I want to estimate parameters of Dirichlet mixture models using Gibbs sampling and I have some questions about that:
Is a mixture of Dirichlet distributions equivalent to a Dirichlet process? What is their main differences if is not?
Also, if I want to estimate a single Dirichlet distribution's parameters, which distribution for parameters should be selected as priors in Bayesian framework?
In all of the papers I found an estimation of a multinomial distribution using Dirichlet priors. I need estimation of a Dirichlet distribution using multinomial priors, perhaps.
Is the posterior function also in the form of DIRICHLET(α+N) similar to the case “estimation of multinomial distribution using Dirichlet priors”? as the multiplication of probability density function for iid samples are not considered in the definition of the likelihood function. I again cannot understand why.
e.g. as expressed in this paper: http://www.stat.ufl.edu/~aa/cda/bayes.pdf or http://research.microsoft.com/en-us/um/people/minka/papers/minka-multinomial.pdf
so thanks for your attention
my data is Hyperion (a kind of hyperspectral remote sensing imagery) and i want to perform hyperspectral unmixing using mixture of Dirichlet sources and i will apply Gibbs sampling method for parameter estimation. my data is in dimension (614*512*224) which is commonly available AVIRIS sensor data for Cuprite Nevada district and is almost 200MB. also this data is available via (http://aviris.jpl.nasa.gov/data/free_data.html). unfortunately i don't know how can i sent my data.
i just ask you to help me in statistical modelling tasks for my PHD thesis. i will be so grateful if you help me to solve my confusions in modelling.
all the best solmaz