  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.
