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The quantity exp((AIC min − AIC i)/2) is known as the relative likelihood of model i. It is closely related to the likelihood ratio used in the likelihood-ratio test . Indeed, if all the models in the candidate set have the same number of parameters, then using AIC might at first appear to be very similar to using the likelihood-ratio test.
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.
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.
In frequentist statistics, the likelihood function is itself a statistic that summarizes a single sample from a population, whose calculated value depends on a choice of several parameters θ 1... θ p, where p is the count of parameters in some already-selected statistical model. The value of the likelihood serves as a figure of merit for the ...
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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.
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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.