Related papers: Dynamic survival analysis: modelling the hazard fu…
Predicting time-to-event outcomes when event times are interval censored is challenging because the exact event time is unobserved. Many existing survival analysis approaches for interval-censored data rely on strong model assumptions or…
Many scientific problems focus on observed patterns of change or on how to design a system to achieve particular dynamics. Those problems often require fitting differential equation models to target trajectories. Fitting such models can be…
We consider Bayesian nonparametric inference in the right-censoring survival model, where modeling is made at the level of the hazard rate. We derive posterior limiting distributions for linear functionals of the hazard, and then for `many'…
Accelerated life tests (ALTs) play a crucial role in reliability analyses, providing lifetime estimates of highly reliable products. Among ALTs, step-stress design increases the stress level at predefined times, while maintaining a constant…
Longitudinal biomedical data are often characterized by a sparse time grid and individual-specific development patterns. Specifically, in epidemiological cohort studies and clinical registries we are facing the question of what can be…
We consider time series data modeled by ordinary differential equations (ODEs), widespread models in physics, chemistry, biology and science in general. The sensitivity analysis of such dynamical systems usually requires calculation of…
Statistical estimation and inference for marginal hazard models with varying coefficients for multivariate failure time data are important subjects in survival analysis. A local pseudo-partial likelihood procedure is proposed for estimating…
Ordinary differential equations (ODEs) are widely used to describe dynamical systems in science, but identifying parameters that explain experimental measurements is challenging. In particular, although ODEs are differentiable and would…
Natural laws are often described through differential equations yet finding a differential equation that describes the governing law underlying observed data is a challenging and still mostly manual task. In this paper we make a step…
We introduce a general, flexible, parametric survival modelling framework which encompasses key shapes of hazard function (constant, increasing, decreasing, up-then-down, down-then-up), various common survival distributions (log-logistic,…
A framework for risk-averse optimization problems is introduced that is resilient to ambiguities in the true form of the underlying probability distribution. The focus is on problems with partial differential equations (PDEs) as…
Machines of all kinds from vehicles to industrial equipment are increasingly instrumented with hundreds of sensors. Using such data to detect anomalous behaviour is critical for safety and efficient maintenance. However, anomalies occur…
We describe a method for the identification of models for dynamical systems from observational data. The method is based on the concept of symbolic regression and uses genetic programming to evolve a system of ordinary differential…
We discuss causal mediation analyses for survival data and propose a new approach based on the additive hazards model. The emphasis is on a dynamic point of view, that is, understanding how the direct and indirect effects develop over time.…
An important issue in survival analysis is the investigation and the modeling of hazard rates. Within a Bayesian nonparametric framework, a natural and popular approach is to model hazard rates as kernel mixtures with respect to a…
This paper introduces a general framework for analyzing recurrent event data by modeling the conditional mean function of the recurrent event process as the solution to an Ordinary Differential Equation (ODE). This approach not only…
This thesis develops a new framework for modelling price processes in finance, such as an equity price or foreign exchange rate. This can be related to the conventional Ito calculus-based framework through the time integral of a price's…
We propose a new method to ensure neural ordinary differential equations (ODEs) satisfy output specifications by using invariance set propagation. Our approach uses a class of control barrier functions to transform output specifications…
Unobserved individual heterogeneity is a common challenge in population cancer survival studies. This heterogeneity is usually associated with the combination of model misspecification and the failure to record truly relevant variables. We…
There are some real life issues that are exists in nature which has early failure. This type of problems can be modelled either by a complex distribution having more than one parameter or by finite mixture of some distribution. In this…