Parameter estimation from aggregate observations: a Wasserstein distance-based sequential Monte Carlo sampler

Area of Science:

• Computational Physics
• Statistical Inference
• Data Science

Background:

• Parameter estimation in particle systems is crucial but challenging when only aggregate data is available, hindering traditional Bayesian inference due to the lack of a likelihood function.
• Existing Bayesian methods struggle with aggregate-level observations, limiting their application in real-world scenarios involving complex particle dynamics.

Purpose of the Study:

• To develop a novel Bayesian inference framework for parameter estimation in particle systems using aggregate observational data.
• To address the challenge of unavailable likelihood functions in Bayesian inference when dealing with aggregate-level data.

Main Methods:

• A Wasserstein distance (WD)-based sequential Monte Carlo (SMC) sampler was developed to measure the similarity between observed and simulated particle distributions.
• The proposed method integrates WD for distribution comparison with SMC samplers to handle sequentially available observations.

Main Results:

• The WD-based SMC sampler effectively estimates parameters in particle systems using aggregate data, even when the likelihood function is not explicitly available.
• The method demonstrated robust performance in two real-world examples, validating its practical applicability.

Conclusions:

• The proposed Wasserstein distance-based sequential Monte Carlo method offers a powerful solution for Bayesian parameter estimation in particle systems with aggregate observational data.
• This approach overcomes limitations of traditional methods by effectively utilizing aggregate data and handling the absence of explicit likelihood functions.