隐马尔可夫模型下的贝叶斯推断在真实多模态情况下的应用及生态时间序列分析
Bayesian inference for hidden Markov models under genuine multimodality with application to ecological time series
AI总结：
本文探讨了在隐马尔可夫模型中处理多模态似然函数的挑战，提出改进的平行温度算法以有效探索高维多模态后验分布，并通过蓝鲸潜水数据验证了该方法在生态时间序列分析中的应用。
摘要：
隐马尔可夫模型（HMMs）中的贝叶斯推断因似然函数的多模态性而具有挑战性，即使在纠正标签切换后也是如此。平行温度（PT）算法作为一种状态空间增强方法，是处理多模态分布的常用方法。然而，标准PT算法的实施可能不足以有效探索HMMs中出现的高维、复杂多模态后验分布。本文展示了在HMMs中实施PT算法时的常见陷阱，介绍了缓解方法，并引入了新的非信息性先验分布以促进后验分布的有效探索。我们分析了包含两个三状态HMMs的蓝鲸潜水时间序列数据，在贝叶斯框架下，其中一个HMM在转移概率矩阵中包含一个类别协变量以考虑声音刺激对鲸鱼行为的影响。我们展示了改进的PT算法在贝叶斯推断中的有效实施如何促进结果多模态后验分布的有效探索，以及这对蓝鲸基础运动模式推断的影响。
英文摘要：
Bayesian inference in hidden Markov models (HMMs) can be challenging due to the presence of multimodality in the likelihood function, and consequently in the joint posterior distribution, even after correcting for label switching. The parallel tempering (PT) algorithm, a state-space augmentation method, is a widely used approach for dealing with multimodal distributions. Nevertheless, standard implementation of the PT algorithm may not always be sufficient to effectively explore the high-dimensional, complex multimodal posterior distributions that arise in HMMs. In this work, we demonstrate common pitfalls when implementing the PT algorithm for HMMs, approaches to remedy them, and introduce new non-informative prior distributions that facilitate effective posterior distribution exploration. We analyse time series of blue whale dive data with two 3-state HMMs in a Bayesian framework, one of which includes a categorical covariate in the transition probability matrix to account for the effect of sound stimuli on the whale's behavior. We demonstrate how effective implementation of the modified PT algorithm for Bayesian inference leads to effective exploration of the resultant multimodal posterior distribution and how that affects inference for the underlying movement patterns of the blue whales.
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