Hello, today I’m gonna share some notes about Bayes Theorem.

A key idea in probability theory and statistics is the Bayes theorem, which explains how to update a hypothesis’ (an event’s or proposition’s) probability in light of fresh data. It bears the Reverend Thomas Bayes’ name and is frequently used in science, statistics, and machine learning, among other fields.

The theorem is often expressed as follows:

P(A\B)=P(B)P(B\A).P(A)

Whereas,

The posterior probability of event A given event B is denoted as P(A\B). This is the revised likelihood of hypothesis A in light of the recently discovered data (B).

The probability of event B given event A is denoted by P(B\A). This is the likelihood that, should hypothesis A be correct, evidence B will be observed.

P(A) represents the event A’s prior probability. This is the hypothesis A’s starting belief or likelihood before any additional evidence is taken into account.

The likelihood that evidence B exists is P(B). This is a normalization factor that shows the overall likelihood of finding evidence B in every scenario.

 

You may measure how new information should affect your beliefs about a hypothesis using the Bayes theorem. It is especially helpful for activities like updating forecasts, making decisions under uncertainty, and statistical inference.

In order to carry out Bayesian inference, which entails updating probability distributions of hypotheses depending on data, Bayes’ theorem is fundamental to Bayesian statistics. Numerous industries, such as banking, machine learning, natural language processing, and medical, heavily rely on Bayesian approaches.

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