[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 . . ================================================================= Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at: . http://jse.stat.ncsu.edu/ . =================================================================
