arXiv subjects

Susanne Ditlevsen

Publications and source records attributed to Susanne Ditlevsen.

At least 19 recordsLinked to original sources

arXiv2026

Early Warning Signals Can Vanish or Amplify: Dimensionality in Complex Systems

Early warning signals (EWS), such as increasing variance and autocorrelation, are widely used to anticipate critical transitions associated with saddle-node bifurcations. However, real-world systems are often high-dimensional and multiscale, potentially altering the classical behavior of EWS. Here, we investigate how dimensionality, inertia, and red noise influence the detectability of EWS prior to tipping points. We show that when observations are not aligned with the critical direction, stable dynamics in orthogonal directions can mask EWS until very near the bifurcation. We further demonstrate that second-order dynamics with damping modify the autocorrelation structure and may either enhance or reduce signatures of critical slowing down. Finally, we study how colored noise influences EWS. Our results show that the presence and strength of EWS are not universal properties of tipping systems but depend critically on system geometry and stochastic forcing, implying that the absence of detectable EWS does not necessarily rule out an approaching critical transition.

math.DS↗

arXiv2026

Choosing optimal Strang splitting estimators of nonlinear stochastic differential equation models

The Strang splitting estimator is a powerful estimator for parametric inference in multivariate stochastic differential equation models with nonlinear drift and additive noise. While the choice of splitting does not affect the asymptotic distribution of the estimator, it makes a huge impact in finite-sample settings and it has not yet been shown how the splitting can be chosen optimally. We derive error measures for the transition densities of the Strang splitting scheme, in particular calculating the bias up to the order of $h^3$, where $h$ is the length of the time step. We study the connection between these error measures and the performance of the Strang splitting estimator in the double-well potential model and the stochastic FitzHugh-Nagumo model, respectively. Our simulation studies suggest that linearization around fixed points yields accurate parameter estimates for potential models, while other splittings perform better for slow-fast excitable models.

stat.ME↗

arXiv2026

Strang splitting estimator for nonlinear multivariate stochastic differential equations with Pearson-type multiplicative noise

Multivariate Pearson diffusions are characterized by a linear drift and a diffusion matrix that is quadratic in the state variables. We derive closed-form expressions for the mean and covariance matrix of this class using matrix exponential integrals, and extend this framework to a broader class of nonlinear diffusions with Pearson-type multiplicative noise. The main contribution is a new parameter estimator for these nonlinear multiplicative models based on Strang splitting, which decomposes the stochastic system into a deterministic nonlinear ordinary differential equation and a multivariate Pearson diffusion. The estimator is constructed by composing their respective flows and applying a Gaussian transition approximation with exact moments from the Pearson component. We prove that the estimator is consistent and asymptotically efficient. We also introduce a new model within this class, the Student Kramers oscillator, and prove existence and uniqueness of the strong solution and of an invariant measure. We evaluate the estimator through simulation studies on this oscillator and on the multivariate Wright-Fisher diffusion from population genetics, where it outperforms the Euler-Maruyama, Gaussian approximation, and local linearization estimators. We conclude with an application to Greenland ice core data using the Student Kramers oscillator.

stat.ME↗

arXiv2026

Fast Sampling for Flows and Diffusions with Lazy and Point Mass Stochastic Interpolants

Stochastic interpolants unify flows and diffusions, popular generative modeling frameworks. A primary hyperparameter in these methods is the interpolation schedule that determines how to bridge a standard Gaussian base measure to an arbitrary target measure. We prove how to convert a sample path of a stochastic differential equation (SDE) with arbitrary diffusion coefficient under any schedule into the unique sample path under another arbitrary schedule and diffusion coefficient. We then extend the stochastic interpolant framework to admit a larger class of point mass schedules in which the Gaussian base measure collapses to a point mass measure. Under the assumption of Gaussian data, we identify lazy schedule families that make the drift identically zero and show that with deterministic sampling one gets a variance-preserving schedule commonly used in diffusion models, whereas with statistically optimal SDE sampling one gets our point mass schedule. Finally, to demonstrate the usefulness of our theoretical results on realistic highly non-Gaussian data, we apply our lazy schedule conversion to a state-of-the-art pretrained flow model and show that this allows for generating images in fewer steps without retraining the model.

