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Global variance-based reliability sensitivity indices arise from a variance decomposition of the indicator function describing the failure event. The first-order indices reflect the main effect of each variable on the variance of the failure event and can be used for variable prioritization; the total-effect indices represent the total effect of each variable, including its interaction with other variables, and can be used for variable fixing. This contribution derives expressions for the variance-based reliability indices of systems with multiple failure modes that are based on the first-order reliability method (FORM). The derived expressions are a function of the FORM results and, hence, do not require additional expensive model evaluations. They do involve the evaluation of multinormal integrals, for which effective solutions are available. We demonstrate that the derived expressions enable an accurate estimation of variance-based reliability sensitivities for general system problems to which FORM is applicable.

Conformal inference is a fundamental and versatile tool that provides distribution-free guarantees for many machine learning tasks. We consider the transductive setting, where decisions are made on a test sample of $m$ new points, giving rise to $m$ conformal $p$-values. While classical results only concern their marginal distribution, we show that their joint distribution follows a P\'olya urn model, and establish a concentration inequality for their empirical distribution function. The results hold for arbitrary exchangeable scores, including adaptive ones that can use the covariates of the test+calibration samples at training stage for increased accuracy. We demonstrate the usefulness of these theoretical results through uniform, in-probability guarantees for two machine learning tasks of current interest: interval prediction for transductive transfer learning and novelty detection based on two-class classification.

To date, most methods for simulating conditioned diffusions are limited to the Euclidean setting. The conditioned process can be constructed using a change of measure known as Doob's $h$-transform. The specific type of conditioning depends on a function $h$ which is typically unknown in closed form. To resolve this, we extend the notion of guided processes to a manifold $M$, where one replaces $h$ by a function based on the heat kernel on $M$. We consider the case of a Brownian motion with drift, constructed using the frame bundle of $M$, conditioned to hit a point $x_T$ at time $T$. We prove equivalence of the laws of the conditioned process and the guided process with a tractable Radon-Nikodym derivative. Subsequently, we show how one can obtain guided processes on any manifold $N$ that is diffeomorphic to $M$ without assuming knowledge of the heat kernel on $N$. We illustrate our results with numerical simulations and an example of parameter estimation where a diffusion process on the torus is observed discretely in time.

Multivariate matching algorithms "pair" similar study units in an observational study to remove potential bias and confounding effects caused by the absence of randomizations. In one-to-one multivariate matching algorithms, a large number of "pairs" to be matched could mean both the information from a large sample and a large number of tasks, and therefore, to best match the pairs, such a matching algorithm with efficiency and comparatively limited auxiliary matching knowledge provided through a "training" set of paired units by domain experts, is practically intriguing. We proposed a novel one-to-one matching algorithm based on a quadratic score function $S_{\beta}(x_i,x_j)= \beta^T (x_i-x_j)(x_i-x_j)^T \beta$. The weights $\beta$, which can be interpreted as a variable importance measure, are designed to minimize the score difference between paired training units while maximizing the score difference between unpaired training units. Further, in the typical but intricate case where the training set is much smaller than the unpaired set, we propose a \underline{s}emisupervised \underline{c}ompanion \underline{o}ne-\underline{t}o-\underline{o}ne \underline{m}atching \underline{a}lgorithm (SCOTOMA) that makes the best use of the unpaired units. The proposed weight estimator is proved to be consistent when the truth matching criterion is indeed the quadratic score function. When the model assumptions are violated, we demonstrate that the proposed algorithm still outperforms some popular competing matching algorithms through a series of simulations. We applied the proposed algorithm to a real-world study to investigate the effect of in-person schooling on community Covid-19 transmission rate for policy making purpose.

In this work, we examine how fact-checkers prioritize which claims to fact-check and what tools may assist them in their efforts. Through a series of interviews with 23 professional fact-checkers from around the world, we validate that harm assessment is a central component of how fact-checkers triage their work. We also clarify the processes behind fact-checking prioritization, finding that they are typically ad hoc, and gather suggestions for tools that could help with these processes. To address the needs articulated by fact-checkers, we present a structured framework of questions to help fact-checkers negotiate the priority of claims through assessing potential harms. Our FABLE Framework of Misinformation Harms incorporates five dimensions of magnitude -- (social) Fragmentation, Actionability, Believability, Likelihood of spread, and Exploitativeness -- that can help determine the potential urgency of a specific message or claim when considering misinformation as harm. The result is a practical and conceptual tool to support fact-checkers and others as they make strategic decisions to prioritize their efforts. We conclude with a discussion of computational approaches to support structured prioritization, as well as applications beyond fact-checking to content moderation and curation.

