Bayesian vs Frequentist Comparison

Compare two fundamental approaches to statistical inference

Coin Flip Experiment

Bayesian Prior Distribution

Higher = stronger prior belief (more data needed to change your mind)

Bayesian Analysis

Frequentist Analysis

Key Philosophical Differences

Bayesian Approach

  • Probability represents degree of belief
  • Parameters have distributions (are random)
  • Combines prior knowledge with data
  • Updates beliefs: prior → posterior
  • Gives P(hypothesis | data)
  • Direct probability statements about parameters

Frequentist Approach

  • Probability is long-run frequency
  • Parameters are fixed (unknown constants)
  • Uses only the current data
  • Tests hypotheses against null
  • Gives P(data | hypothesis)
  • Makes statements about procedures, not parameters

Interpretation Guide

Bayesian Credible Interval: "There is a 95% probability that the true parameter lies in this interval" (direct probability statement)

Frequentist Confidence Interval: "If we repeated this procedure many times, 95% of intervals would contain the true parameter" (statement about the procedure)

Bayesian Posterior: Updated belief about the parameter after seeing the data

Frequentist P-value: Probability of seeing data this extreme if the null hypothesis (p=0.5) were true