BayesFor2GMM {AdaptGauss}

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.

See Also

BayesDecisionBoundaries,AdaptGauss