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.

翻译：许多流行病模型自然被定义为面向个体的模型：我们在易感人群中追踪每个个体的状态。由于这类模型的状态空间维度高（随种群规模呈指数增长），面向个体的模型推断极具挑战性。我们考虑基于序贯蒙特卡洛算法的推断方法，适用于对个体样本状态进行直接观测的面向个体流行病模型。标准实现方法（如自举滤波器或辅助粒子滤波器）因状态提议分布与未来观测不匹配而效率低下。我们开发了兼顾未来观测的新型高效提议分布，其利用以下特性：（i）针对单个个体，可解析计算给定未来观测及其未来感染率的最优提议分布；（ii）若以个体感染率为条件，个体间动态相互独立。由此我们为每个个体构建未来感染率的估计值，并基于该估计值为每个独立个体状态提出独立的提议。实验结果表明，对于SIS和SEIR模型，序贯蒙特卡洛采样器的效率提升了一个数量级。