Yau C, Papaspiliopoulos O, Roberts G O, Holmes C
Department of Statistics and the Oxford-Man Institute for Quantitative Finance, University of Oxford,
J R Stat Soc Series B Stat Methodol. 2011 Jan 1;73(1):37-57. doi: 10.1111/j.1467-9868.2010.00756.x.
We consider the development of Bayesian Nonparametric methods for product partition models such as Hidden Markov Models and change point models. Our approach uses a Mixture of Dirichlet Process (MDP) model for the unknown sampling distribution (likelihood) for the observations arising in each state and a computationally efficient data augmentation scheme to aid inference. The method uses novel MCMC methodology which combines recent retrospective sampling methods with the use of slice sampler variables. The methodology is computationally efficient, both in terms of MCMC mixing properties, and robustness to the length of the time series being investigated. Moreover, the method is easy to implement requiring little or no user-interaction. We apply our methodology to the analysis of genomic copy number variation.
我们考虑为诸如隐马尔可夫模型和变点模型等乘积划分模型开发贝叶斯非参数方法。我们的方法使用狄利克雷过程混合（MDP）模型来处理每个状态下观测值的未知抽样分布（似然），并采用一种计算效率高的数据增强方案来辅助推理。该方法使用了新颖的马尔可夫链蒙特卡罗（MCMC）方法，该方法将最近的回顾性抽样方法与切片采样器变量的使用相结合。该方法在计算效率方面表现出色，无论是在MCMC混合特性方面，还是对所研究时间序列长度的稳健性方面。此外，该方法易于实现，几乎不需要用户交互。我们将我们的方法应用于基因组拷贝数变异的分析。
