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I would like to estimate the statistical significance of a Gaussian Mixture model that is calculated by Mclust.

The output of Mclust includes both the optimal Bayesian information criterion (BIC) used to select the optimal model as well as the Log Likelihood used in the calculation. However, as far as I understand these are only meaningful for comparing different models for the same data.

Is there a way to estimate the statistical significant of the optimal model?

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    $\begingroup$ This question appears to be off-topic because it is about Statistics $\endgroup$ – csgillespie Oct 1 '13 at 13:56
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You will need to use the parametric bootstrap cross-fitting method (PBCM, pdf). The procedure is described on CV here: measures-of-model-complexity. If you need help understanding how to generate data from a Gaussian mixture model, I discuss that on CV here: simulating-random-variables-from-a-mixture-of-normal-distributions).

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