Bayesian vs. Frequentist Statistics

Abstract:

Bayesian and frequentist approaches represent two fundamental paradigms in statistical inference. The Bayesian framework updates prior beliefs using observed data through Bayes’ Rule, yielding a full probability distribution over parameters. In contrast, the frequentist view treats parameters as fixed and bases inference on sampling distributions. Each approach offers distinct advantages in handling uncertainty, with Bayesian methods excelling in incorporating prior knowledge and frequentist methods focusing on long-run error control.

Bayes’ Rule and the Foundations of Bayesian Statistics

Bayesian statistics is a probabilistic framework for inference that models unknown parameters as random variables. It centers on Bayes’ Rule , which provides a mathematical way to update beliefs in light of new evidence.