BAYESIAN NONPARAMETRIC INFERENCE IN MCKEAN-VLASOV MODELS

• 成果类型: Article
• 署名作者: Nickl, Richard; Pavliotis, Grigorios A.; Ray, Kolyan
• 署名单位: University of Cambridge; Imperial College London
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/24-AOS2459
• 发表日期: 2025
• 页码: 170-193
• 关键词: interacting particle-systems; DIFFUSIONS; equation; mcmc

摘要

We consider nonparametric statistical inference on a periodic interaction potential W from noisy discrete space-time measurements of solutions rho = rho W of the nonlinear McKean-Vlasov equation, describing the probability density of the mean field limit of an interacting particle system. We show how Gaussian process priors assigned to W give rise to posterior mean estimators that exhibit fast convergence rates for the implied estimated densities rho towards rho W . We further show that if the initial condition phi is not too smooth and satisfies a standard deconvolvability condition, then one can appropriate theta > 0, where N is the number of measurements. The exponent theta can be taken to approach 1/2 as the regularity of W increases corresponding to 'near-parametric' models.