Note 4 Generating a random sample（乱数の生成）

復習

• Law of large numbers (LLN)
• Convergence concept:
  • in prob. (weak LLN)
  • almost surely (strong LLN)
  • in distribution (central limit theorem, CLT)
• 変数変換

4.1 例： Exponential lifetime (pp.245~)

4.2 直接法

• Prob integral transformation
• Box-Muller algorithm
• Poisson variance

4.3 間接法

• Beta RV

4.4 Accept/Reject Algorithm

• Beta RV

• Metropolis Algorithm

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