A simple mixture model has a probability density function
with weight parameter
Here the components
probability density functions, and assumed to be entirely known.
Given the data
independent observations from the mixture density and the flat
prior, the posterior density
of weight parameter
is proportional to
However, the numerical analysis of posterior density
on the simplex
is rather very hard.
we can devise an MCMC scheme.
Then we introduce the following latent variable setup:
Let be a latent variable indicating to which component the -th
the vector of latent variables on the space
we denote the indicator function
So that we can define
denotes the number of
's set to
In this manner the latent variable
can be together lumped into
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