InformationCriteria4GMM {AdaptGauss} | R Documentation |

## Information Criteria For GMM

### Description

Calculates the AIC and BIC criteria

### Usage

```
InformationCriteria4GMM(Data, Means, SDs, Weights, IsLogDistribution)
```

### Arguments

`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 |

### Details

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

### Value

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) |

### Author(s)

Michael Thrun

### References

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.

*AdaptGauss*version 1.6 Index]