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：本文研究由一组移动粒子组成的系统。在这类系统中，某些重要参数通常是未知的，需要根据观测数据进行估计。此类参数估计问题通常可通过贝叶斯推断框架解决。然而在许多实际问题中，仅能获取聚合层面的数据，导致似然函数不可用，这对贝叶斯方法构成了挑战。具体而言，我们考虑了观测到粒子分布的情况。我们提出一种基于Wasserstein距离的序贯蒙特卡罗采样器来解决该问题：利用Wasserstein距离衡量观测粒子分布与模拟粒子分布之间的相似性，并采用序贯蒙特卡罗采样器处理序列可用的观测数据。我们提供了两个实际案例来验证所提方法的性能。