论文标题
近似基于个体的流行病模型中的最佳SMC建议分布
Approximating optimal SMC proposal distributions in individual-based epidemic models
论文作者
论文摘要
许多流行病模型自然定义为基于个体的模型：我们在易感人群中跟踪每个人的状态。由于此类模型的高维状态空间，基于个体模型的推断很具有挑战性，该模型随着人口规模的指数增加。我们考虑对基于个体的流行模型的推断进行顺序的蒙特卡洛算法，在这些模型中我们直接观察了个体样本的状态。标准实现，例如自举滤波器或辅助粒子过滤器，由于状态的提案分布与未来观察结果之间的不匹配，因此效率低下。我们开发了新的高效提案分布，以考虑未来的观察结果，并利用（i）我们可以分析地计算出一个人的最佳提案分布，并给定未来的观察结果和该个人的未来感染率； （ii）如果我们根据其感染率条件，个体的动态是独立的。因此，我们为每个人构建对未来感染率的估计，然后在此估计中对每个人的状态使用独立的建议。经验结果表明，SIS和SEIR模型的顺序蒙特卡洛采样器效率的数量级提高了。
Many epidemic models are naturally defined as individual-based models: where we track the state of each individual within a susceptible population. Inference for individual-based models is challenging due to the high-dimensional state-space of such models, which increases exponentially with population size. We consider sequential Monte Carlo algorithms for inference for individual-based epidemic models where we make direct observations of the state of a sample of individuals. Standard implementations, such as the bootstrap filter or the auxiliary particle filter are inefficient due to mismatch between the proposal distribution of the state and future observations. We develop new efficient proposal distributions that take account of future observations, leveraging the properties that (i) we can analytically calculate the optimal proposal distribution for a single individual given future observations and the future infection rate of that individual; and (ii) the dynamics of individuals are independent if we condition on their infection rates. Thus we construct estimates of the future infection rate for each individual, and then use an independent proposal for the state of each individual given this estimate. Empirical results show order of magnitude improvement in efficiency of the sequential Monte Carlo sampler for both SIS and SEIR models.
