bayes' theorem

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bayes' theorem

A student uses Bayes' theorem to solve a probability problem.

Definition
  1. Noun:
    • A theorem in probability theory and statistics: Bayes' theorem describes how to update the probability of a hypothesis (or cause) based on new evidence (or an observed event). It mathematically relates the conditional and prior probabilities of events.
Usage
  • Bayes' theorem is used to calculate the probability of an event based on prior knowledge of conditions that might be related to the event.
  • It is a fundamental concept in Bayesian statistics, machine learning, and data science for making inferences from data.
Examples
  • Noun:
    • Bayes' theorem is essential for understanding diagnostic tests in medicine.
    • The researcher applied Bayes' theorem to update the model's predictions with the new data.
    • A simple explanation of Bayes' theorem involves calculating the probability of having a disease given a positive test result.
Advanced Usage
  • "Posterior probability": The updated probability of a hypothesis, calculated using Bayes' theorem, which combines prior probability and new evidence.
    • The posterior probability, computed via Bayes' theorem, indicated the hypothesis was likely true.
  • "Bayesian inference": The process of statistical inference in which Bayes' theorem is used to update the probability for a hypothesis as more evidence becomes available.
    • Bayesian inference relies fundamentally on the application of Bayes' theorem.
Variants and Related Words
  • Bayesian (adj): Relating to or based on the methods and philosophy of Thomas Bayes, especially the use of Bayes' theorem.
    • Bayesian analysis provides a coherent framework for updating beliefs.
  • Prior probability (n): The initial probability of a hypothesis before considering new evidence, a key component in Bayes' theorem.
  • Likelihood (n): The probability of observing the evidence given that a hypothesis is true, another key component in Bayes' theorem.
Synonyms
  • Bayes' rule: Another name for Bayes' theorem.
  • Bayesian theorem: A less common synonym for Bayes' theorem.
Related Phrases
  • "Apply Bayes' theorem": To use the theorem for a specific calculation.
    • To solve this problem, you need to apply Bayes' theorem correctly.
  • "According to Bayes' theorem": As stated or derived from the theorem.
    • According to Bayes' theorem, the probability must be recalculated with the new information.
bayes' theorem

A student uses Bayes' theorem to solve a probability problem.

Noun
  1. (statistics) a theorem describing how the conditional probability of a set of possible causes for a given observed event can be computed from knowledge of the probability of each cause and the conditional probability of the outcome of each cause

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