explain briefly about bayes theorem
Answers
Answer:
Bayes' theorem, named after 18th-century British mathematician Thomas Bayes, is a mathematical formula for determining conditional probability. The theorem provides a way to revise existing predictions or theories (update probabilities) given new or additional evidence.
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Answer:
Bayes' theorem is a formula that describes how to update the probabilities of hypotheses when given evidence. It follows simply from the axioms of conditional probability, but can be used to powerfully reason about a wide range of problems involving belief updates.
Given a hypothesis HH and evidence EE, Bayes' theorem states that the relationship between the probability of the hypothesis before getting the evidence P(H)P(H) and the probability of the hypothesis after getting the evidence P(H \mid E)P(H∣E) is
P(H \mid E) = \frac{P(E \mid H)} {P(E)} P(H).
P(H∣E)=
P(E)
P(E∣H)
P(H).
Many modern machine learning techniques rely on Bayes' theorem. For instance, spam filters use Bayesian updating to determine whether an email is real or spam, given the words in the email. Additionally, many specific techniques in statistics, such as calculating pp-values or interpreting medical results, are best described in terms of how they contribute to updating hypotheses using Bayes' theorem.