Bayes

{
  "asOf": "2026-10-11T14:44:16.580Z",
  "degraded": false,
  "disclaimer": "Screening signal computed from the named public source. Not financial, legal or investment advice; provided as is. Verify at the source before acting.",
  "falseAlarmShareOfPositives": 0.922360248447205,
  "falsePositiveRate": 0.096,
  "likelihoodRatioPositive": 8.333333333333334,
  "naturalFrequencies": {
    "falseNegatives": 20,
    "falsePositives": 950,
    "haveHypothesis": 100,
    "population": 10000,
    "trueNegatives": 8950,
    "truePositives": 80
  },
  "notChecked": [
    "whether the rates apply to the person or case in question (they are population averages)",
    "repeated or dependent tests (the formula assumes one independent piece of evidence)",
    "…1 more"
  ],
  "posteriorGivenNegative": 0.002229753835176596,
  "posteriorGivenPositive": 0.07763975155279504,
  "posteriorOdds": 0.08417508417508418,
  "prior": 0.01,
  "priorOdds": 0.010101010101010102,
  "probabilityOfPositive": 0.10303999999999999,
  "reasons": [
    "P(H | positive) = P(+|H) P(H) / [P(+|H) P(H) + P(+|not H) P(not H)].",
    "A low base rate means most positives are false positives, even with a good test (base-rate fallacy).",
    "…1 more"
  ],
  "sensitivity": 0.8,
  "source": "computed locally (Bayes' theorem)",
  "specificity": 0.904,
  "summary": "Prior 1.000%, sensitivity 80.0%, false-positive rate 9.60%: a positive result means a 7.76% chance the hypothesis is true.",
  "verdict": "STRONG_UPDATE"
}

# bash or zsh: see the payment challenge. Nothing is charged.
curl -sS -g -i 'https://probability-calc.x402tookit.com/bayes?falsePositiveRate=0.096&prior=0.01&sensitivity=0.8'

# x402 v2 sends the challenge base64-encoded in the PAYMENT-REQUIRED header (v1 sends it in the body).
# To read the header:
curl -sS -g -o /dev/null -D - 'https://probability-calc.x402tookit.com/bayes?falsePositiveRate=0.096&prior=0.01&sensitivity=0.8' \
  | grep -i '^payment-required:' | cut -d' ' -f2 | tr -d '\r' | base64 --decode

// npm i @x402/fetch @x402/evm viem
import { wrapFetchWithPayment, x402Client } from "@x402/fetch";
import { registerExactEvmScheme } from "@x402/evm/exact/client";
import { privateKeyToAccount } from "viem/accounts";

// Pays at most $0.02 per call.
const client = new x402Client().setSpendControls({ maxAmountPerPayment: "$0.02" });
registerExactEvmScheme(client, { signer: privateKeyToAccount(process.env.EVM_PRIVATE_KEY) });
const pay = wrapFetchWithPayment(fetch, client);

// Not sure it's safe to pay? ToolVet checks it first for $0.005. Pay for that from a separate
// client: this one is capped at $0.02 per payment. GET https://toolvet.app/api/v1/check?url=https%3A%2F%2Fprobability-calc.x402tookit.com%2Fbayes
const res = await pay("https://probability-calc.x402tookit.com/bayes?falsePositiveRate=0.096&prior=0.01&sensitivity=0.8");
console.log(res.status, await res.text());

# pip install "x402[requests,evm]"
import os
from eth_account import Account
from x402 import x402ClientSync
from x402.http.clients import x402_requests
from x402.mechanisms.evm import EthAccountSigner
from x402.mechanisms.evm.exact.register import register_exact_evm_client

# Pays at most $0.02 per call.
client = x402ClientSync().set_spend_controls({"max_amount_per_payment": "$0.02"})
register_exact_evm_client(client, EthAccountSigner(Account.from_key(os.environ["EVM_PRIVATE_KEY"])))

with x402_requests(client) as session:
    res = session.get("https://probability-calc.x402tookit.com/bayes?falsePositiveRate=0.096&prior=0.01&sensitivity=0.8")
    print(res.status_code, res.text)