arXiv subjects

Christiane Fuchs

Publications and source records attributed to Christiane Fuchs.

9 recordsLinked to original sources

arXiv2026

Time-dependent structural equation modeling of fans' football fever using activity tracking data during the 2025 DFB Cup final

Football fans frequently exhibit pronounced emotional and physiological reactions during high-stakes matches. However, the temporal dynamics of this football fever are rarely modeled as a latent process. Using intensive longitudinal data from Arminia Bielefeld supporters who wore smartwatches during the 2025 German Football Association (DFB) Cup final, we investigate how football fever unfolds. The devices recorded heart rate, stress level, and related indicators in short intervals, allowing us to construct a latent variable for football fever and model its dynamics. We specify a time-dependent structural equation model with latent growth components and autoregressive effects to capture both overall trends and short-term carry-over effects in fans' physiological responses. Results are aggregated across multiple imputations of missing measurements. Model fit is evaluated using adjustments for the high data dimensionality. The results show that football fever follows a V-shaped trajectory: high at kick-off, followed by a steady decline until the renewed arousal in the second half, with substantial between-fan heterogeneity in both baseline level and temporal dynamics. Our findings demonstrate that football fever can be adequately represented as a latent variable using structural equation modeling and reflected by wearable technology data. This highlights the importance of accounting for temporal dependence when studying dynamic emotional phenomena, e. g., in sports spectatorship.

stat.AP↗

arXiv2026

Retrospective Economic Evaluation of Group Testing in the COVID-19 Pandemic

Surveillance of diseases in a pandemic is an important part of public health policy. Diagnostic testing at the individual level is often infeasible due to resource constraints. To circumvent these constraints, group testing can be applied. The economic cost evaluation from the payer's perspective typically focuses only on deterministic costs which overlooks the substantial economic impact of productivity losses resulting from quarantine and workplace disruptions. The objective of this article is to develop a mathematical model for a retrospective economic evaluation of group testing that incorporates both deterministic costs and income-based economic loss. Group testing algorithms are revisited and simulated at optimized pool sizes to determine the required number of tests. Income data from the German Socio-Economic Panel are integrated into a mathematical model to capture the economic loss. Afterward, hybrid Monte Carlo experiments are conducted by evaluating the economic cost in the Coronavirus disease 2019 pandemic in Germany. Monte Carlo experiments show that the optimal choice of group testing algorithms changes substantially when income-based economic losses are included. Evaluations considering only deterministic costs systematically underestimate the total economic cost. Algorithms with a longer quarantine duration are less attractive than shorter quarantine duration if income-based economic loss is accounted for. The findings show that current evaluations underestimate the true economic cost. Group testing algorithms with shorter duration and fewer stages are preferred, even when they require a larger number of tests. These results underscore the importance of incorporating income-based economic loss into a mathematical model.

stat.CO↗

arXiv2026

Dynamic modelling and evaluation of preclinical trials in acute leukaemia

Dynamic models are widely used to mathematically describe biological phenomena that evolve over time. One important area of application is leukaemia research, where leukaemia cells are genetically modified in preclinical studies to explore new therapeutic targets for reducing leukaemic burden. In advanced experiments, these studies are often conducted in mice and generate time-resolved data, the analysis of which may reveal growth-inhibiting effects of the investigated gene modifications. However, the experimental data is oftentimes evaluated using statistical tests which compare measurements from only two different time points. This approach does not only reduce the time series to two instances but also neglects biological knowledge about cell mechanisms. Such knowledge, translated into mathematical models, expands the power to investigate and understand effects of modifications on underlying mechanisms based on experimental data. We utilise two population growth models -- an exponential and a logistic growth model -- to capture cell dynamics over the whole experimental time horizon and to consider all measurement times jointly. This approach enables us to derive modification effects from estimated model parameters. We demonstrate that the exponential and logistic growth model recognise simulated scenarios more reliably than a statistical test. Moreover, we apply the population growth models to evaluate the efficacy of candidate gene knockouts in patient-derived xenograft models of acute leukaemia.

stat.ME↗

arXiv2026

Integrating Household Dynamics in Stochastic Epidemic Modeling: An SDE Approach to the SIR Framework

Understanding infectious disease spread remains a critical public health challenge, particularly given the interplay between household dynamics and community transmission patterns. Traditional epidemiological models often oversimplify these dynamics by treating populations as homogeneous, failing to capture crucial household-level interactions that can significantly impact disease spread. This paper introduces a new stochastic differential equation model extending the SIR framework by capturing the randomness in disease spread and incorporating household structure and heterogeneous mixing patterns. The model divides the population into groups based on age and household size, includes subpopulation-targeted lockdown parameters and constructs detailed contact matrices accounting for both public and within-household interactions. Through the approximation of Markov jump processes by branching processes near the disease free equilibrium, we derive the basic reproduction number of our model and conduct global sensitivity analysis using Sobol indices to identify influential factors. Our simulations reveal that incorporating household structure leads to substantially different predictions compared to traditional models, particularly in epidemic timing and peak intensity. The stochastic framework captures important variations in outbreak trajectories overlooked by deterministic approaches, especially during early and peak phases. This work contributes to both mathematical epidemiology and practical public health planning by providing a sophisticated mathematical understanding of how population structure and randomness influence disease dynamics, offering insights for intervention strategies where household transmission plays a significant role.

