通过马尔可夫调制的非齐次泊松过程框架建模和理解计数过程
Modelling and understanding count processes through a Markov-modulated non-homogeneous Poisson process framework
摘要：
马尔可夫调制泊松过程被用于各种领域的计数建模，如统计，可靠性，网络和保险索赔分析。在本文中，我们通过引入一个灵活的频率扰动措施，扩展了马尔可夫调制泊松过程的框架。这一贡献使已知的观察到的事件到达的信息，自然地纳入一个易于处理的方式，而隐马尔可夫链捕获的数据的不可观察的驱动程序的效果。除了提高准确性和可解释性外，这种方法还补充了对潜在因素的分析。此外，该过程自然地结合了诸如过度分散和自相关的数据特征。可以生成额外的见解来帮助分析，包括迭代模型改进的过程。实施困难也得到解决，重点是处理大型数据集，其中潜在的模型是特别有利的，由于大量的观察，促进识别隐藏的因素。也就是说，计算问题，如数值下溢和高处理成本出现在这种情况下，在本文中，我们产生的程序来克服这些问题。这个建模框架使用一个大型的保险数据集来说明理论，实践和计算的贡献和实证比较其他计数模型突出了所提出的方法的优点。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
