## Posterioris of Bayes Theorem for a two group GMM

### Description

Calculates the posterioris of Bayes theorem, splits the GMM in two groups beforehand.

### Usage

```BayesFor2GMM(Data, Means, SDs, Weights, IsLogDistribution = Means * 0,
Ind1 = c(1:floor(length(Means)/2)), Ind2 = c((floor(length(Means)/2)
+ 1):length(Means)), PlotIt = 0, CorrectBorders = 0)
```

### 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 `Ind1` indices from (1:C) such that [M(Ind1),S(Ind1) ,W(Ind1) ]is one mixture, [M(Ind2),S(Ind2) ,W(Ind2) ] the second mixture default Ind1= 1:C/2, Ind2= C/2+1:C `Ind2` indices from (1:C) such that [M(Ind1),S(Ind1) ,W(Ind1) ]is one mixture, [M(Ind2),S(Ind2) ,W(Ind2) ] the second mixture default Ind1= 1:C/2, Ind2= C/2+1:C `PlotIt` Optional, Default: FALSE; TRUE do a Plot `CorrectBorders` Optional, ==TRUE data at right borders of GMM distribution will be assigned to last gaussian, left border vice versa. (default ==FALSE) normal Bayes Theorem

### Details

See conference presentation for further explanation.

### Value

List With

Posteriors:

(1:N,1:L) of Posteriors corresponding to Data

NormalizationFactor:

(1:N) denominator of Bayes theorem corresponding to Data

### Author(s)

Alfred Ultsch, Michael Thrun

### References

Thrun M.C.,Ultsch, A.: Models of Income Distributions for Knowledge Discovery, European Conference on Data Analysis, DOI 10.13140/RG.2.1.4463.0244, Colchester 2015.