q-bio.PE↗

arXiv2025

Measuring football fever through wearable technology: A case study on the German cup final

Football is the world's most popular sport, evoking strong physiological and emotional responses among its fans. Yet, the specific dynamics of fan attachment to matches have received little attention in the literature. In this paper, we quantify these dynamics through a unique case study from professional football: the 2025 cup final of the German Football Association (DFB) between first-division club VfB Stuttgart and third-division club Arminia Bielefeld. We collected high-resolution smartwatch data, including heart rate and stress level, from 229 Arminia Bielefeld fans over approximately 12 weeks, complemented by survey responses on club attachment, match attendance, and personal characteristics from a subset of 37 participants. By combining physiological data with survey information, we analyse variations in emotional engagement across individuals and contexts, as well as physiological reactions to key match events. This approach provides rare, data-driven insights into the football fever that captivates fans during high-stakes competitions. Furthermore, we compare the vital parameters recorded on the day of the match with baseline levels on non-matchdays throughout the entire observation period. Our findings reveal pronounced physiological responses among fans, beginning hours before the match and peaking at kick-off.

stat.AP↗

arXiv2025

Misspecifications in structural equation modeling: The choice of latent variables, causal-formative constructs or composites

Empirical research in many social disciplines involves constructs that are not directly observable, such as behaviors. To model them, constructs must be operationalized using their relations with indicators. Structural equation modeling (SEM) is the primary approach for this purpose. In SEM, three types of constructs are distinguished: latent variables, causal-formative constructs, and composites. To estimate the parameters of the different models, various estimators have been developed. Many Monte Carlo studies have examined the estimation performances of different estimators for the construct types. One aspect evaluated is the consequences of construct misspecification - when the true construct type differs from the modeling choice - on parameter estimates and model fit. For example, parameter bias in models that misspecify latent variables as composites is often attributed to the chosen estimator, although model parameters depend on different estimators, making it impossible to examine the factors individually. This article aims to disentangle the issues of construct misspecification and parameter estimation by a comprehensive Monte Carlo study of all combinations between true and assumed construct types. To focus on misspecification, we used the same estimator for all models, namely the maximum likelihood (ML) estimator. To generalize beyond ML, we replicated the simulation using another estimator. We aim to examine the role of construct misspecification, not estimator choice, on the estimation performance and show that misspecification leads indeed to biased path coefficient estimates. Further, we evaluate whether fit measures can distinguish models with correct from those with misspecified constructs. We find that none of the criteria considered is suited for this. These findings stress the importance of thoughtful construct specification and the need for further research.

stat.ME↗

arXiv2020

stochprofML: Stochastic Profiling Using Maximum Likelihood Estimation in R

Tissues are often heterogeneous in their single-cell molecular expression, and this can govern the regulation of cell fate. For the understanding of development and disease, it is important to quantify heterogeneity in a given tissue. We introduce the \proglang{R} package \pkg{stochprofML} which is designed to parameterize heterogeneity from the cumulative expression of small random pools of cells. This method outweighs the demixing of mixed samples with a saving in cost and effort and less measurement error. The approach uses the maximum likelihood principle and was originally presented in Bajikar et al.(2014); its extension to varying pool sizes was used in Tirier et al. (2019). We evaluate the algorithm's performance in simulation studies and present further application opportunities.

stat.AP↗

arXiv2019

Statistical inference for fractional diffusion process with random effects at discrete observations

This paper deals with the problem of inference associated with linear fractional diffusion process with random effects in the drift. In particular we are concerned with the maximum likelihood estimators (MLE) of the random effect parameters. First of all, we estimate the Hurst parameter H from one single subject. Second, assuming the Hurst index H is known, we derive the MLE and examine their asymptotic behavior as the number of subjects under study becomes large, with random effects normally distributed.

math.ST↗

arXiv2018

Bayesian Inference for Diffusion Processes: Using Higher-Order Approximations for Transition Densities

Modelling random dynamical systems in continuous time, diffusion processes are a powerful tool in many areas of science. Model parameters can be estimated from time-discretely observed processes using Markov chain Monte Carlo (MCMC) methods that introduce auxiliary data. These methods typically approximate the transition densities of the process numerically, both for calculating the posterior densities and proposing auxiliary data. Here, the Euler-Maruyama scheme is the standard approximation technique. However, the MCMC method is computationally expensive. Using higher-order approximations may accelerate it, but the specific implementation and benefit remain unclear. Hence, we investigate the utilisation and usefulness of higher-order approximations in the example of the Milstein scheme. Our study demonstrates that the MCMC methods based on the Milstein approximation yield good estimation results. However, they are computationally more expensive and can be applied to multidimensional processes only with impractical restrictions. Moreover, the combination of the Milstein approximation and the well-known modified bridge proposal introduces additional numerical challenges.

stat.CO↗