I have a 6-dimensional data which I fitted with a 6-dimensional Gaussian mixture model and I would like to obtain the marginal distribution of all 1-dimensional events. However, I find it difficult to perform integration over the irrelevant variables in a high dimensional mixture model.
This is why, since I have the full data, I assumed I could fit a 1-d mixture model to the desired event dimension, and have the same outcome as performing the integration.
Marginal distribution gives the probabilities of various values of the variables in the subset without reference to the values of the other variables. Then, how can I define the univariate distribution fitted to the variable of interest? Does that distribution have reference to other variable? Or Is a fitted univariate distribution (fitted to the 1-d data exclusively) and the marginal distribution of the variables the same thing?