Definition: Log-likelihood function
Index:
The Book of Statistical Proofs ▷
General Theorems ▷
Frequentist statistics ▷
Likelihood theory ▷
Log-likelihood function
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Metadata: ID: D59 | shortcut: llf | author: JoramSoch | date: 2020-05-17, 22:52.
Definition: Let there be a generative model $m$ describing measured data $y$ using model parameters $\theta$. Then, the logarithm of the probability density function of the distribution of $y$ given $\theta$ is called the log-likelihood function of $m$:
\[\label{eq:llf} \mathrm{LL}_m(\theta) = \log p(y|\theta,m) = \log \mathcal{D}(y; \theta) \; .\]Metadata: ID: D59 | shortcut: llf | author: JoramSoch | date: 2020-05-17, 22:52.