We consider the problem of setting confidence intervals on a parameter of interest from the maximum-likelihood fit of a physics model to a binned data set with a large number of bins, large event-counts per bin, and in the presence of systematic uncertainties modeled as nuisance parameters. We use the profile-likelihood ratio for statistical inference and focus on the case in which the model is determined from Monte Carlo simulated samples of finite size. We start by presenting a toy model in which the properties of widely used approximations of the profile-likelihood ratio in the asymptotic limit, which are commonly expected to hold in the high-statistics regime, are manifestly broken even if the numbers of events per bin in both the data and simulated samples are seemingly large enough to warrant their validity. We then move to the general setting to show how statistical uncertainties in the Monte Carlo predictions can affect the coverage of confidence intervals constructed in the asymptotic approximation always in the same direction, namely they lead to systematic under-coverage.

Physics-guided computational imaging typically aggregates data fidelity, geometric reconstruction, and sensor consistency into a single scalar loss. In low signal-to-noise ratio (low-SNR) non-line-of-sight imaging, this centralized approach creates asymmetric gradient conflicts where the dominant constraints suppress physically meaningful updates. We propose treating multi-constraint training as a gradient coordination problem rather than scalar balancing. Our framework coordinates heterogeneous objectives through branch-wise gradient routing: soft conflict projection (PCGrad), hard physical constraint enforcement (PhysGuard), learnable sensor calibration, and a staged training protocol that decouples representation learning from nuisance parameter estimation. On held-out test scenes, the fully staged model improved the peak signal-to-noise ratio (PSNR) from 19.09 dB to 20.49 dB and the structural similarity index (SSIM) from 0.67 to 0.71 over the baseline, with consistent gains across the 48, 28, and 25 dB SNR levels. Qualitative evaluation on seven real-world scenes indicates sharper structure recovery and fewer artifacts. In this NLOS setting, gradient-level coordination is more reliable than scalar aggregation under heterogeneous constraints.

ABSTRACT Risk prediction models are widely used to guide real‐world decision‐making in areas such as healthcare and economics, and they also play a key role in estimating nuisance parameters in semiparametric inference. The super learner is a machine learning framework that combines a library of prediction algorithms into a meta‐learner using cross‐validated loss. In the context of right‐censored data, careful consideration must be given to both the choice of the loss function and the estimation of expected loss. Moreover, estimators such as the inverse probability of censoring weighting requires accurate modeling and an estimator of the censoring distribution. We propose a novel approach to super learning for survival analysis that jointly evaluates the candidate learners for both the event‐time distribution and the censoring distribution. Our method imposes no restrictions on the algorithms included in the library, accommodates competing risks, and does not rely on a single prespecified estimator of the censoring distribution. We establish a finite‐sample bound on the average price we pay for using cross‐validation, and show that this price vanishes asymptotically, up to poly‐logarithmic terms, provided that the size of the library does not grow faster than at a polynomial rate in the sample size. We demonstrate the practical utility of our method using prostate cancer data and compare it to existing super learner algorithms for survival analysis using synthesized data.

Abstract Reconstructing fast-ion velocity distributions from collective Thomson scattering (CTS) spectra is an ill-posed inverse problem due to the spectral nonlinearity, strong parameter coupling and measurement noise. To mitigate the ill-posed problems in single-view inversions, a hybrid spectrum–parameter conditioned encoder (HSPCE) is proposed to reconstruct two-dimensional fast-ion velocity distributions based on the electromagnetic forward model. For feasibility validation, one-dimensional inversion is firstly carried out using an electrostatic CTS model under HL-3 operating parameters. Compared with the Least Squares with Nuisance Parameters (LSN), the machine-learning approach demonstrates markedly improved robustness and accuracy, maintaining an R2 of 0.950 with 10% Gaussian noise. Extending to two dimensions, the velocity distribution is represented as an image and reduced in dimensionality through principal component analysis (PCA), with additional soft constraints applied in both coefficient and pixel spaces to preserve physical consistency. Benchmarking against the 1D baseline model, HSPCE shows that the higher structural similarity (SSIM) and lower normalized root mean square error (NRMSE) with different gaussian noise, with 0.930 and 0.043 at noise level of 0.1 respectively. Further analysis indicates that the fraction of fast ions plays an important role in enabling the network to extract reliable fast-ion information, with higher fractions yielding clearer reconstructions and reduced uncertainty. Overall, the proposed framework suggests that neural networks offer a promising and robust approach for improving the interpretability and reliability of fast-ion diagnostics based on CTS in magnetically confined plasmas.

