Frequentist vs Bayesian statistics

Sources: rlabbe , blitzstein-hwang

Frequentist

• Probability represents the frequency over an experiment repeated infinitely many times
• Probability of flipping a fair coin infinitely many times is 50%

Bayesian

• Probability represents a belief about the event [ bh ]
  • $\hat{=}$ hypothesis
  • e.g. probability that someone is guilty
• Probability of flipping a fair coin one more time: which way do I believe it landed? [ rlabbe ]
  • Bayesian statistics takes past information (prior) into account
  • If finding the prior is tricky, frequentist techniques are sometimes used

Example

e.g. Weather

• Frequentist: If it rains 4 out of 100 days, the chance of rain today is 25%
• Bayesian: If we know that it’s raining today and the storm front is stalled (prior information), it is likely to rain tomorrow