Related papers: Likelihood-based inference, identifiability and pr…

Automated model discovery of partial differential equations (PDEs) usually considers a single experiment or dataset to infer the underlying governing equations. In practice, experiments have inherent natural variability in parameters,…

This paper introduces a novel approach to quantifying ecological resilience in biological systems, particularly focusing on noisy systems responding to episodic disturbances with sudden adaptations. Incorporating concepts from…

Reliability analysis aims at estimating the failure probability of an engineering system. It often requires multiple runs of a limit-state function, which usually relies on computationally intensive simulations. Traditionally, these…

Transport-dominated partial differential equation models have been used extensively over the past two decades to describe various collective migration phenomena in cell biology and ecology. To understand the behaviour of these models (and…

The employment of nonlocal PDE models to describe biological aggregation and other phenomena has gained considerable traction in recent years. For cell populations, these methods grant a means of accommodating essential elements such as…

Statistical inference in high dimensional settings has recently attracted enormous attention within the literature. However, most published work focuses on the parametric linear regression problem. This paper considers an important…

Calibrating mathematical models of biological processes is essential for achieving predictive accuracy and gaining mechanistic insight. However, this task remains challenging due to limited and noisy data, significant biological…

Time-varying linear state-space models are powerful tools for obtaining mathematically interpretable representations of neural signals. For example, switching and decomposed models describe complex systems using latent variables that evolve…

Studying the development of malignant tumours, it is important to know and predict the proportions of different cell types in tissue samples. Knowing the expected temporal evolution of the proportion of normal tissue cells, compared to…

Many systems in physics, engineering, and biology exhibit multiscale stochastic dynamics, where low-dimensional slow variables evolve under the influence of high-dimensional fast processes. In practice, observations are often limited to a…

We provide a review of recent advancements in nonlocal continuous models for migration, mainly from the perspective of its involvement in embryonal development and cancer invasion. Particular emphasis is placed on spatial nonlocality…

Autoregressive next-step prediction models have become the de-facto standard for building data-driven neural solvers to forecast time-dependent partial differential equations (PDEs). Denoise training that is closely related to diffusion…

Advances in experimental techniques allow the collection of high-resolution spatio-temporal data that track individual motile entities. These tracking data can be used to calibrate mathematical models describing the motility of individual…

Mathematical models of motility are often based on random-walk descriptions of discrete individuals that can move according to certain rules. It is usually the case that large masses concentrated in small regions of space have a great…

We consider Markov models of large-scale networks where nodes are characterized by their local behavior and by a mobility model over a two-dimensional lattice. By assuming random walk, we prove convergence to a system of partial…

Linear birth-and-death processes (LBDPs) are foundational stochastic models in population dynamics, evolutionary biology, and hematopoiesis. Estimating parameters from discretely observed data is computationally demanding due to irregular…

We consider the problem of making nonparametric inference in a class of multi-dimensional diffusions in divergence form, from low-frequency data. Statistical analysis in this setting is notoriously challenging due to the intractability of…

Generative models and those with computationally intractable likelihoods are widely used to describe complex systems in the natural sciences, social sciences, and engineering. Fitting these models to data requires likelihood-free inference…

Stochastic compartmental models are prevalent tools for describing disease spread, but inference under these models is challenging for many types of surveillance data when the marginal likelihood function becomes intractable due to missing…

Motivated by the need for rigorous and scalable evaluation of large language models, we study contextual preference inference for pairwise comparison functionals of context-dependent preference score functions across domains. Focusing on…