We present a practical method to measure the energy of proton beams at a medical cyclotron using the stacked foil technique in combination with a Bayesian inference method. By measuring the 48 V activity induced in a stack of irradiated titanium foils, the proton energy can be inferred without relying on direct current or charge measurements, making the method suitable even for low-vacuum environments or air-exposed setups. This technique is further extended to configurations where the beam energy is degraded to levels around 8 MeV. A Bayesian fit of the measured activity profile allows not only for a robust energy estimation but also for a consistent treatment of uncertainties and nuisance parameters. Monte Carlo simulations are employed to validate the underlying assumptions, including the impact of energy dispersion or cross-section uncertainties. Our results demonstrate that this method provides accurate beam energy measurements across several typical experimental setups used at the Bern Medical Cyclotron. Additionally, we evaluate the sensitivity of the method to the choice of nuclear cross-section data and assess how the number of foils in the stack affects the uncertainty in the inferred beam energy.

We present a simple yet effective method to resolve prior-volume effects, also known as projection effects, in full-shape analyses of the power spectrum multipoles within the Effective Field Theory of Large-Scale Structure (EFTofLSS). By re-defining the EFTofLSS nuisance parameters to incorporate the contribution from the parameters impacting the amplitude of the EFTofLSS modelling components, we substantially mitigate projection effects. With the re-parametrisation the actual posterior maximum values are within the marginalised credible interval, eliminating significant shifts observed in the baseline analysis. We demonstrate the robustness of this method in full-shape w 0 wa CDM analyses on synthetic data in BOSS DR12 and DESI DR1 setups. We find that the re-parametrisation with the Alcock-Paczynski amplitude is important for unbiased constraints in dark energy models beyond Λ. For the evolving dark energy model, we then analyse the BOSS DR12 measurements, in combination with BAO information (from BOSS DR12, 6DF, SDSS DR7 MGS and eBOSS DR16 surveys) and 3 × 2 pt measurements from DES Y3 — all data combinations are converging into the w 0-wa parameter region preferred by DESI+CMB+SNIa. From total combination of these large-scale structure probes without additional CMB information we find w 0 = -0.72 ± 0.21, wa = -0.91+0.78 -0.64. Despite the low significance of deviation from standard cosmology, this result underscores the potential of our re-parametrisation approach in delivering low-redshift cosmological constraints. We argue for the use of this approach in spectroscopic Stage IV surveys, where the potential deviation from standard cosmology can be detected with higher significance.

