Abstract Residual analysis is a useful tool for checking lack of fit and for providing insight into model improvement. However, literature on residual analysis and the goodness of fit for hidden Markov models (HMMs) is limited. As HMMs with complex structures are increasingly used to accommodate different types of data, there is a need for further tools to check the validity of models applied to real world data. We review model checking methods for HMMs and develop new methods motivated by a particular case study involving a two-dimensional HMM developed for time series with many null events. We propose new residual analysis and stochastic reconstruction methods, which are adapted from model checking techniques for point process models. We apply the new methods to the case study model and discuss their adequacy. We find that there is not one “best” test for diagnostics but that our new methods have some advantages over previously developed tools. The importance of multiple tests for complex HMMs is highlighted and we use the results of our model checking to provide suggestions for possible improvements to the case study model. Supplementary materials for this article are available online.

中文翻译：

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隐马尔可夫模型的模型检查

摘要 残差分析是检查不拟合和提供洞察模型改进的有用工具。然而，关于残差分析和隐马尔可夫模型 (HMM) 拟合优度的文献是有限的。随着具有复杂结构的 HMM 越来越多地用于容纳不同类型的数据，需要进一步的工具来检查应用于现实世界数据的模型的有效性。我们回顾了 HMM 的模型检查方法，并开发了受特定案例研究启发的新方法，该案例研究涉及为具有许多空事件的时间序列开发的二维 HMM。我们提出了新的残差分析和随机重建方法，这些方法改编自点过程模型的模型检查技术。我们将新方法应用于案例研究模型并讨论它们的充分性。我们发现没有一种“最佳”的诊断测试方法，但我们的新方法比以前开发的工具有一些优势。强调了对复杂 HMM 进行多次测试的重要性，我们使用模型检查的结果为案例研究模型的可能改进提供建议。本文的补充材料可在线获取。