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.