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Bayes' Theorem Posterior Probability Calculator
x402
Bayes' Theorem Posterior Probability Calculator is a paid API for AI agents from probability-calc.x402tookit.com, paid per call via x402, $0.02/call, status unknown (last checked 2026-10-30).
Computes posterior probability from a prior, sensitivity, and false-positive rate using Bayes' theorem, with natural frequencies and odds form output.
Price / call$0.02
Success—
StatusUnknown
How this service works
Bayes' theorem: posterior probability from a prior, sensitivity and false-positive rate, with natural frequencies and odds form.
Output
Returns posterior probability (P(hypothesis|evidence)), prior and posterior odds, specificity and false positive rate, and a natural frequencies breakdown (true positives, false positives, true negatives, false negatives) for the specified population, along with a plain-language summary and verdict.
Example use cases
Medical diagnostic test accuracy
“A cancer screening test has 85% sensitivity and a 3% false positive rate. If the disease affects 0.5% of the population (prior = 0.005), what's the real probability someone actually has cancer after testing positive? Show natural frequencies for 100000 people.”
Spam filter Bayesian update
“My spam filter flags 95% of real spam (sensitivity = 0.95) but also incorrectly flags 2% of legitimate emails (false positive rate = 0.02). If about 30% of all incoming emails are spam (prior = 0.3), what's the posterior probability that a flagged email is actually spam?”
Drug test reliability assessment
“A workplace drug test has a sensitivity of 0.99 and a specificity of 0.95. Given that roughly 5% of employees use drugs (prior = 0.05), what's the chance an employee who tests positive is actually a user? Give me the natural frequencies for a group of 1000 people.”
Technical details
Endpoint
GEThttps://probability-calc.x402tookit.com/bayes?utm_source=zero.xyzWhen to prefer
Choose this endpoint when you need to perform Bayesian inference from a prior probability, sensitivity, and false-positive rate — especially for medical testing, diagnostic accuracy, or any scenario where you want to update a belief with new evidence. It is ideal when you need natural frequency representations alongside the probability, or when working with non-statisticians who benefit from plain-language summaries. Prefer this over manual calculation when you need both odds form and probability form simultaneously.
Side effects
- Missing required parameters (prior or sensitivity) returns a 400 error
- Prior, sensitivity, specificity, or falsePositiveRate outside [0,1] range returns a validation error
- Providing neither specificity nor falsePositiveRate may result in an incomplete computation
- Population set to 0 or negative integer causes a computation error
- Conflicting specificity and falsePositiveRate values (where fpr != 1 - specificity) may be flagged or one ignored
Input
Schema · Request body
| Field | Type | Description |
|---|---|---|
| inputrequired | object | |
| output | object |
Tags
x402
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