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Dynamical modelling is central to many scientific domains, including pharmacometrics, systems biology, physiology, and epidemiology. In these settings, heterogeneity is often intrinsic: different subjects or units follow related but…
Ordinary differential equation (ODE) models are widely used to describe chemical or biological processes. This article considers the estimation and assessment of such models on the basis of time-course data. Due to experimental limitations,…
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…
We develop a Gaussian-process mixture model for heterogeneous treatment effect estimation that leverages the use of transformed outcomes. The approach we will present attempts to improve point estimation and uncertainty quantification…
Panel data involving longitudinal measurements of the same set of participants taken over multiple time points is common in studies to understand childhood development and disease modeling. Deep hybrid models that marry the predictive power…
Ordinary differential equations (ODEs) are a mathematical model used in many application areas such as climatology, bioinformatics, and chemical engineering with its intuitive appeal to modeling. Despite ODE's wide usage in modeling, the…
Stochastic differential equations (SDEs) provide a natural framework for modelling intrinsic stochasticity inherent in many continuous-time physical processes. When such processes are observed in multiple individuals or experimental units,…
Identification of parameters in ordinary differential equations (ODEs) is an important and challenging task when modeling dynamic systems in biomedical research and other scientific areas, especially with the presence of time-varying…
A key problem in computational biology is discovering the gene expression changes that regulate cell fate transitions, in which one cell type turns into another. However, each individual cell cannot be tracked longitudinally, and cells at…
Neural ordinary differential equations (NODE) have garnered significant attention for their design of continuous-depth neural networks and the ability to learn data/feature dynamics. However, for high-dimensional systems, estimating…
We focus on the problem of uncertainty informed allocation of medical resources (vaccines) to heterogeneous populations for managing epidemic spread. We tackle two related questions: (1) For a compartmental ordinary differential equation…
Statistical models can involve implicitly defined quantities, such as solutions to nonlinear ordinary differential equations (ODEs), that unavoidably need to be numerically approximated in order to evaluate the model. The approximation…
Recently, Neural Ordinary Differential Equations has emerged as a powerful framework for modeling physical simulations without explicitly defining the ODEs governing the system, but instead learning them via machine learning. However, the…
Ordinary differential equations (ODEs) are widely used to model biological, (bio-)chemical and technical processes. The parameters of these ODEs are often estimated from experimental data using ODE-constrained optimisation. This article…
Dynamic systems described by differential equations often involve feedback among system components. When there are time delays for components to sense and respond to feedback, delay differential equation (DDE) models are commonly used. This…
Objective Bayesian inference procedures are derived for the parameters of the multivariate random effects model generalized to elliptically contoured distributions. The posterior for the overall mean vector and the between-study covariance…
This paper presents an intrinsic approach for addressing control problems with systems governed by linear ordinary differential equations (ODEs). We use computer algebra to constrain a Gaussian Process on solutions of ODEs. We obtain…
Early phase, personalized dose-finding trials for combination therapies seek to identify patient-specific optimal biological dose (OBD) combinations, which are defined as safe dose combinations which maximize therapeutic benefit for a…
Identification of optimal dose combinations in early phase dose-finding trials is challenging, due to the trade-off between precisely estimating the many parameters required to flexibly model the possibly non-monotonic dose-response…
This paper introduces a novel hybrid model combining Partial Differential Equations (PDEs) and Ordinary Differential Equations (ODEs) to simulate infectious disease dynamics across geographic regions. By leveraging the spatial detail of…