Calculate Posterior Fraud Probability Using Bayes' Theorem

Quick Overview

Calculate Posterior Fraud Probability Using Bayes' Theorem evaluates statistical assumptions, formulas, estimation strategy, uncertainty, edge cases, and interpretation in a realistic interview setting. A strong answer states assumptions, handles edge cases, explains trade-offs, and shows how to validate the result clearly.

Calculate Posterior Fraud Probability Using Bayes' Theorem

Company: Meta

Role: Data Scientist

Category: Statistics & Math

Difficulty: easy

Interview Round: Onsite

##### Scenario Posterior fraud probability for user accounts ##### Question Given prior fraud rate, true-positive rate, and false-positive rate, use Bayes’ theorem to compute the probability an account is fake after a flag. ##### Hints State the formula, plug numbers, interpret the result for decision thresholds.

Quick Answer: Calculate Posterior Fraud Probability Using Bayes' Theorem evaluates statistical assumptions, formulas, estimation strategy, uncertainty, edge cases, and interpretation in a realistic interview setting. A strong answer states assumptions, handles edge cases, explains trade-offs, and shows how to validate the result clearly.

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Aug 4, 2025, 10:55 AM
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Calculate Posterior Fraud Probability Using Bayes' Theorem

Posterior Fraud Probability After a Flag

Context

You operate a fraud detection system that flags accounts as suspicious. Define:

  • F: account is fraudulent
  • +: system flags the account
  • Prior fraud rate p = P(F)
  • True positive rate (TPR) = P(+ | F)
  • False positive rate (FPR) = P(+ | not F)

Task

  1. Use Bayes’ theorem to derive an expression for the posterior probability that an account is fraudulent after a flag: P(F | +).
  2. Compute P(F | +) for the following example values: p = 1%, TPR = 90%, FPR = 5%.
  3. Briefly interpret the result for decision thresholds (e.g., how the posterior compares to a 10%, 20%, or 50% action threshold).

Constraints & Assumptions

  • Preserve the scope, facts, inputs, and requested outputs from the prompt above.
  • If the prompt leaves a detail unspecified, state a reasonable assumption before relying on it.
  • Keep the answer interview-ready: concise enough to present, but concrete enough to implement or evaluate.

Clarifying Questions to Ask Guidance

  • Clarify the random variables, distributional assumptions, independence assumptions, and desired output.
  • Show enough derivation for the interviewer to follow the reasoning.
  • Explain how you would validate the result with simulation or sensitivity checks.

What a Strong Answer Covers Guidance

  • A correct setup with definitions, formulas, and boundary conditions.
  • A step-by-step derivation or estimation plan.
  • Interpretation of the result, including uncertainty and practical limitations.
  • Checks for assumptions, edge cases, and numerical stability.

Follow-up Questions Guidance

  • How would the result change if the assumptions were relaxed?
  • Can you verify the answer with a simulation?
  • What is the most likely source of estimation error?
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