Beta-lactam allergy labels (BLALs), especially penicillin allergy labels, are frequently recorded in hospitalized patients and are associated with increased use of broad-spectrum and second-line antibiotics. Most BLALs are incorrect, but current allergy workups require invasive testing and specialized resources. We recently developed a strictly noninvasive, electronic patient record-embedded clinical decision support tool, the Allergy Fact Checker (AFC), which proactively identifies potentially incorrect BLALs by detecting uneventful re-exposures to the culprit or other beta-lactams since introduction of the BLAL. This study aims to evaluate the clinical, antimicrobial, and economic impact of the AFC in hospitalized adults with BLALs compared to the standard of care (no AFC). We are conducting a multicenter, open-label, crossover cluster-controlled study in 9 hospitals in Flanders, Belgium. All hospitalized adults with a BLAL are eligible, excluding patients in palliative care, discharged within 24 hours, or previously enrolled. Each hospital will alternate between intervention (use of the AFC) and control (standard practice) phases, separated by washout periods. The primary endpoint is cumulative guideline-concordant prescribing of first-line and/or narrow-spectrum beta-lactams following local antibiotic treatment guidelines, across predefined care windows up to day 100, expressed as a weighted per-patient proportion. Secondary endpoints include delabeling or refinement rate, beta-lactam tolerance, antibiotic switching, hospital length of stay, in-hospital and 3-month mortality, intensive care unit admission, readmission, multidrug-resistant organism colonization or infection, and costs. Based on prior data, we calculated that a total of 3285 participants are required to achieve 80% power to detect superiority of the intervention (4.6% vs 9.9% appropriate prescribing). Recruitment started in March 2025 and is ongoing. The primary outcome will be analyzed using hierarchical mixed-effect models accounting for hospital-level clustering and period effects. Data collection will continue until 200 days after the last patient is discharged. This trial is expected to conclude in 2026. Ethical approval was obtained from the institutional review board in November 2024. Recruitment started in March 2025 and is ongoing. As of manuscript submission, more than 3000 participants have been enrolled across the participating hospitals. According to the prespecified protocol, an interim assessment of nuisance parameters will be performed in the following month to evaluate the initial design assumptions. Data collection is expected to continue until the end of 2026. The main study results are anticipated to be reported in 2027. This is the first multicenter European study evaluating a strictly noninvasive BLAL delabeling approach. If successful, this AFC tool could improve antimicrobial stewardship, reduce costs, and provide a scalable model for centralized allergy label management.

Abstract We consider a threshold regression model in a long-memory setting. A method for estimating the threshold parameter is proposed. Asymptotic results are derived. The asymptotic rate of convergence turns out to be slower than under weak dependence, but approaches the usual fast rate of $$O_{p}(n^{-1})$$ O p ( n - 1 ) when the long-memory parameter of the residuals converges to zero. Furthermore, asymptotic inference for the difference of conditional means below and above an estimated threshold is considered. A statistic is defined to construct confidence intervals. Surprisingly, the rate of convergence of the statistic improves when nuisance parameters are estimated. An algorithm for constructing data driven confidence intervals is proposed. The results are illustrated by a small simulation study and an application to CBOE volumes and volatilities for S&P 500 index options.

ABSTRACT We propose a new omnibus goodness‐of‐fit test based on trigonometric moments of probability‐integral‐transformed data. The test builds on the framework of the LK test introduced by Langholz and Kronmal [J. Amer. Statist. Assoc. 86 (1991), 1077–1084], but fully exploits the covariance structure of the associated trigonometric statistics. As a result, our test statistic converges under the null hypothesis to a distribution, even in the presence of nuisance parameters, yielding a well‐calibrated rejection region. We derive the exact asymptotic covariance matrix required for normalization and propose a unified approach to computing the LK normalizing scalar. The applicability of both the proposed test and the LK test is substantially expanded by providing implementation details for 11 families of continuous distributions, covering most commonly used parametric models. Simulation studies demonstrate accurate empirical size, close to the nominal level, and strong power properties, yielding fully plug‐and‐play procedures. Further insight is provided by an analysis under local alternatives. The methodology is illustrated using surface temperature forecast errors from a numerical weather prediction model.

Graphical models are widely used to represent dependence structures in biological systems, where directed edges may encode causal relationships under appropriate assumptions. We present baycn (BAYesian Causal Network), a novel approximate Bayesian method for inferring probabilities of edge directions and edge absence, while allowing flexible, user-specified priors to encode sparsity and an input graph to incorporate biological knowledge. For inference, we develop a Metropolis-Hastings-like sampler over graph structures based on a pseudo-posterior with a plug-in likelihood, which eliminates potentially high-dimensional nuisance parameters. This formulation substantially improves computational efficiency while yielding posterior probabilities that reflect Markov equivalence. We apply baycn to two genomic applications: distinguishing direct from indirect target genes of a shared genetic variant, and inferring combinatorial binding of transcription factors during tissue differentiation in Drosophila embryos. Both applications involve discrete and continuous data types that are common in genomics. Selected variables in these applications are treated as instrumental variables to help impose constraints on edge direction. Baycn demonstrates substantially improved accuracy at both the graph and edge levels, while existing methods do not handle mixed data, fail to capture weak signals, or are computationally infeasible.

