InformationCriteria4GMM {AdaptGauss} | R Documentation |
Calculates the AIC and BIC criteria
InformationCriteria4GMM(Data, Means, SDs, Weights, IsLogDistribution)
Data |
vector (1:N) of data points |
Means |
vector[1:L] of Means of Gaussians (of GMM),L == Number of Gaussians |
SDs |
vector of standard deviations, estimated Gaussian Kernels, has to be the same length as Means |
Weights |
vector of relative number of points in Gaussians (prior probabilities), has to be the same length as Means |
IsLogDistribution |
Optional, ==1 if distribution(i) is a LogNormal, default vector of zeros of length L, LogNormal Modes are at this point only experimental |
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
List with
K |
Number of gaussian mixtures |
AIC |
Akaike Informations criterium |
BIC |
Bayes Information criterium |
LogLikelihood |
LogLikelihood of GMM, see |
PDFmixture |
probability density function of GMM, see |
LogPDFdata |
log(PDFmixture) |
Michael Thrun
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.