论文标题
通过Markov改编的非同质泊松过程框架进行建模和理解计数过程
Modelling and understanding count processes through a Markov-modulated non-homogeneous Poisson process framework
论文作者
论文摘要
Markov修饰的泊松过程用于在各个领域，例如排队，可靠性，网络和保险索赔分析。在本文中，我们通过引入柔性频率扰动度量来扩展马尔可夫修饰的泊松过程框架。这项贡献使观察到的事件到达的已知信息自然而然地融合在一起，而隐藏的马尔可夫链捕获了数据中无法观察到的驱动因素的效果。除了提高准确性和可解释性外，此方法还补充了潜在因素的分析。此外，此过程自然结合了数据功能，例如过度分散和自相关。可以生成其他见解以协助分析，包括迭代模型改进的程序。 还解决了实施困难，重点是处理大型数据集，因为大量观察结果促进了隐藏因素的识别，因此潜在模型尤其有利。也就是说，在这种情况下，在本文中出现了计算问题，例如数值下水流和高处理成本，我们制定了克服这些问题的程序。 使用大型保险数据集证明了该建模框架，以说明理论，实践和计算贡献，并与其他计数模型进行经验比较突出了所提出方法的优势。
The Markov-modulated Poisson process is utilised for count modelling in a variety of areas such as queueing, reliability, network and insurance claims analysis. In this paper, we extend the Markov-modulated Poisson process framework through the introduction of a flexible frequency perturbation measure. This contribution enables known information of observed event arrivals to be naturally incorporated in a tractable manner, while the hidden Markov chain captures the effect of unobservable drivers of the data. In addition to increases in accuracy and interpretability, this method supplements analysis of the latent factors. Further, this procedure naturally incorporates data features such as over-dispersion and autocorrelation. Additional insights can be generated to assist analysis, including a procedure for iterative model improvement. Implementation difficulties are also addressed with a focus on dealing with large data sets, where latent models are especially advantageous due the large number of observations facilitating identification of hidden factors. Namely, computational issues such as numerical underflow and high processing cost arise in this context and in this paper, we produce procedures to overcome these problems. This modelling framework is demonstrated using a large insurance data set to illustrate theoretical, practical and computational contributions and an empirical comparison to other count models highlight the advantages of the proposed approach.
