Markov chain Monte Carlo Estimation of Classical and Dynamic Switching and Mixture Models
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经典与动态切换及混合模型的马尔可夫链蒙特卡洛估计
- 研究问题
- 当观测分布由离散潜在状态决定时，如何联合估计状态与参数，并处理状态标签不可识别对贝叶斯计算的影响？
- 方法与思路
- 作者提出置换采样：先从无约束后验抽样并置换标签，再探索识别约束，第二轮通过适当置换满足这些约束。
- 材料陈述的贡献
- 摘要称该方法统一处理混合、切换自回归和切换动态线性模型，并用胎羊数据及美国季度实际国民生产总值示例说明。
- 阅读关注点
- 应核对标签置换如何影响后验目标、识别约束如何从第一轮输出选择，以及两轮采样的收敛诊断和计算成本。
- 阅读边界
- 仅据OpenAlex索引摘要，稿件版本未注明；摘要未给出采样收敛保证或比较结果，标签约束也不能直接解释为经济状态识别。
原文摘要
Bayesian estimation of a very general model class, where the distribution of the observations depends on a latent process taking values in a discrete state space, is discussed in this article. This model class covers finite mixture modeling, Markov switching autoregressive modeling, and dynamic linear models with switching. The consequences the unidentifiability of this type of model has on Markov chain Monte Carlo (MCMC) estimation are explicitly dealt with. Joint Bayesian estimation of all latent variables, model parameters, and parameters that determine the probability law of the latent process is carried out by a new MCMC method called permutation sampling. The permutation sampler first samples from the unconstrained posterior–which often can be done in a convenient multimove manner–and then applies a permutation of the current labeling of the states of the latent process. In a first run, the random permutation sampler used selected the permutation randomly. The MCMC output of the random permutation sampler is explored to find suitable identifiability constraints. In a second run, the permutation sampler was used to sample from the constrained posterior by imposing identifiablity constraints. This time a suitable permutation is applied if the identifiability constraint is violated. For illustration, two detailed case studies are presented, namely finite mixture modeling of fetal lamb data and Markov switching autoregressive modeling of the U.S. quarterly real gross national product data.