[EMAIL PROTECTED] (nicolexz) wrote in message news:<[EMAIL PROTECTED]>...
> Another question regarding the mixture distribution.  Suppose a random
> variable (Y) follows a mixed normal distribution with a certain weight
> (p) for each component.  You can always rewrite out this model into a
> hierarchical model by introducing a latent guy (Z) while Z represents
> the component of mixture.  Therefore, the probability of Z equals to
> the weight of each component in the mixture.  (See Chapter 24 of
> 'Markov Chain Monte Carlo in Practice'--- Richardson & Spiegelhalter
> for detailed discussion.)  My question is that during the Gibbs
> sampling, if the weight of a certain component (i) is extremely small,
> say around .002, the chance of Z being sampled is very small.  You may
> run into the situation that Z takes any values but i after a round of
> Gibbs sampling, this causes problem in next round of simulation.  Who
> can tell me how to handle this situation?  

If I understand correctly, your concern is that for components with
small enough probability, they may not show up in a sampling run. This
should only happen if the sampling period is so short that the
expected number of times the i-th class is selected is very small (no
more than a few). If your sampling runs are that short, then, yes, you
can miss a component. Yes, that can cause a problem

If your sampling run is long enough that even the rare components
should show up many times, but they still don't, it most likely
indicates a problem with your sampler (getting stuck in some portion
of the space).

If you simply cannot sample enough times to be confident of getting a
good representation of the rare components, then don't use a straight
sampling approach. What you might do instead depends on what it is
you're trying to achieve.

Glen
.
.
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