Statistical models that involve latent Markovian state processes have become immensely popular tools for analysing time series and other sequential data. However, the plethora of model formulations, the inconsistent use of terminology, and the various inferential approaches and software packages can be overwhelming to practitioners, especially when they are new to this area. With this review-like paper, we thus aim to provide guidance for both statisticians and practitioners working with latent Markov models by offering a unifying view on what otherwise are often considered separate model classes, from hidden Markov models over state-space models to Markov-modulated Poisson processes. In particular, we provide a roadmap for identifying a suitable latent Markov model formulation given the data to be analysed. Furthermore, we emphasise that it is key to applied work with any of these model classes to understand how recursive techniques exploiting the models' dependence structure can be used for inference. The R package LaMa adapts this unified view and provides an easy-to-use framework for very fast (C++ based) evaluation of the likelihood of any of the models discussed in this paper, allowing users to tailor a latent Markov model to their data using a Lego-type approach.

翻译：涉及隐马尔可夫状态过程的统计模型已成为分析时间序列及其他序列数据的极受欢迎的工具。然而，模型公式的多样性、术语使用的不一致性以及各种推断方法和软件包，可能会让实践者感到无所适从，尤其是该领域的新手。因此，通过这篇综述性论文，我们旨在为使用隐马尔可夫模型的统计学家和实践者提供指导，提供一个统一视角，涵盖从隐马尔可夫模型、状态空间模型到马尔可夫调制泊松过程等常被视为独立模型类别的各种形式。特别地，我们提供了一份路线图，用于根据待分析数据确定合适的隐马尔可夫模型公式。此外，我们强调，对于任何此类模型的应用工作，关键在于理解如何利用模型的依赖结构，通过递归技术进行推断。R 包 LaMa 采纳了这一统一视角，并提供了一个易于使用的框架，能够非常快速（基于 C++）地评估本文讨论的任何模型的似然函数，允许用户使用类似乐高的方法，为其数据量身定制隐马尔可夫模型。