Asymptotic theory for iteration required Monte Carlo algorithms

本研究的目的是研究需要迭代的蒙特卡罗(ITRMC)算法的行为，特别是马尔可夫链蒙特卡罗算法。我为这些算法引入了退化和弱一致性的概念。将结果应用于混合模型和分类数据模型，证明了ITRMC算法的简并性。利用我们的方法，我提出了高效的蒙特卡罗方法，该方法具有更好的收敛特性。

The aim of my research was to study the behaviors of Iteration Required Monte Carlo(ITRMC) algorithm, in particular, Markov chain Monte Carlo. I introduced the notion of degeneracy and weak consistency for those algorithms. I applied the result to mixture model and categorical data model and showed degeneracy of ITRMC algorithms for them. Taking advantage of our approach, I proposed efficient Monte Carlo methods which have better convergence property.