llf.md

layout	mathjax	author	affiliation	e_mail	date	title	chapter	section	topic	definition	sources	def_id	shortcut	username
definition	true	Joram Soch	BCCN Berlin	joram.soch@bccn-berlin.de	2020-05-17 15:52:00 -0700	Log-likelihood function	General Theorems	Frequentist statistics	Likelihood theory	Log-likelihood function		D59	llf	JoramSoch

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 $m$:

$$ \label{eq:llf} \mathrm{LL}_m(\theta) = \log p(y|\theta,m) = \log \mathcal{D}(y; \theta) ; . $$