# Bayesian Statistics: From Concept to Data Analysis

0.15MB. 0 audio & 82 images. Updated 2021-11-05.

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Front |
How does the posterior mean decompose? |

Back |
[$$]\mu_{posterior} = w_{prior}\mu_{prior}+w_{data}\mu_{data}[/$$] |

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Front |
What is the uninformative prior for the Bernoulli/Binomial distribution and what is its limitation? |

Back |
[$]Beta(0,0) \propto \theta^{-1}(1-\theta)^{-1}[/$]At least one success and one failure is required to use it (otherwise, the integral is not a density) |

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Prior |

Front |
Define the Beta distribution |

Back |
[$]X \sim Beta(\alpha, \beta)[/$][$]Beta(1,1) = U(0,1)[/$][$]X \in (0;1)[/$][$]\alpha >0[/$] - shape[$]\beta > 0[/$] - shape[$]f(x|\alpha, \beta) = \dfrac{\Gamma(\alpha+\beta)}{\Gamma(\alpha)\Gamma(\beta)} x^{\alpha-1} (1-x)^{\beta-1}) [/$][$]\mathbb{E}(X) = \dfrac{\alpha}{\alpha +\beta}[/$][$]Var(X) = \dfrac{\alpha\beta}{(\alpha +\beta)^2(\alpha +\beta+1)}[/$] |

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Distribution |

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