Hypoelliptic diffusions: filtering and inference from complete and partial observations

• 成果类型: Article
• 署名作者: Ditlevsen, Susanne; Samson, Adeline
• 署名单位: University of Copenhagen; Communaute Universite Grenoble Alpes; Universite Grenoble Alpes (UGA); Centre National de la Recherche Scientifique (CNRS)
• 刊物名称: JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY
• ISSN/ISSBN: 1369-7412
• DOI: 10.1111/rssb.12307
• 发表日期: 2019
• 页码: 361-384
• 关键词: damping hamiltonian-systems; parameter-estimation; CONVERGENCE; MODEL; inhibition; version

摘要

The statistical problem of parameter estimation in partially observed hypoelliptic diffusion processes is naturally occurring in many applications. However, because of the noise structure, where the noise components of the different co-ordinates of the multi-dimensional process operate on different timescales, standard inference tools are ill conditioned. We propose to use a higher order scheme to approximate the likelihood, such that the different timescales are appropriately accounted for. We show consistency and asymptotic normality with non-typical convergence rates. When only partial observations are available, we embed the approximation in a filtering algorithm for the unobserved co-ordinates and use this as a building block in a stochastic approximation expectation-maximization algorithm. We illustrate on simulated data from three models: the harmonic oscillator, the FitzHugh-Nagumo model used to model membrane potential evolution in neuroscience and the synaptic inhibition and excitation model used for determination of neuronal synaptic input.