Definition: Univariate Gaussian with known variance
Index: The Book of Statistical Proofs ▷ Statistical Models ▷ Univariate normal data ▷ Univariate Gaussian with known variance ▷ Definition
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Metadata: ID: D136 | shortcut: ugkv | author: JoramSoch | date: 2021-03-23, 16:12.
Definition: A univariate Gaussian data set with known variance is given by a set of real numbers $y = \left\lbrace y_1, \ldots, y_n \right\rbrace$, independent and identically distributed according to a normal distribution with unknown mean $\mu$ and known variance $\sigma^2$:
\[\label{eq:ug} y_i \sim \mathcal{N}(\mu, \sigma^2), \quad i = 1, \ldots, n \; .\]- Bishop, Christopher M. (2006): "Bayesian inference for the Gaussian" ; in: Pattern Recognition for Machine Learning , ch. 2.3.6, p. 97, eq. 2.137 ; URL: http://users.isr.ist.utl.pt/~wurmd/Livros/school/Bishop%20-%20Pattern%20Recognition%20And%20Machine%20Learning%20-%20Springer%20%202006.pdf .
Metadata: ID: D136 | shortcut: ugkv | author: JoramSoch | date: 2021-03-23, 16:12.