SRaI
@LMU
@LMU
125
0.0 (0)
Kartei Details
| Karten | 125 |
|---|---|
| Sprache | English |
| Kategorie | Informatik |
| Stufe | Universität |
| Erstellt / Aktualisiert | 04.10.2019 / 11.10.2019 |
| Lizenzierung | Keine Angabe |
| Weblink |
https://card2brain.ch/box/20191004_srai
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| Einbinden |
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Name bayes roule
\(P(A|B) = \frac{P(B|A) ~\cdot~ P(A)}{P(B)}\)
What is a random variable?
- random variable y maps from event-space omega to real values
Define the expected value and variance
\(E(Y) = \int_{-\infty}^{\infty}u ~f(u)~du = \mu\)
\(Var(Y) = \int_{-\infty}^{\infty}(y - \mu)^2~f(y)~dy = E((Y - \mu)^2) = \sigma^2 = E(Y^2) - \mu^2\)
Define the exponential family
\(f(y,\theta) = exp(t^T(y)~\theta - K(\theta)~h(y))\)
- with t(y) = statistics = function of data
- theta = parameter (vector)
- K(theta) = normalisation constant s.t. integral (f(y,theta)) = 1
- h(y) >= 0, unimportant
- and \(\frac{\partial K(\theta)}{\partial\theta} = E(t(Y))\)
