What is Bayes' theorem?

Bayes' theorem is named after the English clergyman Thomas Bayes Mathematical theorem that originates from probability theory and is used to make statements about the calculation of conditional probabilities..

Thus, one starts from a completely known value P A ( B ) and with its help one can calculate P B ( A ). This theorem establishes the direct connection between the conditional probability and the inverse conditional probability. This procedure is also called backward induction. It is important to know the a priori probability P(A) and to take it into account. The theorem can only be used if P ( A ) and P ( B ) are approximately equal.

Bayes' theorem, also called Bayes' formula or Bayes' theoremis also used in Bayesian statistics and in inductive statistics to estimate parameters and test hypotheses.

What is Bayes' theorem?

The mathematical theorem reads:

P(A|B) = P(B|A) * P(A) / P(B).

Here, P(A|B) is precisely the conditional probability of A if B has already occurred. Correspondingly, P(B|A) is simply the probability of the event B, under the condition that A has occurred. P(A) and P(B) are the respective probabilities of these events. To calculate them, one starts from the known value P(B|A) and is interested in the value P(A|B). Bayes' theorem calculates the inverse form of the conditional probability.

What are the applications of Bayes' Theorem?

In all questions of learning from certain experiences, this theorem can be used in statistics. This is possible in a priori probability estimation based on experience, where this is changed and transformed into an a posteriori distribution (Bayesian statistics).

The Bayes theorem is also used in the Data mining in Bayes classifiers, which use theoretical decision rules with provable minimum error rates. Bayesian filters can also be used for spam detection. Thus, characteristic words in an email (event A) can be used to infer the spam property (event B).

In the Artificial intelligence Bayes' theorem is used to draw conclusions in domains with uncertain knowledge. This is not a deductive approach and it is possible that conclusions are not always correct. The approach is therefore abductive. This hypothesis generation is very useful for learning in artificial systems.

In addition, there are areas of application in quality management, decision theory, information economics, the basic model of traffic distribution, bioinformatics, communication theory, econometrics and neuroscience.

Bayes' theorem is applied in computer science in the field of Big Data. There are Bayes classifiers there. There are also certain procedures in bioinformatics and neuroscience that apply this theorem. Most empirical studies can be conducted based on inferences by this rule.