The paper obtains analytical results for the asymptotic properties of Model Selection Criteria -- widely used in practice -- for a general family of hidden Markov models (HMMs), thereby substantially extending the related theory beyond typical i.i.d.-like model structures and filling in an important gap in the relevant literature. In particular, we look at the Bayesian and Akaike Information Criteria (BIC and AIC) and the model evidence. In the setting of nested classes of models, we prove that BIC and the evidence are strongly consistent for HMMs (under regularity conditions), whereas AIC is not weakly consistent. Numerical experiments support our theoretical results.

中文翻译：

---

一般隐马尔可夫模型的模型选择准则的渐近分析

该论文获得了模型选择准则的渐近特性的分析结果——在实践中广泛使用——对于隐马尔可夫模型 (HMM) 的一般族，从而大大扩展了相关理论，超出了典型的类 iid 模型结构，并填充了一个相关文献中的重要空白。我们特别关注贝叶斯和 Akaike 信息标准（BIC 和 AIC）以及模型证据。在模型的嵌套类的设置中，我们证明了 BIC 和证据对于 HMM（在规律性条件下）是强一致的，而 AIC 不是弱一致的。数值实验支持我们的理论结果。