# Probability Predictions

A *probability prediction* for an outcome $\omega\in\Omega$ is a probability measure $\gamma$ on $\Omega$. This is a task of probability forecasting. The quality of the probability prediction $\gamma$ is often measured by the minus log-likelihood $-\log\gamma(\omega)$ (in the discrete case) or $-\log f(\omega)$ (in the continuous case, where $f$ is the probability density function of $\gamma$). Another popular loss function in the case of finite $\Omega$ is the Brier loss function. For other kinds of predictions, see game of prediction.