2017/07/13 by Susanne Ditlevsen, Ditlevsen, Susanne, Adeline Samson +1
Economics, Econometrics and Finance · Mathematics · Medicine · Neuroscience · #Advanced Neuroimaging Techniques and Applications #Complex Systems and Time Series Analysis #FOS: Computer and information sciences #Methodology (stat.ME) #Neural dynamics and brain function #stat.ME
paper · pdf · doi:10.48550/arxiv.1707.04235
36 pages, 2 figures, 3 tables
openalex publication_date 2017/07/13 · arxiv created 2018/11/11 · arxiv updated 2018/11/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The statistical problem of parameter estimation in partially observed hypoelliptic diffusion processes is naturally occurring in many applications. However, due to the noise structure, where the noise components of the different coordinates of the multi-dimensional process operate on different time scales, standard inference tools are ill conditioned. In this paper, we propose to use a higher order scheme to approximate the likelihood, such that the different time scales 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 into a filtering algorithm for the unobserved coordinates, 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 the membrane potential evolution in neuroscience, and the Synaptic Inhibition and Excitation model used for determination of neuronal synaptic input.