베이지안 통계학(Bayesian Statistics)

created : 2021-10-03T10:46:55+00:00
modified : 2021-10-03T12:45:59+00:00

Historical Perspective (관점의 변화)

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Frequentist/Classical Paradigm (빈도주의/고전적 패러다임)

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Bayesian Paradigm (베이지안주의 패러다임)

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Differences Between Frequentist and Bayesian (빈도주의와 베이지안주의 간의 차이)

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Overall Recommendation

Bayesian Approach (베이지안적 접근)

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Bayes’ Theorem

Bayesian Modeling

  1. Model specification:
    • $p(y \vert \theta)$ : likelihood function of y
    • $p(\theta)$ : prior distribution of $\theta$
  2. Performing inference:
    • $p(\theta \vert y)$ : posterior distribution of $\theta$ given y
    • $p(\theta \vert y) \propto p(y \vert \theta) p(\theta)$
    • How ?:
    • analystically-only possibile for certain models.
    • using simulation when we are not able to write down the exact form of the posterior density.
  3. Inference results:
    • ex) posterior mean : $E[\theta \vert y] = \int _{\theta} \theta p(\theta \vert y) d \theta$

Binomial Model

Binomial Model with Beta Prior