Deviance (statistics)

In statistics, deviance is a quality-of-fit statistic for a model that is often used for statistical hypothesis testing. It is a generalization of the idea of using the sum of squares of residuals in ordinary least squares to cases where model-fitting is achieved by maximum likelihood. It plays an important role in exponential dispersion models and generalized linear models.

The unit deviance${\displaystyle d(y,\mu )}$ is a bivariate function that satisfies the following conditions:

The total deviance ${\displaystyle D(\mathbf {y} ,{\hat {\boldsymbol {\mu }}})}$ of a model with predictions ${\displaystyle {\hat {\boldsymbol {\mu }}}}$ of the observation ${\displaystyle \mathbf {y} }$ is the sum of its unit deviances: ${\displaystyle D(\mathbf {y} ,{\hat {\boldsymbol {\mu }}})=\sum _{i}d(y_{i},{\hat {\mu }}_{i})}$.

...
Wikipedia