stat.ML↗

arXiv2025

Spatial constraints improve filtering of measurement noise from animal tracks

Advances in tracking technologies for animal movement require new statistical tools to better exploit the increasing amount of data. Animal positions are usually calculated using the GPS or Argos satellite system and include potentially non-Gaussian and heavy-tailed measurement error patterns. Errors are usually handled through a Kalman filter algorithm, which can be sensitive to non-Gaussian error distributions. We introduce a latent movement model through an underdamped Langevin stochastic differential equation (SDE) that includes an additional drift term to ensure that the animal remains in a known spatial domain of interest. This can be applied to aquatic animals moving in water or terrestrial animals moving in a restricted zone delimited by fences or natural barriers. We demonstrate that the incorporation of these spatial constraints into the latent movement model can improve the accuracy of filtering for noisy observations of the positions. We implement an Extended Kalman Filter as well as a particle filter adapted to non-Gaussian error distributions. Our filters are based on solving the SDE through splitting schemes to approximate the latent dynamic. We illustrate the approach on a real Argos telemetry track of a bowhead whale in Foxe Basin, Canada.

stat.AP↗

arXiv2025

Robust Parameter Estimation in Dynamical Systems by Stochastic Differential Equations

Ordinary and stochastic differential equations (ODEs and SDEs) are widely used to model continuous-time processes across various scientific fields. While ODEs offer interpretability and simplicity, SDEs incorporate randomness, providing robustness to noise and model misspecifications. Recent research highlights the statistical advantages of SDEs, such as improved parameter identifiability and stability under perturbations. This paper investigates the robustness of parameter estimation in SDEs versus ODEs under three types of model misspecifications: unrecognized noise sources, external perturbations, and simplified models. Furthermore, the effect of missing data is explored. Through simulations and an analysis of Danish COVID-19 data, we demonstrate that SDEs yield more stable and reliable parameter estimates, making them a strong alternative to traditional ODE modeling in the presence of uncertainty.

stat.ME↗

arXiv2024

A time warping model for seasonal data with application to age estimation from narwhal tusks

Signals with varying periodicity frequently appear in real-world phenomena, necessitating the development of efficient modelling techniques to map the measured nonlinear timeline to linear time. Here we propose a regression model that allows for a representation of periodic and dynamic patterns observed in time series data. The model incorporates a hidden strictly positive stochastic process that represents the instantaneous frequency, allowing the model to adapt and accurately capture varying time scales. A case study focusing on age estimation of narwhal tusks is presented, where cyclic element signals associated with annual growth layer groups are analyzed. We apply the methodology to data from one such tusk collected in West Greenland and use the fitted model to estimate the age of the narwhal. The proposed method is validated using simulated signals with known cycle counts and practical considerations and modelling challenges are discussed in detail. This research contributes to the field of time series analysis, providing a tool and valuable insights for understanding and modeling complex cyclic patterns in diverse domains.

stat.AP↗

arXiv2024

Varying coefficients correlated velocity models in complex landscapes with boundaries applied to narwhal responses to noise exposure

Narwhals in the Arctic are increasingly exposed to human activities that can temporarily or permanently threaten their survival by modifying their behavior. We examine GPS data from a population of narwhals exposed to ship and seismic airgun noise during a controlled experiment in 2018 in the Scoresby Sound fjord system in Southeast Greenland. The fjord system has a complex shore line, restricting the behavioral response options for the narwhals to escape the threats. We propose a new continuous-time correlated velocity model with varying coefficients that includes spatial constraints on movement. To assess the sound exposure effect we compare a baseline model for the movement before exposure to a response model for the movement during exposure. Our model, applied to the narwhal data, suggests increased tortuosity of the trajectories as a consequence of the spatial constraints, and further indicates that sound exposure can disturb narwhal motion up to a couple of tens of kilometers. Specifically, we found an increase in velocity and a decrease in the movement persistence.

stat.AP↗

arXiv2024

Strang Splitting for Parametric Inference in Second-order Stochastic Differential Equations

We address parameter estimation in second-order stochastic differential equations (SDEs), which are prevalent in physics, biology, and ecology. The second-order SDE is converted to a first-order system by introducing an auxiliary velocity variable, which raises two main challenges. First, the system is hypoelliptic since the noise affects only the velocity, making the Euler-Maruyama estimator ill-conditioned. We propose an estimator based on the Strang splitting scheme to overcome this. Second, since the velocity is rarely observed, we adapt the estimator to partial observations. We present four estimators for complete and partial observations, using the full pseudo-likelihood or only the velocity-based partial pseudo-likelihood. These estimators are intuitive, easy to implement, and computationally fast, and we prove their consistency and asymptotic normality. Our analysis demonstrates that using the full pseudo-likelihood with complete observations reduces the asymptotic variance of the diffusion estimator. With partial observations, the asymptotic variance increases as a result of information loss but remains unaffected by the likelihood choice. However, a numerical study on the Kramers oscillator reveals that using the partial pseudo-likelihood for partial observations yields less biased estimators. We apply our approach to paleoclimate data from the Greenland ice core by fitting the Kramers oscillator model, capturing transitions between metastable states reflecting observed climatic conditions during glacial eras.

