date = 2023-04-28 tags = ["deno", "statistics"] title = "Beta distribution script"
The Beta distribution is the distribution of the underlying probability `p` given the result of a binomial trial, coin tosses for an example .
Using the Beta distribution, the posterior distribution of `p` given your prior belief and observations can be calculated with the following formula:
"Beta"(alpha_"posterior", beta_"posterior") = "Beta"(alpha_"likelihood" + alpha_"prior", beta_"likelihood" + beta_"prior")
I uploaded a Deno script that plots the posterior distribution of `p` on the terminal.
% deno run https://jaeyoung.se/toys/beta_dist.js
Beta Distribution Visualizer
Enter prior alpha and beta values.
alpha = 1 and beta = 1 means an uninformed prior.
alpha = 1
beta = 1
Prior probability distribution
1.00 ┼───────────────────────────────────────────────────────────────────────────────────────────────────
Observed alpha = 0, beta = 0
Enter observed (+/-) alpha and (+/-) beta values.
alpha = 1
beta = 10
Posterior probability distribution
0.04 ┼ ╭───╮
0.03 ┤ ╭╯ ╰╮
0.03 ┤ ╭╯ ╰─╮
0.03 ┤ ╭╯ ╰╮
0.03 ┤ │ ╰╮
0.03 ┤ ╭╯ ╰╮
0.02 ┤ │ ╰╮
0.02 ┤ ╭╯ ╰╮
0.02 ┤ │ ╰╮
0.02 ┤ │ ╰╮
0.02 ┤ │ ╰─╮
0.02 ┤ ╭╯ ╰╮
0.01 ┤ │ ╰╮
0.01 ┤ │ ╰─╮
0.01 ┤ │ ╰╮
0.01 ┤╭╯ ╰─╮
0.01 ┤│ ╰─╮
0.01 ┤│ ╰──╮
0.00 ┤│ ╰───╮
0.00 ┤│ ╰──────╮
0.00 ┼╯ ╰────────────────────────────────────────────────────
https://learning.oreilly.com/library/view/bayesian-statistics-the/9781098122492