Definition: Deviance

Index: The Book of Statistical Proofs ▷ Model Selection ▷ Classical information criteria ▷ Deviance information criterion ▷ Deviance

Definition: Let there be a generative model $m$ describing measured data $y$ using model parameters $\theta$. Then, the deviance of $m$ is a function of $\theta$ which multiplies the log-likelihood function with $-2$:

\[\label{eq:dev} D(\theta) = -2 \log p(y|\theta,m) \; .\]

The deviance function serves the definition of the deviance information criterion.

 

Sources:

• Spiegelhalter DJ, Best NG, Carlin BP, Van Der Linde A (2002): "Bayesian measures of model complexity and fit"; in: Journal of the Royal Statistical Society, Series B: Statistical Methodology, vol. 64, iss. 4, pp. 583-639; URL: https://rss.onlinelibrary.wiley.com/doi/10.1111/1467-9868.00353; DOI: 10.1111/1467-9868.00353.
• Soch J, Allefeld C (2018): "MACS – a new SPM toolbox for model assessment, comparison and selection"; in: Journal of Neuroscience Methods, vol. 306, pp. 19-31, eqs. 10-12; URL: https://www.sciencedirect.com/science/article/pii/S0165027018301468; DOI: 10.1016/j.jneumeth.2018.05.017.
• Wikipedia (2022): "Deviance information criterion"; in: Wikipedia, the free encyclopedia, retrieved on 2022-03-01; URL: https://en.wikipedia.org/wiki/Deviance_information_criterion#Definition.

Metadata: ID: D172 | shortcut: dev | author: JoramSoch | date: 2022-03-01, 07:48.