Statistical deviance
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Statistical deviance is a quantity whose expected values can be used for statistical hypothesis testing.
It is defined as:
- <math>D(y,\theta) = -2 \log p(\theta|y)<math>
As a function of <math>\theta<math> with <math>y<math> treated as fixed, it is −2 times the log-likelihood. In the framework of the generalized linear model, if <math>\theta<math> is the true parameter, <math>D(y,\theta)<math> follows a chi-squared distribution.