Related papers: Variational Bayes method for ordinary differential…

Objective: COVID-19 has spread worldwide and made a huge influence across the world. Modeling the infectious spread situation of COVID-19 is essential to understand the current condition and to formulate intervention measurements.…

The hazard function is central to the formulation of commonly used survival regression models such as the proportional hazards and accelerated failure time models. However, these models rely on a shared baseline hazard, which, when…

Recently, Gaussian processes have been used to model the vector field of continuous dynamical systems, referred to as GPODEs, which are characterized by a probabilistic ODE equation. Bayesian inference for these models has been extensively…

Most ordinary differential equation (ODE) models used to describe biological or physical systems must be solved approximately using numerical methods. Perniciously, even those solvers which seem sufficiently accurate for the forward…

We consider the utilization of a computational model to guide the optimal acquisition of experimental data to inform the stochastic description of model input parameters. Our formulation is based on the recently developed consistent…

Modern statistical applications involving large data sets have focused attention on statistical methodologies which are both efficient computationally and able to deal with the screening of large numbers of different candidate models. Here…

Parameter inference of dynamical systems is a challenging task faced by many researchers and practitioners across various fields. In many applications, it is common that only limited variables are observable. In this paper, we propose a…

The discovery of partial differential equations (PDEs) is a challenging task that involves both theoretical and empirical methods. Machine learning approaches have been developed and used to solve this problem; however, it is important to…

Genetic variations in the COVID-19 virus are one of the main causes of the COVID-19 pandemic outbreak in 2020 and 2021. In this article, we aim to introduce a new type of model, a system coupled with ordinary differential equations (ODEs),…

In this paper, we address the fundamental problem of line spectral estimation in a Bayesian framework. We target model order and parameter estimation via variational inference in a probabilistic model in which the frequencies are…

Ordinary differential equations (ODEs) are central to scientific modelling, but inferring their vector fields from noisy trajectories remains challenging. Current approaches such as symbolic regression, Gaussian process (GP) regression, and…

Stochastic differential equations (SDEs) are established tools to model physical phenomena whose dynamics are affected by random noise. By estimating parameters of an SDE intrinsic randomness of a system around its drift can be identified…

We address the problem of optimal experimental design (OED) for Bayesian nonlinear inverse problems governed by PDEs. The goal is to find a placement of sensors, at which experimental data are collected, so as to minimize the uncertainty in…

The hazard function represents one of the main quantities of interest in the analysis of survival data. We propose a general approach for parametrically modelling the dynamics of the hazard function using systems of autonomous ordinary…

Ordinary differential equation models have become a standard tool for the mechanistic description of biochemical processes. If parameters are inferred from experimental data, such mechanistic models can provide accurate predictions about…

It is well known that exact notions of model abstraction and reduction for dynamical systems may not be robust enough in practice because they are highly sensitive to the specific choice of parameters. In this paper we consider this problem…

Conditional density estimation (CDE) models can be useful for many statistical applications, especially because the full conditional density is estimated instead of traditional regression point estimates, revealing more information about…

Ordinary differential equations (ODE) are widely used for modeling in Systems Biology. As most commonly only some of the kinetic parameters are measurable or precisely known, parameter estimation techniques are applied to parametrize the…

In this paper, we propose a progressive Bayesian procedure, where the measurement information is continuously included into the given prior estimate (although we perform observations at discrete time steps). The key idea is to derive a…

We develop a variational Bayes approach for dynamic variable selection in high-dimensional regression models with time-varying parameters and predictors that exhibit a predefined group structure. Through comprehensive simulation studies, we…