Akaike Information Criterion AIC

Confining their study to monofunctional molecules, Roberts et al. [38] compared seven different models for predicting human stratum corneum permeability coefficients. The performance of the models was assessed by the adjusted coefficient of determination r2dj and the Akaike Information Criterion (AIC) [39], Both r2dj and AIC allow for comparing models with different numbers of variables (degrees of freedom). Exclusion of polyfunctional molecules led to a comparatively small set of only 24 molecules. The previously reported... 

In order to compare the performance of models containing different non-linear terms it is necessary to use a criterion which achieves a compromise between the overly simple model and the overly complex model. One such criterion is the Akaike Information Criterion, AIC(0) (see e.g. Akaike [Akaike, 1974]) given by ... 

The selection of the appropriate population pharmacokinetic base model was guided by the following criteria a significant reduction in the objective function value (p < 0.01,6.64 points) as assessed by the Likelihood Ratio Test the Akaike Information Criterion (AIC) a decrease in the residual error a decrease in the standard error of the model parameters randomness of the distribution of individual weighted residuals versus the predicted concentration and versus time post start of cetuximab administration randomness of the distribution of the observed concentration versus individual predicted concentration values around the line of identity in a respective plot. 

In order to choose the model that predicts most accurately for the test data, we need a new rule or a new information criterion. The usual criteria, the Akaike Information Criterion (AIC), the Bayesian Information Criterion (BIC), Leave One Out (LOO or Qsquared), and so on, are all insufficient for our needs. This motivated Kerry Bemis to propose a new measure which he called predictive R2 or pR2 (described below). 

With GAM the data (covariate and individual Bayesian PM parameter estimates) would be subjected to a stepwise (single-term addition/deletion) modeling procedure. Each covariate is allowed to enter the model in any of several functional representations. The Akaike information criterion (AIC) is used as the model selection criterion (22). At each step, the model is changed by addition or deletion of a covariate that results in the largest decrease in the AIC. The search is stopped when the AIC reached a minimum value. 

Akaike Information Criterion (AIC). A parameter used to choose among models with different parameters [Akaike, 1974] and defined as... 

The addition of a 3-compartment model dropped the Akaike Information Criterion (AIC) from 5.788 to 5.134. Although the model fit under the 3-compartment model was better than the 2-compartment model, a trend in the weighted residuals versus time plot was still apparent indicating that the model tended to underpredict (from 1 to 12 h), then overpredict (from 20 to... 

When the uncertainty in the parameter values becomes too large, the analyst should consider reducing the model. The correlation matrix between parameters can be useful in selecting the parameters that can be removed to make the model smaller. There are statistical criteria that can be used to select the better model. These include the Akaike Information Criterion (AIC) value and the F-test. The AIC value is calculated using the WSS, the number of parameters in the model, and the number of data points. The model with the lower AIC values is usually selected as the better model. The statistical F-test involves the calculation of an F value from the WSS and degrees of freedom from two analyses. The calculated F value is compared with the tabled values and a decision can be made whether the more complex model provides a significant improvement in the fit to the data. The analyst using a combination of subjective and objective criteria can make an educated decision about the best model. 

These extended equations can be used for the analysis of molecules with multiple diffusion states. This model assumes that molecules have multiple populations of different diffusion coefficients. A suitable number of states for data can be determined by a statistical method such as Akaike information criterion (AIC). 

Prom (2.62) it can be taken that the model s goodness of fit and the number of parameters used are counterbalanced. Among a set of model specifications, the specification with minimal IC value is recommended. In other words, information criteria aim at minimizing the residuals variance with as few parameters as possible. Often used information criteria for time series models are the Akaike information criterion (AIC)," the Schwarz information criterion (SIC) or the Hannan-Quinn information criterion (HQIC) with the following k functions ... 

The Akaike information criterion (AIC) [2] states that the best model class among the Cj, j = 1,2,..., Nc, is chosen by maximizing an objective function AIC(CyjP) over j that is defined by ... 

When the value of a is 2 in the expression for GIC, it takes the form of the Akaike information criterion (AIC). The optimum model order p is one that minimizes the generalized or Akaike information criterion. More recent methods to estimate model order for signal sequences with a finite number of sample points include predictive least squares (PLS) and finite sample information criteria (FSIC). ... 

Alternatively, criteria can be estimated for each model based on the principle of parsimony, that is, all else being equal, select the simplest model. The Akaike Information Criterion (AIC) is one of the most widely used information criterion that combines the model error sum of squares and the number of parameters in the model. 

Number of states selection Selecting the number of states in an HMM model is always an interesting but difficult question. It exists several methods as well as criteria for this selection purpose, such as Akaike Information Criterion (AIC), Bayes Information Criterion (BIC), Cross-validation, etc. (Knoblauch 2004). In this study, we investigate the use of BIC for selecting the number of state N. 

The ARIMA method uses historical values to set the parameters described above. These datasets can only be used when they have specific properties like homoscedasticity and uniformity. The datasets of inflation do not have these properties, therefore some deformations on the dataset need to be performed. The number of deformations needed is described by the letter d. The theory speaks of ARIMA (p,d,q) models to describe the lag structure. In this research, different ARIMA lag structures are used to model the different indexes. The choices of the p d and q are based on the Akaike Information Criterion (AIC). The model-hng is executed with Palisade s RISK software as plug-in in Microsoft Excel. 

As an additional experiment, we apply the MOEA-based method to a different formulation of the neural network optimal design, one in which the optimization criteria are the minimization of validation error and network computational complexity. The latter is measured here via the Akaike Information Criterion (AIC) [6], defined as —2 In(MSE) - - 2k, where k is the number of weights in the ANNs. This second goal might be important, for instance, in contexts where the classifier ANN must be used in real-time and therefore should be computationally cheap, still guaranteeing robust classification performance. 

When several competing models are used to fit the same data set, the best model can be discriminated by using the Akaike information criterion (AIC), which uses the following statistic to evaluate the fitting performance of each model ... 

A second approach considered both the Akaike and Bayesian information criteria. The Akaike information criterion (AIC) is an operational way of considering both the complexity of a model and how well it hts the data (Burnham and Anderson, 1998). The AIC methodology attempts to hnd the model that best explains the data with a minimum of free parameters. When residuals are randomly distributed, the AIC is calculated as... 

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