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Conditional Probability

Install and import#

bash
npm install fintech-algorithms
ts
import { conditionalProbability } from "fintech-algorithms/foundations/probability-and-random-variables/conditional-probability";

Signature#

conditionalProbability(input)

Rescales the joint probability of two events by each marginal in turn, giving the probability of A once B is known and the probability of B once A is known.

Parameters#

NameTypeNotes
input{ pA: number; pB: number; pAB: number }pA and pB are the marginal probabilities and pAB the joint. Both marginals must be strictly positive, since each one is used as a denominator.
pA: 0 <= pA <= 1 · pB: 0 <= pB <= 1 · pAB: 0 <= pAB <= min(pA, pB) · conditioning: pA and pB must both be strictly greater than 0

Returns#

{ pAGivenB: number; pBGivenA: number }

pAGivenB is pAB / pB and pBGivenA is pAB / pA.

Errors#

  • When input is null, an array, or not an object — throws TypeError
  • When pA, pB, or pAB falls outside [0, 1], or pAB exceeds min(pA, pB) — throws RangeError
  • When pA or pB is exactly zero, which would divide by a zero-probability conditioning event — throws RangeError

Complexity: time O(1), space O(1).

Worked example#

verified This is the worked example published in the article, replayed by the test suite on every run. The output cannot drift.

Input#

input
{
  "pA": 0.6,
  "pB": 0.5,
  "pAB": 0.3,
  "outcomes": ["up", "flat", "down"],
  "event": ["up", "flat"],
  "prior": 0.01,
  "sensitivity": 0.9,
  "falsePositiveRate": 0.05,
  "randomValues": [0, 1, 2],
  "probabilities": [0.2, 0.5, 0.3],
  "randomVariableKind": "discrete",
  "joint": [
    {
      "x": 0,
      "y": 0,
      "p": 0.3
    },
    {
      "x": 0,
      "y": 1,
      "p": 0.2
    },
    {
      "x": 1,
      "y": 0,
      "p": 0.1
    }
  ],
  "conditionY": 1
}

Call#

conditionalProbability(input)

Returns#

object with 2 fields: pAGivenB, pBGivenA

{
  "pAGivenB": 0.6,
  "pBGivenA": 0.5
}

Diagrams#

Conditional Probability — article hero
Conditional Probability — calculation ledger
Conditional Probability — concept anatomy
Conditional Probability — failure boundary
Conditional Probability — method map
Conditional Probability — scenario contrast

How it works#

This page states the contract — how to call it correctly. The article explains the concept: why it works, and where it breaks.

Read the article →

References#

The rest of the Probability and Random Variables family#