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The Volume of data set, the length of sequence and the dimensions of Integera drastically affect the performance of the sequential implementation of Gibbs sampler. The parallel implementation with functional decomposition method provides an alternate way to calculate those computation-intensive algorithm such as Gibbs sampler. By breaking the sequential dependent relationships among the variables, then distrubuting the computation over all other processors, it provides statisticians a much faster solution towards their large amount of data.
Limited by the available resources and time, I currently only parallized the two dimensions Gibbs sampler. All the evaluation and analysis are based on 2-dimension. Implementation of parallel Multi-dimension Gibbs sampler will be explored in the near future.
Moreover, since the computation over each sequence may varies, how to balance the weight of each chain need to be taken care of especially in the high-dimension case.