In this work we study systems consisting of a group of moving particles. In such systems, often some important parameters are unknown and have to be estimated from observed data. Such parameter estimation problems can often be solved via a Bayesian inference framework. However in many practical problems, only data at the aggregate level is available and as a result the likelihood function is not available, which poses challenge for Bayesian methods. In particular, we consider the situation where the distributions of the particles are observed. We propose a Wasserstein distance based sequential Monte Carlo sampler to solve the problem: the Wasserstein distance is used to measure the similarity between the observed and the simulated particle distributions and the sequential Monte Carlo samplers is used to deal with the sequentially available observations. Two real-world examples are provided to demonstrate the performance of the proposed method.

翻译：本研究关注由一组运动粒子构成的系统。在这类系统中，某些重要参数往往未知，需通过观测数据进行估计。此类参数估计问题通常可借助贝叶斯推理框架解决。然而在许多实际问题中，仅能获取聚合层面的数据，导致似然函数不可得，这对贝叶斯方法构成了挑战。具体而言，我们考虑粒子分布被观测的情形。本文提出一种基于Wasserstein距离的序贯蒙特卡洛采样器来解决该问题：利用Wasserstein距离度量观测粒子分布与模拟粒子分布之间的相似性，并采用序贯蒙特卡洛采样器处理序贯到达的观测数据。通过两个实际案例验证了所提方法的性能。