Definition

1. Adjective:
   • Relating to statistical methods based on Bayes' theorem: The term "Bayesian" describes an approach to probability and statistics that interprets probability as a measure of belief or certainty, which can be updated as new evidence is acquired, using the mathematical framework of Bayes' theorem.

Usage Examples

• Adjective:
  • The researcher used a Bayesian approach to update the model's predictions with the new data.
  • Bayesian inference is a powerful tool for dealing with uncertainty in complex systems.
  • This analysis contrasts frequentist and Bayesian methods.

Advanced Usage

• "Bayesian statistics": The branch of statistics that applies probability to statistical problems, providing a mathematical procedure for updating beliefs in light of new evidence.

  • Bayesian statistics offers a coherent framework for parameter estimation.

• "Bayesian network": A probabilistic graphical model that represents a set of variables and their conditional dependencies via a directed acyclic graph.

  • The system's reliability was modeled using a Bayesian network.

• "Bayesian prior/posterior": Key components in Bayesian inference. The "prior" represents initial beliefs about a parameter before seeing data. The "posterior" represents the updated beliefs after considering the evidence.

  • The choice of an informative prior significantly influenced the posterior distribution.

Variants and Related Words

• Bayesianism (noun): The philosophical interpretation or advocacy of the Bayesian approach to probability.

  • His work is grounded in a firm belief in Bayesianism.

• Bayes' theorem (noun): The fundamental mathematical rule at the core of Bayesian methods, describing how to update the probability for a hypothesis as more evidence becomes available.

  • The calculation is a direct application of Bayes' theorem.

Synonyms

• Probabilistic (in a specific context): Involving or based on probability, though this is a broader term.
• Evidential: Relating to or based on evidence, which aligns with the Bayesian principle of updating beliefs.

Related Phrases

• "Empirical Bayes method": A statistical approach that uses observed data to estimate the prior distribution in a Bayesian analysis.

  • The empirical Bayes method was used to borrow strength across similar experiments.

• "Fully Bayesian analysis": An analysis that treats all unknown parameters as random variables and uses prior distributions for each.

  • The paper presents a fully Bayesian analysis of the hierarchical model.

Adjective

1. of or relating to statistical methods based on Bayes' theorem