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Surrogate data testing for linearity is frequently applied to confirm the results of nonlinear time series analysis. We argue that this, in general, is not possible.

During the COVID-19 crisis, mechanistic models have guided evidence-based decision making. However, time-critical decisions in a dynamical environment limit the time available to gather supporting evidence. We address this bottleneck by…

The generalized likelihood ratio (GLR) test proposed by Fan, Zhang and Zhang [Ann. Statist. 29 (2001) 153-193] and Fan and Yao [Nonlinear Time Series: Nonparametric and Parametric Methods (2003) Springer] is a generally applicable…

We consider the problem of constructing surrogate operators for parameter-to-solution maps arising from parametric partial differential equations, where repeated forward model evaluations are computationally expensive. We present a…

Accurate calibration of finite element (FE) models is essential across various biomechanical applications, including human intervertebral discs (IVDs), to ensure their reliability and use in diagnosing and planning treatments. However,…

Assessing model adequacy is a crucial step in regression analysis, ensuring the validity of statistical inferences. For Generalized Functional Linear Models (GFLMs), which are widely used for modeling relationships between scalar responses…

We propose the Gaussian-Linear Hidden Markov model (GLHMM), a generalisation of different types of HMMs commonly used in neuroscience. In short, the GLHMM is a general framework where linear regression is used to flexibly parameterise the…

Extreme-mass-ratio-inspiral observations from future space-based gravitational-wave detectors such as LISA will enable strong-field tests of general relativity with unprecedented precision, but at prohibitive computational cost if existing…

Parametric surrogate models for partial differential equations (PDEs) are a necessary component for many applications in the computational sciences, and convolutional neural networks (CNNs) have proved as an excellent tool to generate these…

The method of surrogates is one of the key concepts of nonlinear data analysis. Here, we demonstrate that commonly used algorithms for generating surrogates often fail to generate truly linear time series. Rather, they create surrogate…

Recent advancements in the Generative Reward Model (GRM) have demonstrated its potential to enhance the reasoning abilities of LLMs through Chain-of-Thought (CoT) prompting. Despite these gains, existing implementations of GRM suffer from…

Evaluating treatment effects is critical in clinical trials but sometimes involves lengthy, invasive, or costly follow-up procedures. In these cases, surrogate markers, which provide intermediate measures of the long-term treatment effect,…

Linear mixed models (LMM) are widely adopted in genome-wide association studies (GWAS) to account for population stratification and cryptic relatedness. However, the parameter estimation of LMMs imposes substantial computational burdens due…

The general linear model (GLM) is a well established tool for analyzing functional magnetic resonance imaging (fMRI) data. Most fMRI analyses via GLM proceed in a massively univariate fashion where the same design matrix is used for…

Brain-Computer Interfaces (BCIs) rely on accurately decoding electroencephalography (EEG) motor imagery (MI) signals for effective device control. Graph Neural Networks (GNNs) outperform Convolutional Neural Networks (CNNs) in this regard,…

A major goal in genomics is to properly capture the complex dynamical behaviors of gene regulatory networks (GRNs). This includes inferring the complex interactions between genes, which can be used for a wide range of genomics analyses,…

Increasing resolution and coverage of astrophysical and climate data necessitates increasingly sophisticated models, often pushing the limits of computational feasibility. While emulation methods can reduce calculation costs, the neural…

In high-dimensional linear models, the sparsity assumption is typically made, stating that most of the parameters are equal to zero. Under the sparsity assumption, estimation and, recently, inference have been well studied. However, in…

Exponential family models, generalized linear models (GLMs), generalized linear mixed models (GLMMs) and generalized additive models (GAMs) are widely used methods in statistics. However, many scientific applications necessitate constraints…

We propose employing a high-dimensional generalized method of moments (GMM) estimator, regularized for dimension reduction and subsequently debiased to correct for shrinkage bias (referred to as a debiased-regularized estimator), for…