arXiv subjects

S. Knutsen Furset

Publications and source records attributed to S. Knutsen Furset.

3 recordsLinked to original sources

arXiv2026

ARMA approximation of a Non-separable Spatio-Temporal Model with Fractional Smoothnesses in Space and Time

The Matérn covariance model is ubiquitous in spatial modelling, but there is no default choice for spatio-temporal modelling. In this paper, we consider the recently proposed ``diffusion-based'' extension of the spatial Matérn covariance model to a spatio-temporal non-separable covariance model that allows fractional smoothnesses in space and in time. The model is described in terms of a space-time fractional stochastic partial differential equation, but currently proposed computational approaches have strong restrictions on the possible smoothnesses in time. We propose a discretization method based on rational approximations in time to handle arbitrary smoothnesses, which leads to a vector autoregressive moving average process (VARMA). We prove that the covariance function of the approximation converges pointwise, determine explicit convergence rates as a function of spatial and temporal resolutions and the accuracy of the rational approximation, and conduct numerical verification to demonstrate small pointwise error for low orders of the VARMA process. Through a simulation study, we demonstrate that the parameters can be estimated back and that correctly specifying the temporal smoothness is especially important for forecasting. The approach is illustrated for three months of daily mean temperatures in mainland France.

stat.ME↗

arXiv2026

Unbiased likelihood estimation of the Langevin diffusion for animal movement modelling

An ongoing challenge in animal ecology is developing movement models that account for the autocorrelation, and often temporal irregularity, in telemetry data. Continuous-time Langevin diffusion models have been proposed to model temporally autocorrelated and irregularly sampled data. However, current estimation techniques obtain increasingly biased parameter estimates as the time between observations increases. In this paper, we propose using Brownian bridges in an importance sampling scheme to improve the likelihood approximation of the Langevin diffusion model. In a series of simulation studies, we showed that our approach effectively removed the bias under various scenarios. We found that the precision of the estimated habitat coefficients increased for data spanning a longer duration at a lower frequency than for shorter, more frequently sampled tracks. This suggests that the model may be well suited for modelling tracking data sampled at a coarser resolution, as is common in datasets collected with older generations of animal tags. We illustrated the application of our model using tracking data from Steller sea lions, \textit{Eumetopias jubatus}. We found that the coefficient estimates converged to values significantly different than those estimated in previous studies, suggesting that bias in conventional estimation methods may meaningfully affect ecological conclusions about habitat preference. Together, these improvements broaden the applicability of Langevin diffusion models, thereby improving ecological insight into habitat selection.

stat.ME↗

arXiv2026

Spectral approximation of a new class of stochastic fractional evolution equations

A method for numerical approximation of a new class of fractional parabolic stochastic evolution equations is introduced and analysed. This class of equations has recently been proposed as a space-time extension of the SPDE-method in spatial statistics. A truncation of the spectral basis function expansion is used to discretise in space, and then a quadrature is used to approximate the temporal evolution of each basis coefficient. Strong error bounds are proved both for the spectral and temporal approximations. The method is tested and the results are verified by several numerical experiments.

math.NA↗