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content/notes/dimensionalityreduction/optimalitycriteria.md
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@ -6,7 +6,7 @@ Falling under wrapper methods, optimality criterion are often used to aid in mod
## Akaike Information Criterion (AIC)
AIC is an estimator of <u>relative</u> quality of statistical models for a given set of data. Given a collection of models for the data, AIC estimates the quality of each model relative to each other.
AIC is an estimator of *relative<* quality of statistical models for a given set of data. Given a collection of models for the data, AIC estimates the quality of each model relative to each other.
This way, AIC provides a means for model selection. AIC offers an estimate of the relative information lost when a given model is used.
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## Deviance Information Criterion
The DIC is a hierarchical modeling generalization of the AIC and BIC. it is useful in Bayesian model selection problems where posterior distributions of the model was <u>obtained by a Markov Chain Monte Carlo simulation</u>.
The DIC is a hierarchical modeling generalization of the AIC and BIC. it is useful in Bayesian model selection problems where posterior distributions of the model was *obtained by a Markov Chain Monte Carlo simulation*.
This method is only valid if the posterior distribution is approximately multivariate normal.