卡尔曼滤波技术指导下的部分观测流行病动力学推断
Inference for partially observed epidemic dynamics guided by Kalman filtering techniques
摘要：
尽管最近开发的方法处理部分观察到的流行病动态（未观察到的模型坐标，离散和嘈杂的爆发数据），在实践中仍然存在局限性，主要涉及的数量的扩增数据和众多的调整参数的校准。特别地，由于动态流行病模型的坐标是耦合的，不可观测坐标的存在导致了统计困难的问题。我们的目的是提出一个易于使用和通用的推理方法，能够解决这些问题。首先，利用流行病在大群体中的性质，构造了一个两层模型。通过一个基于扩散的方法，高斯近似的流行病密度依赖马尔可夫跳过程，得到的状态模型。观测模型，由某些模型坐标的噪声观测，近似高斯分布。在此基础上，提出了一种基于卡尔曼滤波递推近似似然估计的状态模型和观测模型参数估计方法。关键模型参数的估计的性能进行评估SIR流行动力学的模拟数据，为不同的情况下，人口规模和观察的数量。这种性能相比，使用著名的最大迭代滤波方法获得的。最后，推理方法被应用到一个真实的数据集在1978年英国寄宿学校流感爆发。
英文摘要：
Despite the recent development of methods dealing with partially observed epidemic dynamics (unobserved model coordinates, discrete and noisy outbreak data), limitations remain in practice, mainly related to the quantity of augmented data and calibration of numerous tuning parameters. In particular, as coordinates of dynamic epidemic models are coupled, the presence of unobserved coordinates leads to a statistically difficult problem. The aim is to propose an easy-to-use and general inference method that is able to tackle these issues. First, using the properties of epidemics in large populations, a two-layer model is constructed. Via a diffusion-based approach, a Gaussian approximation of the epidemic density-dependent Markovian jump process is obtained, representing the state model. The observational model, consisting of noisy observations of certain model coordinates, is approximated by Gaussian distributions. Then, an inference method based on an approximate likelihood using Kalman filtering recursion is developed to estimate parameters of both the state and observational models. The performance of estimators of key model parameters is assessed on simulated data of SIR epidemic dynamics for different scenarios with respect to the population size and the number of observations. This performance is compared with that obtained using the well-known maximum iterated filtering method. Finally, the inference method is applied to a real data set on an influenza outbreak in a British boarding school in 1978.
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