Bayesian Theorem

The Bayes theorem is a formula that tells you how to calculate conditional probabilities to a hypothesis given a piece of evidence. The formula can be used to see how the probability of an event occurring is affected by new information, supposing the new information is true.

Conditional probabilities

Conditional probability is a measure of the probability of an event given that another event has occurred. If an event called A and an event called B take place, then the conditional probability of event. For example, a simple question could be “What is the probability that a person who has an age of 30 liked a woman who was 20 years old?” Conditional probability takes this question a step further by asking “What is the probability that a person who has an age of 30 liked a women who is 20 years old given that he liked a 20 year woman old earlier”.

Event A given event B is written as:

Prior:

Posterior

Evidence

Likelihood

Our dataset contains the information of a man that liked a women on a dating platform.

We have 100 men that are 20 years old and 50 men that are 30 years old.

Thus, Bayesian Theorem is a prior that you update based on your measurements to get a revised set of beliefs.

Before I can elaborate on this, follow concepts need to be explained.

Join probabilities

Joint probability is the probability of both A and B occurring. This is the same as the probability of A occurring times the probability that B occurs given that A occurred, described as:

Using the same reasoning, is also the probability that B occurs times the probability that A occurs given that B occurs, expressed as:

Which can be combined to:

Where and are the probabilities of event A and B independently of each other. The formula explains the relationship between probability before evidence is gathered and the probability after getting the evidence. Therefore Bayes Theorem can be used to built a model which captures different events in respect of their probabilities. TV1