Bayesian Probability Calculator API

Endpoint: https://www.promptbox.cn/api/bayes.php

Overview

This REST API calculates the updated (posterior) probability using Bayes' Theorem. It accepts prior probability, likelihood, and false positive rate, then returns the computed probability in JSON format.

HTTP Method

The API supports both GET and POST requests.

Parameters

Name Type Required Description
prior float (percent) Yes Initial probability (e.g., 1 for 1%).
likelihood float (percent) Yes Probability of seeing evidence if hypothesis is true (e.g., 95 for 95%).
altLikelihood float (percent) Yes Probability of seeing evidence if hypothesis is false (false positive rate, e.g., 5 for 5%).

Example Request (GET)

https://www.promptbox.cn/api/bayes.php?prior=1&likelihood=95&altLikelihood=5

Example Request (cURL)

curl -X GET "https://www.promptbox.cn/api/bayes.php?prior=1&likelihood=95&altLikelihood=5"

Successful Response

{
  "input": {
    "prior_percent": 1,
    "likelihood_percent": 95,
    "altLikelihood_percent": 5
  },
  "result": {
    "updated_probability_percent": 16.09
  }
}

Error Response

{
  "error": "Missing parameters. Required: prior, likelihood, altLikelihood (all in %).",
  "example": "bayesian_api.php?prior=1&likelihood=95&altLikelihood=5"
}

Formula Used

Bayes' theorem is applied as: 

P(H|E) = [ P(E|H) * P(H) ] / [ P(E|H) * P(H) + P(E|¬H) * (1 - P(H)) ]