stat.ME↗

arXiv2023

Network inference via approximate Bayesian computation. Illustration on a stochastic multi-population neural mass model

In this article, we propose an adapted sequential Monte Carlo approximate Bayesian computation (SMC-ABC) algorithm for network inference in coupled stochastic differential equations (SDEs) used for multivariate time series modeling. Our approach is motivated by neuroscience, specifically the challenge of estimating brain connectivity before and during epileptic seizures. To this end, we make four key contributions. First, we introduce a 6N-dimensional SDE to model the activity of N coupled neuronal populations, extending the (single-population) stochastic Jansen and Rit neural mass model used to describe human electroencephalography (EEG) rhythms, particularly epileptic activity. Second, we construct a reliable and efficient numerical splitting scheme for the model simulation. Third, we apply the proposed adapted SMC-ABC algorithm to the neural mass model and validate it on different types of simulated data. Compared to standard SMC-ABC, our approach significantly reduces computational cost by requiring fewer model simulations to reach the desired posterior region, thanks to the inclusion of binary parameters describing the presence or absence of coupling directions. Finally, we apply our method to real multi-channel EEG data, uncovering potential similarities in patients' brain activities across different epileptic seizures, as well as differences between pre-seizure and seizure periods.

stat.ME↗

arXiv2023

Uniform Inference for Cointegrated Vector Autoregressive Processes

Uniformly valid inference for cointegrated vector autoregressive processes has so far proven difficult due to certain discontinuities arising in the asymptotic distribution of the least squares estimator. We extend asymptotic results from the univariate case to multiple dimensions and show how inference can be based on these results. Furthermore, we show that lag augmentation and a recent instrumental variable procedure can also yield uniformly valid tests and confidence regions. We verify the theoretical findings and investigate finite sample properties in simulation experiments for two specific examples.

math.ST↗

arXiv2023

Warning of a forthcoming collapse of the Atlantic meridional overturning circulation

Tipping to an undesired state in the climate when a control parameter slowly approaches a critical value is a growing concern with increasing greenhouse gas concentrations. Predictions rely on detecting early warning signals (EWSs) in observations of the system. The primary EWSs are increase in variance, (loss of resilience), and increased autocorrelation (critical slow down). These measures are statistical in nature, which implies that the reliability and statistical significance of the detection depends on the sample size in observations and the magnitude of the change away from the base value prior to the approach to the tipping point. Thus, the possibility of providing useful early warning depends on the relative magnitude of several interdependent time scales in the system. These are (a) the time before the critical value is reached, (b) the (inverse) rate of approach to the tipping point, (c) the size of the time window required to detect a significant change in the EWS and finally, (d) the escape time for noise-induced transition (prior to the tipping). Conditions for early warning of tipping of the Atlantic meridional overturning circulation (AMOC) are marginally fulfilled for the existing past $\sim$150 years of proxy observations where indicators of tipping have recently been reported. Here we provide statistical significance and data driven estimators for the time of tipping. We estimate a collapse of the AMOC to occur around the year 2057 under the assumption of a "business as usual" scenario of future emissions.

physics.ao-ph↗

arXiv2022

Parameter Estimation in Nonlinear Multivariate Stochastic Differential Equations Based on Splitting Schemes

The likelihood functions for discretely observed nonlinear continuous-time models based on stochastic differential equations are not available except for a few cases. Various parameter estimation techniques have been proposed, each with advantages, disadvantages, and limitations depending on the application. Most applications still use the Euler-Maruyama discretization, despite many proofs of its bias. More sophisticated methods, such as Kessler's Gaussian approximation, Ozaki's Local Linearization, A\"it-Sahalia's Hermite expansions, or MCMC methods, might be complex to implement, do not scale well with increasing model dimension, or can be numerically unstable. We propose two efficient and easy-to-implement likelihood-based estimators based on the Lie-Trotter (LT) and the Strang (S) splitting schemes. We prove that S has $L^p$ convergence rate of order 1, a property already known for LT. We show that the estimators are consistent and asymptotically efficient under the less restrictive one-sided Lipschitz assumption. A numerical study on the 3-dimensional stochastic Lorenz system complements our theoretical findings. The simulation shows that the S estimator performs the best when measured on precision and computational speed compared to the state-of-the-art.

