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Bayes Calculator

Apply Bayesian reasoning to real-world decisions. Enter your scenario and adjust probabilities to see how evidence updates your beliefs.

Need Inspiration? Try These Examples

Each example clearly defines the hypothesis, evidence, and reasoning behind the probabilities

📧Email Spam Detection

You received an email with suspicious keywords ("urgent", "click here", "limited time"). Your spam filter flagged it.

Prior Reasoning: About 30% of emails in typical inboxes are spam based on email traffic patterns
Hypothesis: The email is spam
Evidence: Email contains 3+ spam keywords and was flagged by filter
Prior:30%
Likelihood P(E|H):90%
False Positive P(E|¬H):10%
Posterior Probability:~79%

Probability the email is spam given it was flagged

🏥Disease Testing

You tested positive for a disease that affects 2% of the population. The test is 95% accurate.

Prior Reasoning: The disease affects 2% of the population (epidemiological base rate)
Hypothesis: You have the disease
Evidence: Positive test result
Prior:2%
Likelihood P(E|H):95%
False Positive P(E|¬H):5%
Posterior Probability:~28%

Probability you have the disease given the positive test

💼Job Candidate Quality

A job candidate aced the technical interview (top 10% score). You're deciding whether to make an offer.

Prior Reasoning: Historically, about 20% of hires become excellent long-term employees at your company
Hypothesis: The candidate will be an excellent long-term employee
Evidence: Top 10% score on technical interview
Prior:20%
Likelihood P(E|H):70%
False Positive P(E|¬H):15%
Posterior Probability:~54%

Probability the candidate will excel given their interview score

⭐Product Review Authenticity

A product has 50+ five-star reviews, all posted within one week, with similar phrasing.

Prior Reasoning: About 15% of products with review surges have fake/paid reviews based on platform data
Hypothesis: The reviews are fake/paid
Evidence: 50+ five-star reviews in one week with similar phrasing
Prior:15%
Likelihood P(E|H):85%
False Positive P(E|¬H):5%
Posterior Probability:~77%

Probability the reviews are fake given this pattern

Your Scenario

Your initial belief before considering the evidence. What's the base rate?

%

If your hypothesis is true, how likely would you see this evidence?

%

If your hypothesis is false, how likely would you still see this evidence?

%

Bayesian Analysis

Posterior Probability
80%

After considering the evidence, your belief should be updated to 80%

Calculation

P(H|E) = [P(E|H) × P(H)] / [P(E|H) × P(H) + P(E|¬H) × P(¬H)]
= [0.8000 × 0.5000] / [0.8000 × 0.5000 + 0.2000 × 0.5000]
= 0.800000 (80%)

Interpretation

Moderate evidence supports your hypothesis. Consider additional information if possible.

Change from prior: +30.0% (significant update)

Tips for Better Analysis

  • • Be honest about your prior—don't let desired outcomes bias your starting point
  • • Consider the base rate: how common is this situation in general?
  • • Think about false positives: how often would you see this evidence even if wrong?
  • • Update incrementally: run multiple Bayesian updates as new evidence comes in