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.

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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