Related papers: Structured methods for parameter inference and unc…

Linear causal models are important tools for modeling causal dependencies and yet in practice, only a subset of the variables can be observed. In this paper, we examine the parameter identifiability of these models by investigating whether…

Constitutive model discovery refers to the task of identifying an appropriate model structure, usually from a predefined model library, while simultaneously inferring its material parameters. The data used for model discovery are measured…

Scientists use mathematical modelling to understand and predict the properties of complex physical systems. In highly parameterised models there often exist relationships between parameters over which model predictions are identical, or…

Probabilistic graphical models are a fundamental tool in probabilistic modeling, machine learning and artificial intelligence. They allow us to integrate in a natural way expert knowledge, physical modeling, heterogeneous and correlated…

When employing mechanistic models to study biological phenomena, practical parameter identifiability is important for making accurate predictions across wide range of unseen scenarios, as well as for understanding the underlying mechanisms.…

In the presence of modeling errors, the mainstream Bayesian methods seldom give a realistic account of uncertainties as they commonly underestimate the inherent variability of parameters. This problem is not due to any misconception in the…

The modeling and uncertainty quantification of closed curves is an important problem in the field of shape analysis, and can have significant ramifications for subsequent statistical tasks. Many of these tasks involve collections of closed…

Advances in architectural design, data availability, and compute have driven remarkable progress in semantic segmentation. Yet, these models often rely on relaxed Bayesian assumptions, omitting critical uncertainty information needed for…

We explore the application of uncertainty quantification methods to agent-based models (ABMs) using a simple sheep and wolf predator-prey model. This work serves as a tutorial on how techniques like emulation can be powerful tools in this…

Probabilistic programming has emerged as a powerful paradigm in statistics, applied science, and machine learning: by decoupling modelling from inference, it promises to allow modellers to directly reason about the processes generating…

Nonlinear dynamic models are widely used for characterizing functional forms of processes that govern complex biological pathway systems. Over the past decade, validation and further development of these models became possible due to data…

Mathematical models simulate various events under different conditions, enabling an early overview of the system to be implemented in practice, reducing the waste of resources and in less time. In project optimization, these models play a…

The comprehensive integration of machine learning healthcare models within clinical practice remains suboptimal, notwithstanding the proliferation of high-performing solutions reported in the literature. A predominant factor hindering…

Dynamical systems modeling, particularly via systems of ordinary differential equations, has been used to effectively capture the temporal behavior of different biochemical components in signal transduction networks. Despite the recent…

We present a simple comparative framework for testing and developing uncertainty modeling in uncertain marching cubes implementations. The selection of a model to represent the probability distribution of uncertain values directly…

Identifiability is a necessary condition for successful parameter estimation of dynamic system models. A major component of identifiability analysis is determining the identifiable parameter combinations, the functional forms for the…

Methods for model parameter estimation, uncertainty quantification and experimental design are summarized in this paper. They are based on the generalized least squares estimator and different approximations of its covariance matrix using…

Linear mixed-effects models are widely used in analyzing clustered or repeated measures data. We propose a quasi-likelihood approach for estimation and inference of the unknown parameters in linear mixed-effects models with high-dimensional…

Statistical models typically capture uncertainties in our knowledge of the corresponding real-world processes, however, it is less common for this uncertainty specification to capture uncertainty surrounding the values of the inputs to the…

Modeling biological processes is a highly demanding task because not all processes are fully understood. Mathematical models allow us to test hypotheses about possible mechanisms of biological processes. The mathematical mechanisms…