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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 | [$$]\mu_{posterior} = w_{prior}\mu_{prior}+w_{data}\mu_{data}[/$$] |
| Tags |
| 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) |
| Tags | 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[$]f(x|\alpha, \beta) = \dfrac{\Gamma(\alpha+\beta)}{\Gamma(\alpha)\Gamma(\beta)} x^{\alpha-1} (1-x)^{\beta-1}) [/$][$]\mathbb{E}(X) = \dfrac{\alpha}{\alpha +\beta}[/$][$]Var(X) = \dfrac{\alpha\beta}{(\alpha +\beta)^2(\alpha +\beta+1)}[/$] |
| Tags | Distribution |
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