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Akaike (1974) showed, however, that we can estimate, via AIC, how much more (or less) information is lost by g 1 than by g 2. The estimate, though, is only valid asymptotically ; if the number of data points is small, then some correction is often necessary (see AICc , below).
In statistics, the Widely Applicable Information Criterion (WAIC), also known as Watanabe–Akaike information criterion, is the generalized version of the Akaike information criterion (AIC) onto singular statistical models. [1] It is used as measure how well will model predict data it wasn't trained on.
Both BIC and AIC attempt to resolve this problem by introducing a penalty term for the number of parameters in the model; the penalty term is larger in BIC than in AIC for sample sizes greater than 7. [1] The BIC was developed by Gideon E. Schwarz and published in a 1978 paper, [2] as a large-sample approximation to the Bayes factor.
Model selection is the task of selecting a model from among various candidates on the basis of performance criterion to choose the best one. [1] In the context of machine learning and more generally statistical analysis, this may be the selection of a statistical model from a set of candidate models, given data. In the simplest cases, a pre ...
The version of BIC as described here is not compatible with the definition of AIC in wikipedia. There is a divisor n stated with BIC, but not AIC in the Wikipedia entries. It would save confusion if they were consistently defined! I would favour not dividing by n: i.e. BIC = -2log L + k ln(n) AIC = -2log L + 2k
That measurement ( R^2_{AIC}= 1 - \frac{AIC_0}{AIC_i} ) doesn't make sense to me. R^2 values range from 0-1. If the AIC is better than the null model, it should be smaller. If the numerator is larger than the denominator, the R^2_{AIC} will be less than 1. This is saying that better models will generate a negative R^2_{AIC}.
They also note that HQC, like BIC, but unlike AIC, is not an estimator of Kullback–Leibler divergence. Claeskens & Hjort (2008, ch. 4) note that HQC, like BIC, but unlike AIC, is not asymptotically efficient ; however, it misses the optimal estimation rate by a very small ln ( ln ( n ) ) {\displaystyle \ln(\ln(n))} factor.
The deviance information criterion (DIC) is a hierarchical modeling generalization of the Akaike information criterion (AIC). It is particularly useful in Bayesian model selection problems where the posterior distributions of the models have been obtained by Markov chain Monte Carlo (MCMC) simulation.