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The optimal number of clusters k (discrete classes) is maximizing the model explained variance (R-square), namely, the ratio between the variance of the distribution of the single statistical units coded by the relative cluster centroid value and the original distribution total variance.
This means that maximizing the model evidence corresponds to maintaining an accurate explanation for the data while minimizing complexity [ 50].
We describe an asymmetric approach to fMRI and MEG/EEG fusion in which fMRI data are treated as empirical priors on electromagnetic sources, such that their influence depends on the MEG/EEG data, by virtue of maximizing the model evidence.
It is applied to the pairs of expression profiles in ℒ and aims at maximizing the model likelihood: (1) with P g, g' |Θ) being the probability of generating the expression profiles associated with genes g and g' with the HMM with parameters Θ.
The balance between maximizing the model's entropy and minimizing the penalty is controlled by parameter ∈. (A ) The effect of the tradeoff parameter on the accuracy of the model is shown as the Jensen Shannon divergence (DJS) between the third order maximum entropy model with the penalty term and the model without the penalty term (as in Figure 3 ).
Because evolutionary models are not in general nested, we performed model selection via the popular Akaike information criterion, a method that penalizes a model's fit by its number of included variables (Akaike 1973) and is asymptotically equivalent to maximizing the model's predictive performance on unseen data (Stone 1977).
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Because the priors factorize, maximizing the model-evidence, p(Y| M), is equivalent to maximizing: where F is the variational "free-energy" and here is equal to (bar a constant): where C = LC(2) LT + C(1), and Σ is the posterior covariance of the hyperparameters (see Friston et al. [ 2007] for details).
Beagle applies a Markov model to the hidden states (the haplotype phase and the true genotype) along the chromosome using an EM (Expectation-Maximization) algorithm that iteratively updates model parameters to maximize the model likelihood up to the moment where convergence is achieved.
Our modelling strategy was to develop a predictive model that maximized the model R2.
The BIC is a model selection criteria that helps to maximize the model performance.
A Weibull distribution of lag time was assumed, as this choice proved to maximize the model likelihood.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com