Abstract

We develop a mixture model and diagnostic for Bayesian estimation and selection in high-order, discrete-state Markov chains. Both extend the mixture transition distribution, which constructs a transition probability tensor by aggregating probabilities from a set of single-lag transition matrices, through inclusion of mixture components dependent on multiple lags. We demonstrate two uses for the proposed model: identification of relevant lags through over-specification and shrinkage via priors for sparse probability vectors, and parsimonious approximation of multi-lag dynamics by mixing low-order transition models. The diagnostic yields a general and interpretable mixture decomposition for transition probability tensors estimated by any means. We demonstrate the utility of the model and diagnostic with simulation studies, and further apply the methodology to a data analysis from the high-order Markov chain literature, and to a time series of pink salmon abundance in Alaska, United States. Supplemental files for this article are available online.

摘要

我们为高阶离散状态马尔可夫链中的贝叶斯估计和选择开发了一个混合模型和诊断。两者都扩展了混合转移分布，通过包含依赖于多个滞后的混合分量，通过聚合一组单滞后转移矩阵的概率来构建转移概率张量。我们展示了所提出模型的两种用途：通过超规范识别相关滞后，并通过稀疏概率向量的先验收缩来识别相关滞后，以及通过混合低阶过渡模型对多滞后动态的简约逼近。该诊断为通过任何方式估计的转移概率张量产生一般且可解释的混合分解。我们通过模拟研究证明了模型和诊断的实用性，并进一步将该方法应用于来自高阶马尔可夫链文献的数据分析，以及美国阿拉斯加粉红鲑鱼丰度的时间序列。本文的补充文件可在线获取。