English
Related papers

Related papers: Structural identifiability analysis of PDEs: A cas…

200 papers

Practical identifiability is a critical concern in data-driven modeling of mathematical systems. In this paper, we propose a novel framework for practical identifiability analysis to evaluate parameter identifiability in mathematical models…

Quantitative Methods · Quantitative Biology 2026-01-06 Shun Wang , Wenrui Hao

Identifiability is a desirable property of a statistical model: it implies that the true model parameters may be estimated to any desired precision, given sufficient computational resources and data. We study identifiability in the context…

Machine Learning · Statistics 2020-07-09 Geoffrey Roeder , Luke Metz , Diederik P. Kingma

Modern data analysis depends increasingly on estimating models via flexible high-dimensional or nonparametric machine learning methods, where the identification of structural parameters is often challenging and untestable. In linear…

Statistics Theory · Mathematics 2026-01-21 Andrii Babii , Jean-Pierre Florens

Regression models with functional responses and covariates constitute a powerful and increasingly important model class. However, regression with functional data poses well known and challenging problems of non-identifiability. This…

Methodology · Statistics 2016-02-22 Fabian Scheipl , Sonja Greven

Methods of causal discovery aim to identify causal structures in a data driven way. Existing algorithms are known to be unstable and sensitive to statistical errors, and are therefore rarely used with biomedical or epidemiological data. We…

Methodology · Statistics 2024-07-01 Christine W Bang , Janine Witte , Ronja Foraita , Vanessa Didelez

Modeling sequential patterns from data is at the core of various time series forecasting tasks. Deep learning models have greatly outperformed many traditional models, but these black-box models generally lack explainability in prediction…

Machine Learning · Computer Science 2023-05-23 Yingtao Luo , Chang Xu , Yang Liu , Weiqing Liu , Shun Zheng , Jiang Bian

A new age-structured diffusive model for the mathematical modelling of epidemics is suggested. The model can be considered as a generalization of two models suggested earlier for the same purposes. The Lie symmetry classification of the…

Populations and Evolution · Quantitative Biology 2025-07-31 Roman Cherniha , Vasyl' Davydovych

We propose a versatile framework for survival analysis that combines advanced concepts from statistics with deep learning. The presented framework is based on piecewise exponential models and thereby supports various survival tasks, such as…

Machine Learning · Computer Science 2021-03-02 Philipp Kopper , Sebastian Pölsterl , Christian Wachinger , Bernd Bischl , Andreas Bender , David Rügamer

A fundamental challenge of scientific research is inferring causal relations based on observed data. One commonly used approach involves utilizing structural causal models that postulate noisy functional relations among interacting…

Methodology · Statistics 2024-08-13 David Strieder , Mathias Drton

In this paper, we propose a data-driven method to learn interpretable topological features of biomolecular data and demonstrate the efficacy of parsimonious models trained on topological features in predicting the stability of synthetic…

Machine Learning · Statistics 2024-08-12 Amish Mishra , Francis Motta

Recent outbreaks of monkeypox and Ebola, and worrying waves of COVID-19, influenza and respiratory syncytial virus, have all led to a sharp increase in the use of epidemiological models to estimate key epidemiological parameters. The…

Populations and Evolution · Quantitative Biology 2023-12-01 B. K. M. Case , Jean-Gabriel Young , Laurent Hébert-Dufresne

As data from monitored structures become increasingly available, the demand grows for it to be used efficiently to add value to structural operation and management. One way in which this can be achieved is to use structural response…

Applications · Statistics 2025-05-14 Nicholas E. Silionis , Konstantinos N. Anyfantis

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…

Dynamical Systems · Mathematics 2025-11-18 Kristina Kehrer , Martin Weiser , Tim Conrad

Combining additive models and neural networks allows to broaden the scope of statistical regression and extend deep learning-based approaches by interpretable structured additive predictors at the same time. Existing attempts uniting the…

Machine Learning · Statistics 2022-07-12 David Rügamer , Chris Kolb , Nadja Klein

Current concerns regarding the dependability of psychological findings call for methodological developments to provide additional evidence in support of scientific conclusions. This paper highlights the value and importance of two distinct…

Methodology · Statistics 2017-07-11 Jolynn Pek , Hao Wu

Machine Learning explainability techniques have been proposed as a means of `explaining' or interrogating a model in order to understand why a particular decision or prediction has been made. Such an ability is especially important at a…

Machine Learning · Statistics 2022-02-28 Matthew J. Vowels

Recently, we have shown that the age-specific prevalence of a disease can be related to the transition rates in the illness-death model via a partial differential equation (PDE). In case of a chronic disease, we show that the PDE can be…

Populations and Evolution · Quantitative Biology 2017-12-29 Ralph Brinks

The illness-death model of a chronic disease consists of the states 'Normal', 'Disease' and 'Death'. In general, the transition rates between the states depend on three time scales: calendar time, age and duration of the chronic disease.…

Populations and Evolution · Quantitative Biology 2013-08-30 Ralph Brinks

This paper establishes fundamental results for statistical inference of diagnostic classification models (DCM). The results are developed at a high level of generality, applicable to essentially all diagnostic classification models. In…

Statistics Theory · Mathematics 2025-01-08 Guanhua Fang , Jingchen Liu , Zhiliang Ying

Clinical decisions are high-stakes and require explicit justification, making model interpretability essential for auditing deep clinical models prior to deployment. As the ecosystem of model architectures and explainability methods…

Machine Learning · Computer Science 2026-03-27 Yongda Fan , John Wu , Andrea Fitzpatrick , Naveen Baskaran , Jimeng Sun , Adam Cross