 # Bayes' theorem

## Bayes theorem,

### Definition of Bayes theorem:

1. A theorem describing how the conditional probability of each of a set of possible causes for a given observed outcome can be computed from knowledge of the probability of each cause and the conditional probability of the outcome of each cause.

2. Relates the probability of the occurrence of an event to the occurrence or non-occurrence of an associated event. For example, the probability of drawing an ace from a pack of cards is 0.077 (4 ÷ 52). If two cards are drawn at random, the probability of the second card being an ace depends on whether the first card is an ace or not: if it is, then the probability of the second card being an ace is 0.058 (3 ÷ 52); if not, the probability remains 0.077. Bayes theorem provides a mathematical rule for revising an estimate or forecast in light of experience and observation. It differs from other methods of hypothesis testing in that it assigns after the fact (posterior) probabilities to the hypotheses instead of just accepting or rejecting them. Named after its proponent, the UK mathematician Thomas Bayes (1702-1761) who researched probability and statistical inference.

### How to use Bayes theorem in a sentence?

1. You may want to try to break down any new project using bayes theorem to see if it has a good chance of success.
2. If you want to figure out if a project should be worth taking on use bayes theorem to try and come up with its probability of success.
3. Following Bayes theorem, the posterior distribution over the parameter space is proportional to the likelihood times the prior distribution.
4. With Bayes theorem , we were able to judge the probability of an event happening and the probability of it not happening at the same time.

Meaning of Bayes theorem & Bayes theorem Definition