## 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.