1. Hidden Markov models (HMMs) are powerful tools for modelling time-series data with underlying state structure. However, selecting appropriate parametric forms for the state-dependent distributions is often challenging and can lead to model misspecification. To address this, P-spline-based nonparametric estimation of state-dependent densities has been proposed. While offering great flexibility, these approaches can result in overly complex densities (e.g. bimodal) that hinder interpretability. 2. We propose a straightforward method that builds on shape-constrained spline theory to enforce unimodality in the estimated state-dependent densities through enforcing unimodality of the spline coefficients. This constraint strikes a practical balance between model flexibility, interpretability, and parsimony. 3. Through two simulation studies and a real-world case study using narwhal (Monodon monoceros) dive data, we demonstrate the proposed approach yields more stable estimates compared to fully flexible, unconstrained models improving model performance and interpretability. 4. Our method bridges a key methodological gap, by providing a parsimonious HMM framework that balances the interpretability of parametric models with the flexibility of nonparametric estimation. This provides ecologists with a powerful tool to derive ecologically meaningful inference from telemetry data while avoiding the pitfalls of overly complex models.

翻译：1. 隐马尔可夫模型（HMMs）是建模具有潜在状态结构的时间序列数据的强大工具。然而，为状态依赖分布选择合适的参数形式通常具有挑战性，并可能导致模型设定错误。为解决此问题，已提出基于P样条的状态依赖密度的非参数估计方法。尽管这些方法提供了极大的灵活性，但可能导致过于复杂的密度（如双峰分布），从而阻碍可解释性。2. 我们提出一种基于形状约束样条理论的直接方法，通过强制样条系数的单峰性来确保估计的状态依赖密度具有单峰特性。该约束在模型灵活性、可解释性和简约性之间实现了实用的平衡。3. 通过两项模拟研究和使用独角鲸（Monodon monoceros）潜水数据的真实案例研究，我们证明所提出的方法相较于完全灵活的无约束模型能产生更稳定的估计，从而提升模型性能和可解释性。4. 我们的方法填补了一个关键的方法学空白，提供了一个简约的HMM框架，平衡了参数模型的可解释性与非参数估计的灵活性。这为生态学家提供了一个强大工具，可从遥测数据中得出具有生态学意义的推断，同时避免过度复杂模型的缺陷。