Likelihood
#Math
The probability of an observation (the data being what it is) given some parameters
Topics
$\displaystyle L(p_{i}|Y_{i})=P(Y_{i}=y_{i}|p_{i})$
- Likelihood for a single observation $\displaystyle y_{i}$ which occurs at a conditional probability of $\displaystyle p_{i}=P(Y_{i}=1|X_{i})$
$\displaystyle L(p|Y)=\prod_{i}P(Y_{i}=y_{i})=\prod_{i}p_{i}^{y_{i}}(1-p_{i})^{1-y_{i}}$
- The likelihood of an observation of $\displaystyle p$ given $\displaystyle x$ and $\displaystyle y$