Calculates the AIC and BIC criteria
InformationCriteria4GMM(Data, Means, SDs, Weights, IsLogDistribution)List with
Number of gaussian mixtures
Akaike Informations criterium
Bayes Information criterium
LogLikelihood of GMM, see LogLikelihood4Mixtures
probability density function of GMM, see Pdf4Mixtures
log(PDFmixture)
vector (1:N) of data points
vector[1:L] of Means of Gaussians (of GMM),L == Number of Gaussians
vector of standard deviations, estimated Gaussian Kernels, has to be the same length as Means
vector of relative number of points in Gaussians (prior probabilities), has to be the same length as Means
Optional, ==1 if distribution(i) is a LogNormal, default vector of zeros of length L, LogNormal Modes are at this point only experimental
Michael Thrun
AIC = 2*k -2*LogLikelihood, k = nr. of model parameter = 3*Nr. of Gaussians One Gaussian: K=2 (Weight is then not an parameter!) SMALL SAMPLE CORRECTION: for n= nr of Data and n < 40 * k, AIC is adjusted to AIC=AIC+ (2*k*(k+1))/(n-k-1)
BIC = k* log(n) - 2*LogLikelihood
Only for a Gaussian Mixture Model (GMM) verified, for the Log Gaussian, Gaussian, Log Gaussian (LGL) Model only experimental
Aubert, A. H., Thrun, M. C., Breuer, L., & Ultsch, A.: Knowledge discovery from data structure: hydrology versus biology controlled in-stream nitrate concentration, Scientific reports, Vol. (in revision), pp., 2016.
Aho, K., Derryberry, D., & Peterson, T.: Model selection for ecologists: the worldviews of AIC and BIC. Ecology, 95(3), pp. 631-636, 2014.