeing 6 successes out of 9 trials, with prior assuming one earlier success and one earlier failure:

binomial_hpdi(6, 9, 0.5, 2, 2)

     |0.5      0.5| 
0.5419229 0.7242251

plot_binomial_hpdi(6, 9, 0.5, 2, 2)

binomial_pi(6, 9, 0.5, 2, 2)

     |0.5      0.5| 
0.5269063 0.7101529

plot_binomial_pi(6, 9, 0.5, 2, 2)

50% credible intervals after seeing 7 successes our of 11 trials (equivalent to 6/9 with prior_shape1=2, beta=2):

binomial_hpdi(7, 11, 0.5, 1, 1)

     |0.5      0.5| 
0.5419229 0.7242251

plot_binomial_hpdi(7, 11, 0.5)

binomial_pi(7, 11, 0.5)

     |0.5      0.5| 
0.5269063 0.7101529

plot_binomial_pi(7, 11, 0.5)

50% credible intervals after seeing 1 successes out of 2 trials, with flat prior:

binomial_hpdi(1, 1, 0.5)

     |0.5      0.5| 
0.7070744 0.9999771

plot_binomial_hpdi(1, 1, 0.5)

binomial_pi(1, 1, 0.5)

     |0.5      0.5| 
0.5000000 0.8660254

plot_binomial_pi(1, 1, 0.5)

Probability of parameter being larger than 0.5 after seeing 6 successes out of 9 trials with flat prior:

binomial_prob(6, 9, 0.5)

[1] 0.828125

Probability of parameter being larger than 0.5 after seeing 6 successes out of 9 trials with prior assuming one earlier success and one earlier failure:

binomial_prob(6, 9, 0.5, prior_shape1=2, prior_shape2=2)

[1] 0.8061523

Probability of parameter being smaller than 0.5 after seeing 6 successes out of 9 trials with prior assuming one earlier success and one earlier failure:

binomial_prob(6, 9, prob_upper=0.5, prior_shape1=2, prior_shape2=2)

[1] 0.1938477

Probability of parameter being larger than 0.5 and smaller than 0.75 after seeing 6 successes our of 9 trials:

binomial_prob(6, 9, 0.5, 0.75)

[1] 0.6040001

Plot the same interval:

plot_binomial_cri(6, 9, 0.5, 0.75)

Probability of parameter being smaller than 0.5 after seeing 6 successes our of 9 trials:

binomial_prob(6, 9, prob_upper=0.5)

[1] 0.171875

Plot:

plot_binomial_cri(6, 9, prob_upper=0.5)