带有移民的隐线性生灭过程的参数估计
Parameter estimation for a hidden linear birth and death process with immigration
AI总结：
本文用带移民的线性生灭过程建模传染病传播，针对感染人数隐藏且仅有周期性累计新移除计数的观测方案，推导未知参数解析表达式并改进Baum-Welch算法估计转移概率，在合成与真实数据上验证了估计量性能。
摘要：
在本文中，我们使用带有移民的线性生灭过程来对传染病传播进行建模，其中污染源于人与人之间的接触以及与环境的接触。我们的目标是估计该过程的参数。主要的创新点和难点来自于观测方案。感染人群的计数是隐藏的。唯一可用的数据是周期性的累计新移除计数。尽管这种观测方案在流行病学中非常普遍，但即使对于这种标准的随机过程，在数学上仍具有挑战性。我们首先推导出未知参数的解析表达式，作为精心选择的离散时间转移概率的函数。其次，我们扩展并调整了标准的Baum-Welch算法，以便在我们的隐数据框架中估计所述离散时间转移概率。我们的估计量的性能通过合成数据和马约特岛伤寒热的真实数据得到了说明。
英文摘要：
In this paper, we use a linear birth and death process with immigration to model infectious disease propagation when contamination stems from both person-to-person contact and contact with the environment. Our aim is to estimate the parameters of the process. The main originality and difficulty comes from the observation scheme. Counts of infected population are hidden. The only data available are periodic cumulated new retired counts. Although very common in epidemiology, this observation scheme is mathematically challenging even for such a standard stochastic process. We first derive an analytic expression of the unknown parameters as functions of well-chosen discrete time transition probabilities. Second, we extend and adapt the standard Baum-Welch algorithm in order to estimate the said discrete time transition probabilities in our hidden data framework. The performance of our estimators is illustrated both on synthetic data and real data of typhoid fever in Mayotte.
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。
