TY - JOUR
T1 - Hypoelliptic diffusions
T2 - filtering and inference from complete and partial observations
AU - Ditlevsen, Susanne
AU - Samson, Adeline
PY - 2019/4
Y1 - 2019/4
N2 - 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.
AB - 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.
KW - 1.5 strong order discretization scheme
KW - Approximate maximum likelihood
KW - Hypoelliptic diffusion
KW - Parameter estimation
KW - Particle filter
KW - Stochastic approximation expectation–maximization algorithm
UR - http://www.scopus.com/inward/record.url?scp=85058976830&partnerID=8YFLogxK
U2 - 10.1111/rssb.12307
DO - 10.1111/rssb.12307
M3 - Journal article
AN - SCOPUS:85058976830
SN - 1369-7412
VL - 81
SP - 361
EP - 384
JO - Journal of the Royal Statistical Society. Series B: Statistical Methodology
JF - Journal of the Royal Statistical Society. Series B: Statistical Methodology
IS - 2
ER -