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# Bayes Theorem

The Bayes theorem (also Bayes' theorem) is an application of probability theory, named after the mathematician Thomas Bayes. It provides simple mathematical formulas for calculating conditional probabilities.

It is extremely useful for the evaluation of test procedures in genetic diagnostics, as it shows the actual predictive value and thus the usefulness of a test procedure. Calculating with Bayes' theorem is widely used (source: Wikipedia):

Statistics: All questions of learning from experience, in which an a priori probability estimation is changed on the basis of experience and transformed into an a posteriori likelihood distribution (cf. Bayesian statistics).

Medicine: From one or more positive medical test results (laboratory results, symptoms of a disease), the presence of a disease (cause) is inferred abductively.

Computer science: Bayesian filter - From characteristic words in an e-mail (event), the characteristic of being spam (cause) is inferred.

Artificial intelligence: Here, the Bayes theorem is used to draw conclusions even in domains with "uncertain" knowledge. These are then not deductive and therefore not always correct, but rather abductive in nature, but have proven to be quite useful for hypothesis formation and learning in such systems.

Quality management: assessing the validity of test series.

Decision theory/information economics: determining the expected value of additional information.

Bioinformatics: determining functional similarity of sequences.

Communication theory: solving detection and decoding problems.

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