stat.ME↗

arXiv2022

High-dimensional cointegration and Kuramoto systems

This paper presents a novel estimator for a non-standard restriction to both symmetry and low rank in the context of high dimensional cointegrated processes. Furthermore, we discuss rank estimation for high dimensional cointegrated processes by restricted bootstrapping of the Gaussian innovations. We demonstrate that the classical rank test for cointegrated systems is prone to underestimate the true rank and demonstrate this effect in a 100 dimensional system. We also discuss the implications of this underestimation for such high dimensional systems in general. Also, we define a linearized Kuramoto system and present a simulation study, where we infer the cointegration rank of the unrestricted $p\times p$ system and successively the underlying clustered network structure based on a graphical approach and a symmetrized low rank estimator of the couplings derived from a reparametrization of the likelihood under this unusual restriction.

stat.ME↗

arXiv2022

Weighted Reduced Rank Estimators Under Cointegration Rank Uncertainty

Cointegration analysis was developed for non-stationary linear processes that exhibit stationary relationships between coordinates. Estimation of the cointegration relationships in a multi-dimensional cointegrated process typically proceeds in two steps. First the rank is estimated, then the cointegration matrix is estimated, conditionally on the estimated rank (reduced rank regression). The asymptotics of the estimator is usually derived under the assumption of knowing the true rank. In this paper, we quantify the asymptotic bias and find the asymptotic distributions of the cointegration estimator in case of misspecified rank. Furthermore, we suggest a new class of weighted reduced rank estimators that allow for more flexibility in settings where rank selection is hard. We show empirically that a proper choice of weights can lead to increased predictive performance when there is rank uncertainty. Finally, we illustrate the estimators on empirical EEG data from a psychological experiment on visual processing.

math.ST↗

arXiv2021

Detection of foraging behavior from accelerometer data using U-Net type convolutional networks

Narwhal is one of the most mysterious marine mammals, due to its isolated habitat in the Arctic region. Tagging is a technology that has the potential to explore the activities of this species, where behavioral information can be collected from instrumented individuals. This includes accelerometer data, diving and acoustic data as well as GPS positioning. An essential element in understanding the ecological role of toothed whales is to characterize their feeding behavior and estimate the amount of food consumption. Buzzes are sounds emitted by toothed whales that are related directly to the foraging behaviors. It is therefore of interest to measure or estimate the rate of buzzing to estimate prey intake. The main goal of this paper is to find a way to detect prey capture attempts directly from accelerometer data, and thus be able to estimate food consumption without the need for the more demanding acoustic data. We develop 3 automated buzz detection methods based on accelerometer and depth data solely. We use a dataset from 5 narwhals instrumented in East Greenland in 2018 to train, validate and test a logistic regression model and the machine learning algorithms random forest and deep learning, using the buzzes detected from acoustic data as the ground truth. The deep learning algorithm performed best among the tested methods. We conclude that reliable buzz detectors can be derived from high-frequency-sampling, back-mounted accelerometer tags, thus providing an alternative tool for studies of foraging ecology of marine mammals in their natural environments. We also compare buzz detection with certain movement patterns, such as sudden changes in acceleration (jerks), found in other marine mammal species for estimating prey capture. We find that narwhals do not seem to make big jerks when foraging and conclude that their hunting patterns in that respect differ from other marine mammals.

stat.AP↗

arXiv2019

Age Dependent Hawkes Process

In the last decade, Hawkes processes have received a lot of attention as good models for functional connectivity in neural spiking networks. In this paper we consider a variant of this process, the Age Dependent Hawkes process, which incorporates individual post-jump behaviour into the framework of the usual Hawkes model. This allows to model recovery properties such as refractory periods, where the effects of the network are momentarily being suppressed or altered. We show how classical stability results for Hawkes processes can be improved by introducing age into the system. In particular, we neither need to a priori bound the intensities nor to impose any conditions on the Lipschitz constants. When the interactions between neurons are of mean field type, we study large network limits and establish the propagation of chaos property of the system.

math.PR↗

arXiv2018

Hypoelliptic diffusions: discretization, filtering and inference from complete and partial observations

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.

stat.ME↗