[R] simulating Gaussian Mixture Method

[Bill.Venables at csiro.au]

Adding them together will not give you a sample from a mixture, it gives you a sample from another multivariate normal distribution.

Rather than add them together what you have to do is select from each of the two samples with the appropriate probability.

e.g. suppose your mixing probability was 0.6 for the first component and hence 0.4 for the second.  Also suppose S1 (1000 x 6) and S2 (1000 x 6) are the two samples generated by mvrnorm.  Then to get a sample from a mixture of the two you would need to do

S12 <- array(c(S1, S2), dim = c(1000*6, 2))  ## both in the one matrix, as two columns
comp <- cbind(1:6000, ifelse(runif(1000) < 0.6, 1, 2))
Smix <- matrix(S12[comb], nrow = 1000)

This should give you a sample from the mixture.

Bill Venables

-----Original Message-----
From: r-help-bounces at r-project.org [mailto:r-help-bounces at r-project.org] On Behalf Of Peng Jiang
Sent: Monday, 16 June 2008 3:48 PM
To: R-help at r-project.org
Subject: [R] simulating Gaussian Mixture Method


  Hi,

  I have a mixture pdf which has three components, each satisfies the  
6 dimension normal distribution.

   I use mvrnorm() from the MASS library to generate 1000 samples for  
each component  and I add them
  to get the random samples which satisfies with the mixture  
distribution.

  I use Mclust() from the mclust library to get the model of the  
samples and strange things happened.
  First it gave a warning

 > samplesMclust <- Mclust( samples )

  Warning messages:
1: In summary.mclustBIC(Bic, data, G = G, modelNames = modelNames) :
   best model occurs at the min or max # of components considered
2: In Mclust(samples) : optimal number of clusters occurs at min choice

Then I input
 > samplesMclust

  best model: XXI with 1 components

  it says the best model is with 1 component !

   I am confused ... Is it because the way that I generate samples is  
wrong???

   thanks so much !




--------------------------
Peng Jiang
江鹏
Ph.D. Candidate

Antai College of Economics & Management
安泰经济管理学院
Department of Mathematics
数学系
Shanghai Jiaotong University (Minhang Campus)
800 Dongchuan Road
200240 Shanghai
P. R. China

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