To understand how Bayes’ Theorem relates to Bayesian Inference, we have to understand the theorem through probabilitydistributions rather than just point probabilities. A probability distribution just gives the probability of all possible outcomes in any scenario, not just the most likely outcome.

A probability distribution can be continuous, as in the expected IQ of a randomly selected person (Normally distributed with mean=100, standard deviation=10):

Or discrete, as in our previous example. We’ll show the probability of a positive test result given disease P(T=1|D). This is simply a Bernoulli probability distribution:

In Bayesian Inference, we want to learn some probability distribution for parameters of a model given some data and prior beliefs about those parameters. We use Bayes’ Theorem to do this inference:

The quick proof of Bayes’ theorem Including some added words on independence. Main video: https://youtu.be/HZGCoVF3YvM Help fund future projects: https://www.patreon.com/3blue1brown An equally valuable form of support......

Bayes theorem Perhaps the most important formula in probability. Help fund future projects: https://www.patreon.com/3blue1brown An equally valuable form of support is to......

Formal Introduction to Statistical Inference A technical walk through Hypothesis Testing Photo taken by the author. Connecting with nature! When facing the decision on whether......

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