STATISTICAT

Bayesian Inference

Bayesian inference is one of two dominant approaches to statistical inference. The word "Bayesian" refers to the influence of Reverend Thomas Bayes, who introduced what is now known as Bayes' Theorem.  Bayesian inference was developed prior to what is incorreclty called classical statistics, which is more appropriately referred to as frequentist inference.  Bayesian inference is a modern revival of the classical definition of probability, associated with Pierre Simon Laplace, in contrast to the frequentist definition of probability, most often associated with R. A. Fisher.

Advantages

Below are internal links to webpages that discuss the advantages of Bayesian inference compared to frequentist inference:

• Credible Intervals vs. Confidence Intervals
• Exact Estimation vs. Approximate Estimation
• Hypothesis Testing
• Identifiability
• Interpretability
• Model Fit
• Sample Size

Criticisms

Below are internal links to webpages that discuss criticisms of Bayesian inference:

• Prior Probabilities