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Animal telemetry data are often analysed with discrete time movement models assuming rotation in the movement. These models are defined with equidistant distant time steps. However, telemetry data from marine animals are observed…
We study the problem of tracking an object moving through a network of wireless sensors. In order to conserve energy, the sensors may be put into a sleep mode with a timer that determines their sleep duration. It is assumed that an asleep…
Understanding pedestrian behavior is crucial for the safe deployment of Autonomous Vehicles (AVs) in urban environments. Traditional pedestrian behavior models often fall into two categories: mechanistic models, which do not generalize well…
Modern canine applications span medical and service roles, while robotic legged dogs serve as autonomous platforms for high-risk industrial inspection, disaster response, and search and rescue operations. For both, accurate positioning…
The diversity of diffusive systems exhibiting long-range correlations characterized by a stochastically varying Hurst exponent calls for a generic multifractional model. We present a simple, analytically tractable model which fills the gap…
The analysis of animal tracking data provides an important source of scientific understanding and discovery in ecology. Observations of animal trajectories using telemetry devices provide researchers with information about the way animals…
Consider a Poisson process on $\mathbb{R}$ with intensity $f$ where $0 \leq f(x)<\infty$ for ${x}\geq 0$ and ${f(x)}=0$ for $x<0$. The "points" of the process represent sleeping frogs. In addition, there is one active frog initially located…
In empirical studies of random walks, continuous trajectories of animals or individuals are usually sampled over a finite number of points in space and time. It is however unclear how this partial observation affects the measured…
Passive and non-obtrusive health monitoring using wearables can potentially bring new insights into the user's health status throughout the day and may support clinical diagnosis and treatment. However, identifying segments of free-living…
New types of high-resolution animal movement data allow for increasingly comprehensive biological inference, but method development to meet the statistical challenges associated with such data is lagging behind. In this contribution, we…
Recent developments in automated tracking allow uninterrupted, high-resolution recording of animal trajectories, sometimes coupled with the identification of stereotyped changes of body pose or other behaviors of interest. Analysis and…
Improved communication systems, shrinking battery sizes and the price drop of tracking devices have led to an increasing availability of trajectory tracking data. These data are often analyzed to understand animal behavior. In this work, we…
Discrete-time random walks and their extensions are common tools for analyzing animal movement data. In these analyses, resolution of temporal discretization is a critical feature. Ideally, a model both mirrors the relevant temporal scale…
An innovative extension of Geometric Brownian Motion model is developed by incorporating a weighting factor and a stochastic function modelled as a mixture of power and trigonometric functions. Simulations based on this Modified Brownian…
Hidden Markov models (HMMs) are commonly used to model animal movement data and infer aspects of animal behavior. An HMM assumes that each data point from a time series of observations stems from one of $N$ possible states. The states are…
Human motion detection is getting considerable attention in the field of Artificial Intelligence (AI) driven healthcare systems. Human motion can be used to provide remote healthcare solutions for vulnerable people by identifying particular…
GPS technology is currently easily accessible to researchers, and many animal movement datasets are available. Two of the main features that a model which describes an animal's path can possess are directional persistence and attraction to…
A novel first-order autoregressive moving average model for analyzing discrete-time series observed at irregularly spaced times is introduced. Under Gaussianity, it is established that the model is strictly stationary and ergodic. In the…
The processes influencing animal movement and resource selection are complex and varied. Past efforts to model behavioral changes over time used Bayesian statistical models with variable parameter space, such as reversible-jump Markov chain…
We present a hidden Markov model that describes variation in an animal's position associated with varying levels of activity in action potential spike trains of individual place cell neurons. The model incorporates a coarse-graining of…