论文标题
部分观察到的随机隔室模型的贝叶斯数据增强
Bayesian Data Augmentation for Partially Observed Stochastic Compartmental Models
论文作者
论文摘要
确定性隔室模型主要用于传染病的建模，尽管随机模型被认为更现实，但由于缺少数据而估计很复杂。在本文中，我们提出了一种新型算法，用于估计贝叶斯框架中随机的SIR/SEIR流行模型，该模型可以很容易地扩展到更复杂的随机隔室模型。具体而言，基于模型的无限条件独立性，我们能够找到一个非常接近正确后验分布的大都市算法的建议分布。结果，我们可以一次更新一个缺失的数据点，而不是像当前的基准马尔可夫链蒙特卡洛（MCMC）算法一样，我们能够将我们的建议扩展到整个缺失的观测值。这大大改进了MCMC方法，并使随机模型现在成为可行的建模选项。介绍了许多真实的数据图和支持我们结果的必要数学理论。
Deterministic compartmental models are predominantly used in the modeling of infectious diseases, though stochastic models are considered more realistic, yet are complicated to estimate due to missing data. In this paper we present a novel algorithm for estimating the stochastic SIR/SEIR epidemic model within a Bayesian framework, which can be readily extended to more complex stochastic compartmental models. Specifically, based on the infinitesimal conditional independence properties of the model, we are able to find a proposal distribution for a Metropolis algorithm which is very close to the correct posterior distribution. As a consequence, rather than perform a Metropolis step updating one missing data point at a time, as in the current benchmark Markov chain Monte Carlo (MCMC) algorithm, we are able to extend our proposal to the entire set of missing observations. This improves the MCMC methods dramatically and makes the stochastic models now a viable modeling option. A number of real data illustrations and the necessary mathematical theory supporting our results are presented.
