Frequentists and Bayesian Inference

Frequentist MLE

• , Likelihood function

Bayesian

Bayesian Inference

1. , prior distribution
3. With observed data , calculate , posterior distribution

Continuous Random Variable

• posterior mean
• max a posterior

Examples

Bernoulli

• p=P(x=1)
• prior , or,
  posterior
  posterior mean

Normal

• , known
• prior
  posterior
  posterior mean

Bayesian Interval

Simulation

• Generate I.I.D
• Estimate posterior mean
• ...