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Mathematical models of real life phenomena are highly nonlinear involving multiple parameters and often exhibiting complex dynamics. Experimental data sets are typically small and noisy, rendering estimation of parameters from such data…

Uncertainty propagation in high-dimensional nonlinear dynamic structural systems is pivotal in state-of-the-art performance-based design and risk assessment, where uncertainties from both excitations and structures, i.e., the aleatoric…

Robust physics (e.g., governing equations and laws) discovery is of great interest for many engineering fields and explainable machine learning. A critical challenge compared with general training is that the term and format of governing…

Wave transport devices, such as amplifiers, frequency converters, and nonreciprocal devices, are essential for modern communication, signal processing, and sensing applications. Of particular interest are traveling wave setups, which offer…

Mathematical models are invaluable for understanding and predicting how biological systems behave, although their construction requires specifying mechanisms and relationships that are often not perfectly known. In the presence of multiple…

Many important stochastic counting models can be written as general birth-death processes (BDPs). BDPs are continuous-time Markov chains on the non-negative integers and can be used to easily parameterize a rich variety of probability…

We propose a new parameter-adaptive uncertainty-penalized Bayesian information criterion (UBIC) to prioritize the parsimonious partial differential equation (PDE) that sufficiently governs noisy spatial-temporal observed data with few…

We investigate statistical properties of a likelihood approach to nonparametric estimation of a singular distribution using deep generative models. More specifically, a deep generative model is used to model high-dimensional data that are…

We propose a methodology for modeling and comparing probability distributions within a Bayesian nonparametric framework. Building on dependent normalized random measures, we consider a prior distribution for a collection of discrete random…

Microbial ecology serves as a foundation for a wide range of scientific and biomedical studies. Rapidly-evolving high-throughput sequencing technology enables the comprehensive search for microbial biomarkers using longitudinal experiments.…

Ordinary differential equation (ODE) models are widely used to describe systems in many areas of science. To ensure these models provide accurate and interpretable representations of real-world dynamics, it is often necessary to infer…

Measuring the growth rate of large-scale structures (f) as a function of redshift has the potential to break degeneracies between modified gravity and dark energy models, when combined with expansion-rate probes. Direct estimates of…

Inferring parameters of models of biochemical kinetics from single-cell data remains challenging because of the uncertainty arising from the intractability of the likelihood function of stochastic reaction networks. Such uncertainty falls…

A key goal of systems biology is the predictive mathematical description of gene regulatory circuits. Different approaches are used such as deterministic and stochastic models, models that describe cell growth and division explicitly or…

Likelihood-free Bayesian inference algorithms are popular methods for calibrating the parameters of complex, stochastic models, required when the likelihood of the observed data is intractable. These algorithms characteristically rely…

The increasing integration of intermittent renewable generation, especially at the distribution level,necessitates advanced planning and optimisation methodologies contingent on the knowledge of thegrid, specifically the admittance matrix…

The inclusion of cognitive processes, such as perception, learning and memory, are inevitable in mechanistic animal movement modelling. Cognition is the unique feature that distinguishes animal movement from mere particle movement in…

The development of statistical approaches for the joint modelling of the temporal changes of imaging, biochemical, and clinical biomarkers is of paramount importance for improving the understanding of neurodegenerative disorders, and for…

Certifiable, adaptive uncertainty estimates for unknown quantities are an essential ingredient of sequential decision-making algorithms. Standard approaches rely on problem-dependent concentration results and are limited to a specific…

Count outcomes in longitudinal studies are frequent in clinical and engineering studies. In frequentist and Bayesian statistical analysis, methods such as Mixed linear models allow the variability or correlation within individuals to be…