相关论文: Dynamic survival analysis: modelling the hazard fu…

By interpreting the forward dynamics of the latent representation of neural networks as an ordinary differential equation, Neural Ordinary Differential Equation (Neural ODE) emerged as an effective framework for modeling a system dynamics…

Mechanistic dynamic models of biochemical networks such as Ordinary Differential Equations (ODEs) contain unknown parameters like the reaction rate constants and the initial concentrations of the compounds. The large number of parameters as…

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…

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…

Traditional survival models often rely on restrictive assumptions such as proportional hazards or instantaneous effects of time-varying covariates on the hazard function, which limit their applicability in real-world settings. We consider…

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 introduce a numerically tractable formulation of Bayesian joint models for longitudinal and survival data. The longitudinal process is modelled using generalised linear mixed models, while the survival process is modelled using a…

Inferring the parameters of ordinary differential equations (ODEs) from noisy observations is an important problem in many scientific fields. Currently, most parameter estimation methods that bypass numerical integration tend to rely on…

Regular and rapid variation have been extensively studied in the literature and applied across various fields, particularly in extreme value theory. In this paper, we examine regular and rapid variation through the lens of generalized…

Statistical regression models whose mean functions are represented by ordinary differential equations (ODEs) can be used to describe phenomenons dynamical in nature, which are abundant in areas such as biology, climatology and genetics. The…

Neural ordinary differential equations (Neural ODEs) is a class of machine learning models that approximate the time derivative of hidden states using a neural network. They are powerful tools for modeling continuous-time dynamical systems,…

The order/dimension of models derived on the basis of data is commonly restricted by the number of observations, or in the context of monitored systems, sensing nodes. This is particularly true for structural systems (e.g., civil or…

Ordinary differential equations (ODEs) are widely used to model dynamical behavior of systems. It is important to perform identifiability analysis prior to estimating unknown parameters in ODEs (a.k.a. inverse problem), because if a system…

Autonomous vehicles (AV) look set to become common on our roads within the next few years. However, to achieve the final breakthrough, not only functional progress is required, but also satisfactory safety assurance must be provided. Among…

Survival analysis, or time-to-event modelling, is a classical statistical problem that has garnered a lot of interest for its practical use in epidemiology, demographics or actuarial sciences. Recent advances on the subject from the point…

Survival Analysis (SA) constitutes the default method for time-to-event modeling due to its ability to estimate event probabilities of sparsely occurring events over time. In this work, we show how to improve the training and inference of…

The Proportional Hazards (PH) model is one of the most widely used models in survival analysis, typically assuming a log-linear relationship between covariates and the hazard function. However, in the context of spatial survival data, where…

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…

In this paper, we model dependence between operational risks by allowing risk profiles to evolve stochastically in time and to be dependent. This allows for a flexible correlation structure where the dependence between frequencies of…

Ordinary differential equations (ODEs) are used to model dynamic systems appearing in engineering, physics, biomedical sciences and many other fields. These equations contain unknown parameters, say $\theta$ of physical significance which…