Bayesian Analysis Helper

What is Bayesian Reasoning?

Bayesian reasoning is a powerful way to update your beliefs based on new evidence. Instead of treating probabilities as fixed facts, Bayes' theorem gives you a mathematical framework to systematically adjust your confidence as you gather more information.

Quick Example: You think there's a 30% chance it will rain today (your prior). Then you see dark clouds rolling in. Bayes' theorem tells you exactly how much to update that 30% based on how likely those clouds are when it actually rains versus when it doesn't.

What is a "Prior"?

Your prior probability is your initial belief before seeing any new evidence. It represents what you think is true based on your existing knowledge. As you gather evidence, this prior gets updated into a posterior probability — your new, evidence-informed belief.

Who Was Bayes?

Thomas Bayes (1701–1761) was an English statistician, philosopher, and Presbyterian minister. His famous theorem was published posthumously in 1763 and has become one of the most important concepts in statistics, machine learning, artificial intelligence, and scientific reasoning.

Bayes' Theorem

P(H|E) = P(E|H) × P(H) / P(E)

P(H|E)
Posterior: Updated belief after seeing evidence

P(H)
Prior: Initial belief before evidence

P(E|H)
Likelihood: Probability of evidence if hypothesis is true

P(E)
Total probability of the evidence

Try It Out

Choose an example scenario or create your own:

Your Claim/Belief

Prior Probability (Initial Belief)

Evidence

Final Probability

Calculation Steps: