Note 5 Sufficient Statistics（十分統計量）

復習

• Exponential family
• Statistic
• Likelihood

Principles of data reduction

• Sufficiency principle
• Likelihood principal
• Formal likelihood Principal*
  • Formal sufficiency principle
  • Conditional principle
  • Formal likelihood principal
• Equivariance Principle*

5.1 Sufficiency Principle

5.2 Sufficient Statistics

5.3 Ancillary Statistics

5.4 Complete Statistics

5.5 Basu’ Theorem

5.6 Likelihood Principle

応用：ベイズ推測法

• Bayesian Markov chain Monte Carlo method
• STAN programming: https://mc-stan.org/docs/reference-manual/mcmc.html
• Using R: https://jtr13.github.io/cc20/a-basic-introduction-to-markov-chain-monte-carlo-method-in-r.html