Mendelian randomization uses genetic variants as instrumental variables to make causal inferences about the effects of modifiable risk factors on diseases from observational data. One of the major challenges in Mendelian randomization is that many genetic variants are only modestly or even weakly associated with the risk factor of interest, a setting known as many weak instruments. Many existing methods, such as the popular inverse-variance weighted (IVW) method, could be biased when the instrument strength is weak. To address this issue, the debiased IVW (dIVW) estimator, which is shown to be robust to many weak instruments, was recently proposed. However, this estimator still has non-ignorable bias when the effective sample size is small. In this paper, we propose a modified debiased IVW (mdIVW) estimator by multiplying a modification factor to the original dIVW estimator. After this simple correction, we show that the bias of the mdIVW estimator converges to zero at a faster rate than that of the dIVW estimator under some regularity conditions. Moreover, the mdIVW estimator has smaller variance than the dIVW estimator.We further extend the proposed method to account for the presence of instrumental variable selection and balanced horizontal pleiotropy. We demonstrate the improvement of the mdIVW estimator over the dIVW estimator through extensive simulation studies and real data analysis.

Mediation analysis aims to decipher the underlying causal mechanisms between an exposure, an outcome, and intermediate variables called mediators. Initially developed for fixed-time mediator and outcome, it has been extended to the framework of longitudinal data by discretizing the assessment times of mediator and outcome. Yet, processes in play in longitudinal studies are usually defined in continuous time and measured at irregular and subject-specific visits. This is the case in dementia research when cerebral and cognitive changes measured at planned visits in cohorts are of interest. We thus propose a methodology to estimate the causal mechanisms between a time-fixed exposure ($X$), a mediator process ($\mathcal{M}_t$) and an outcome process ($\mathcal{Y}_t$) both measured repeatedly over time in the presence of a time-dependent confounding process ($\mathcal{L}_t$). We consider three types of causal estimands, the natural effects, path-specific effects and randomized interventional analogues to natural effects, and provide identifiability assumptions. We employ a dynamic multivariate model based on differential equations for their estimation. The performance of the methods are explored in simulations, and we illustrate the method in two real-world examples motivated by the 3C cerebral aging study to assess: (1) the effect of educational level on functional dependency through depressive symptomatology and cognitive functioning, and (2) the effect of a genetic factor on cognitive functioning potentially mediated by vascular brain lesions and confounded by neurodegeneration.

Fourth-order variational inequalities are encountered in various scientific and engineering disciplines, including elliptic optimal control problems and plate obstacle problems. In this paper, we consider additive Schwarz methods for solving fourth-order variational inequalities. Based on a unified framework of various finite element methods for fourth-order variational inequalities, we develop one- and two-level additive Schwarz methods. We prove that the two-level method is scalable in the sense that the convergence rate of the method depends on $H/h$ and $H/\delta$ only, where $h$ and $H$ are the typical diameters of an element and a subdomain, respectively, and $\delta$ measures the overlap among the subdomains. This proof relies on a new nonlinear positivity-preserving coarse interpolation operator, the construction of which was previously unknown. To the best of our knowledge, this analysis represents the first investigation into the scalability of the two-level additive Schwarz method for fourth-order variational inequalities. Our theoretical results are verified by numerical experiments.

In recent years, power analysis has become widely used in applied sciences, with the increasing importance of the replicability issue. When distribution-free methods, such as Partial Least Squares (PLS)-based approaches, are considered, formulating power analysis turns out to be challenging. In this study, we introduce the methodological framework of a new procedure for performing power analysis when PLS-based methods are used. Data are simulated by the Monte Carlo method, assuming the null hypothesis of no effect is false and exploiting the latent structure estimated by PLS in the pilot data. In this way, the complex correlation data structure is explicitly considered in power analysis and sample size estimation. The paper offers insights into selecting statistical tests for the power analysis procedure, comparing accuracy-based tests and those based on continuous parameters estimated by PLS. Simulated and real datasets are investigated to show how the method works in practice.

This paper develops an in-depth treatment concerning the problem of approximating the Gaussian smoothing and Gaussian derivative computations in scale-space theory for application on discrete data. With close connections to previous axiomatic treatments of continuous and discrete scale-space theory, we consider three main ways discretizing these scale-space operations in terms of explicit discrete convolutions, based on either (i) sampling the Gaussian kernels and the Gaussian derivative kernels, (ii) locally integrating the Gaussian kernels and the Gaussian derivative kernels over each pixel support region and (iii) basing the scale-space analysis on the discrete analogue of the Gaussian kernel, and then computing derivative approximations by applying small-support central difference operators to the spatially smoothed image data. We study the properties of these three main discretization methods both theoretically and experimentally, and characterize their performance by quantitative measures, including the results they give rise to with respect to the task of scale selection, investigated for four different use cases, and with emphasis on the behaviour at fine scales. The results show that the sampled Gaussian kernels and derivatives as well as the integrated Gaussian kernels and derivatives perform very poorly at very fine scales. At very fine scales, the discrete analogue of the Gaussian kernel with its corresponding discrete derivative approximations performs substantially better. The sampled Gaussian kernel and the sampled Gaussian derivatives do, on the other hand, lead to numerically very good approximations of the corresponding continuous results, when the scale parameter is sufficiently large, in the experiments presented in the paper, when the scale parameter is greater than a value of about 1, in units of the grid spacing.