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What is the difference between (Dirichlet) distribution and (Dirichlet) process? The difference between a Dirichlet distribution and a Dirichlet process is perhaps easier to understand when you understand the difference between a Gaussian distribution and a Gaussian process. A Gaussian distribution pertains to the possible realizations of a single random ...


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Mixture models are generic probability density functions which are the weighted sums of independent processes that add to a total density function with a total area of 1, which area is common to all probability density functions. Consider, for example that two people are cutting pencils on an assembly line. The first cuts a fraction $0<p<1$ of the ...


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The OpenMx project can estimate growth mixture models, though you have to install the package from their website since it isn't on CRAN. They have examples in the user documentation (section 2.8) for how to set this up as well.


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It is often something more involved, though what you have said is not that far off for many applications. In a mixture model, generally speaking, you can choose to freely estimate parameters across levels of an otherwise unobserved multinomial variable, the number of levels of which are specfied by the user. The underlying model/parameters could just be ...


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In order to use a mixture of Gaussians for your problem, you have to assume that your three measurements are multivariate normal. In that setting, you have many measurements of a mixture of 3 dimensional normals, generated by k different underlying densities. You could start by setting k=3, one for "/ shape", one for "/\ shape", and one for "-- shape" you ...


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These are two great tutorials, "Introduction to the Dirichlet Distribution and Related Processes" "A Very Gentle Note on the Construction of Dirichlet Process" specially the first one, with a reference to a very succinct tutorial on measure theory. I would start with the first one, because it starts by introducing the Dirichlet distribution and sampling, ...


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No credit for this as I found it on the OpenMx forum http://openmx.psyc.virginia.edu/thread/717 & http://openmx.psyc.virginia.edu/sites/default/files/gmm_0.R, however to complete the question I will post the answer here nevertheless. Everything you posted is fine, you "only" have to add this: # view the class probabilities gmmFit$classProbs ...


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You don't want a test, because you have no definite hypothesis to assess: you are exploring. This calls for graphical display of relationships among bacterial counts and the potential explanatory variables. It's likely you will need to re-express the grain size fractions, because basic science suggests many possible meaningful properties including surface ...


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You have highlighted one important issue: estimates on the boundaries of the parameter space can cause convergence issues. From the documentation: the program may not converge and reach the maximum number of iterations fixed at 100. In this case, the user should check that parameter estimates at the last iteration are not on the boundaries of the ...


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You have also the package Kml and Kml3d (joint trajectories) that estimate the non-parametric equivalent of a GMM. You don't get any parameters as a result of these analyses, only the classification of each observation in the classes. However, in most applications, people don't use the parameters of LCGA and GMM anyway, and it is also much more robust than ...


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