论文标题
在完整图上的随机SIS流行病的未知参数的统计推断
Statistical inference for unknown parameters of stochastic SIS epidemics on complete graphs
论文作者
论文摘要
在本文中，我们关注随机易感性易感性（SIS）流行病模型，并带有$ n $顶点。该模型有两个参数，即感染率和恢复率。通过利用密度依赖的马尔可夫链的理论，我们在有限的时间间隔内根据模型的样本路径对上述两个参数进行一致的估计。此外，我们建立了估计的中心极限定理（CLT）和中等偏差原理（MDP）。作为我们CLT的应用，给出了两个参数的假设检验区域。作为我们的MDP的应用，长度为$ 0 $的置信区间，而置信度融合到$ 1 $的置信区间则为$ n $增长到无限。
In this paper, we are concerned with the stochastic susceptible-infectious-susceptible (SIS) epidemic model on the complete graph with $n$ vertices. This model has two parameters, which are the infection rate and the recovery rate. By utilizing the theory of density-dependent Markov chains, we give consistent estimations of the above two parameters as $n$ grows to infinity according to the sample path of the model in a finite time interval. Furthermore, we establish the central limit theorem (CLT) and the moderate deviation principle (MDP) of our estimations. As an application of our CLT, reject regions of hypothesis testings of two parameters are given. As an application of our MDP, confidence intervals with lengths converging to $0$ while confidence levels converging to $1$ are given as $n$ grows to infinity.
