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Ideally, a meta-analysis will summarize data from several unbiased studies. Here we consider the less than ideal situation in which contributing studies may be compromised by measurement error. Measurement error affects every study design,…

Construction of kinetic models has become an indispensable step in the development and scale up of processes in the industry. Model-based design of experiments (MBDoE) has been widely used for the purpose of improving parameter precision in…

Systems and Control · Electrical Eng. & Systems 2021-04-15 Panagiotis Petsagkourakis , Federico Galvanin

In this paper we consider the parameter estimation problem associated to partially-observed time changed SDEs, with observations that are given at discrete times. In particular we consider both likelihood and Bayesian estimation. We develop…

Numerical Analysis · Mathematics 2026-05-12 Ke Zhao , Ajay Jasra

Probabilistic ordinary differential equation (ODE) solvers have been introduced over the past decade as uncertainty-aware numerical integrators. They typically proceed by assuming a functional prior to the ODE solution, which is then…

Numerical Analysis · Mathematics 2025-03-25 Yvann Le Fay , Simo Särkkä , Adrien Corenflos

In this paper we study application of Le Cam's one-step method to parameter estimation in ordinary differential equations models. This computationally simple technique can serve as an alternative to numerical evaluation of the popular…

Methodology · Statistics 2018-04-20 Itai Dattner , Shota Gugushvili

Computer models are commonly used to represent a wide range of real systems, but they often involve some unknown parameters. Estimating the parameters by collecting physical data becomes essential in many scientific fields, ranging from…

Applications · Statistics 2020-05-27 Chih-Li Sung , Beau David Barber , Berkley J. Walker

Gaussian processes models are widely adopted for nonparameteric/semi-parametric modeling. Identifiability issues occur when the mean model contains polynomials with unknown coefficients. Though resulting prediction is unaffected, this leads…

Methodology · Statistics 2016-11-02 Matthew Plumlee , V. Roshan Joseph

1. Understanding the mechanisms underlying biological systems, and ultimately, predicting their behaviours in a changing environment requires overcoming the gap between mathematical models and experimental or observational data.…

Quantitative Methods · Quantitative Biology 2017-04-19 Philipp H Boersch-Supan , Sadie J Ryan , Leah R Johnson

In the usual Bayesian setting, a full probabilistic model is required to link the data and parameters, and the form of this model and the inference and prediction mechanisms are specified via de Finetti's representation. In general, such a…

Methodology · Statistics 2026-01-21 Yu Luo , David A. Stephens , Daniel J. Graham , Emma J. McCoy

This paper introduces an Ordinary Differential Equation (ODE) notion for survival analysis. The ODE notion not only provides a unified modeling framework, but more importantly, also enables the development of a widely applicable, scalable,…

Methodology · Statistics 2021-12-07 Weijing Tang , Kevin He , Gongjun Xu , Ji Zhu

The problem of detecting the Out-of-Distribution (OoD) inputs is of paramount importance for Deep Neural Networks. It has been previously shown that even Deep Generative Models that allow estimating the density of the inputs may not be…

Machine Learning · Statistics 2023-01-02 Misha Glazunov , Apostolis Zarras

Implicit sampling is a weighted sampling method that is used in data assimilation, where one sequentially updates estimates of the state of a stochastic model based on a stream of noisy or incomplete data. Here we describe how to use…

Numerical Analysis · Mathematics 2016-01-20 Matthias Morzfeld , Xuemin Tu , Jon Wilkening , Alexandre J. Chorin

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…

Machine Learning · Computer Science 2020-10-19 Daehoon Gwak , Gyuhyeon Sim , Michael Poli , Stefano Massaroli , Jaegul Choo , Edward Choi

In this paper we consider the estimation of unknown parameters in Bayesian inverse problems. In most cases of practical interest, there are several barriers to performing such estimation, This includes a numerical approximation of a…

Methodology · Statistics 2025-02-07 Neil K. Chada , Ajay Jasra , Mohamed Maama , Raul Tempone

In this article we consider Bayesian parameter inference associated to partially-observed stochastic processes that start from a set B0 and are stopped or killed at the first hitting time of a known set A. Such processes occur naturally…

Computation · Statistics 2012-01-19 Ajay Jasra , Nikolas Kantas

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…

Machine Learning · Computer Science 2026-05-14 Julien Martinelli , Maksim Sinelnikov , Harri Lähdesmäki , Quentin Clairon , Mélanie Prague

The recent advancements in mathematical modeling of biochemical systems have generated increased interest in sensitivity analysis methodologies. There are two primary approaches for analyzing these mathematical models: the stochastic…

Computation · Statistics 2025-10-14 Kannon Hossain , Roger Sidje , Fahad Mostafa

A novel probabilistic numerical method for quantifying the uncertainty induced by the time integration of ordinary differential equations (ODEs) is introduced. Departing from the classical strategy to randomize ODE solvers by adding a…

Numerical Analysis · Mathematics 2020-06-26 Assyr Abdulle , Giacomo Garegnani

Differential equations in general and neural ODEs in particular are an essential technique in continuous-time system identification. While many deterministic learning algorithms have been designed based on numerical integration via the…

Machine Learning · Computer Science 2021-10-18 Lenart Treven , Philippe Wenk , Florian Dörfler , Andreas Krause

High dimensional space-time data pose known computational challenges when fitting spatio-temporal models. Such data show dependence across several dimensions of space as well as in time, and can easily involve hundreds of thousands of…

Methodology · Statistics 2025-06-02 Staci Hepler , Rob Erhardt
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