High-sensitivity accelerometers and gravimeters, achieving the ultimate limits of measurement sensitivity are key tools for advancing both fundamental and applied physics. While numerous platforms have been proposed to achieve this goal, from atom interferometers to optomechanical systems, all of these studies neglect the effects of intrinsic quantum uncertainty in time estimation. Starting from the Hamiltonian of a generic linear quantum sensor, we derive the two-parameter quantum Fisher information matrix and establish the corresponding Cram'er-Rao bound, treating time as an uncertain (nuisance) parameter. Our analysis reveals a fundamental coupling between time and signal estimation that inherently degrades measurement sensitivity, with the standard single-parameter quantum limit recovered only at specific interrogation times or under special decoupling conditions. We then apply these results to an optomechanical gravimeter and explicitly derive an optimal decoupling condition under which the effects of time uncertainty are averaged out in a continuous measurement scheme. Our approach is general and can be readily extended to a broad class of quantum sensors.

Abstract Overlapping galaxies, in which a foreground galaxy partially overlaps a background galaxy, offer a unique opportunity to measure dust attenuation, a key nuisance parameter in galaxy studies, empirically and in great detail by modelling the light of both the foreground and background galaxy and inferring the missing light in the overlapping region. However, the current catalogue of overlapping pairs is relatively limited in number compared to catalogues dedicated to individual galaxies. Expanding this catalogue is not only a necessity to facilitate further detailed dust studies beyond the few limited studies conducted thus far, but also to improve pair-to-pair variance and support automated identification through machine learning techniques. To achieve this, we utilise galaxies classified as “overlapping” from Galaxy Zoo DECaLS (GZD-1, -2, and -5), along with images from Data Release 10 (DR10) of the DESI Legacy Survey, in our individual citizen science project to classify these pairs directly using volunteers. This new catalogue will not only provide a wealth of targets for future dust studies but will also contribute to a deeper understanding of these pairs and dust as a whole.

Bayesian designs for clinical trials using assurance to choose the sample size have been proposed in various trial contexts. Assurance allows for the incorporation of uncertainty on both the treatment effect and nuisance parameters into the sample size calculation. In the case of two-arm cluster randomised trials with continuous outcomes, assurance has been proposed with both a frequentist analysis (hybrid designs) and a Bayesian analysis (fully Bayesian designs). A Bayesian analysis in this context ensures a consistent treatment of probability throughout the design and analysis of the trial. In the fully Bayesian design, inference has been achieved via Markov chain Monte Carlo sampling, and since assurance itself is evaluated via simulation, the result is a computationally intensive and often slow-to-run approach. In the case of two-arm cluster randomised trials with binary outcomes, assurance has not yet been explored to specify sample sizes, either in the hybrid or fully Bayesian case. This article considers fully Bayesian designs for two-arm cluster randomised trials with continuous and binary outcomes. For the analysis of the trial, we use a (generalised) linear mixed-effects model. We summarise the inference for the treatment effect based on quantiles of the posterior distribution. We use assurance to choose the sample size. In the continuous case, we investigate Integrated Nested Laplace Approximations for inference to speed up calculation of the assurance and compare Integrated Nested Laplace Approximations in computation time and accuracy to Markov chain Monte Carlo. In the binary case, we develop the first fully Bayesian design for cluster randomised trials and conduct a similar comparison between Integrated Nested Laplace Approximations and Markov chain Monte Carlo. We demonstrate our novel approach using assurance to choose sample sizes for the SPEEDY cluster randomised trial, based on the results of a formal prior elicitation exercise with two clinical experts. We report comparisons of Integrated Nested Laplace Approximations and Markov chain Monte Carlo for a range of different scenarios for cluster randomised controlled trials (RCTs), to determine when each inference scheme should be used, balancing the computational cost in terms of speed and accuracy. Overall Markov chain Monte Carlo with a very large number of samples produces very accurate inference but does not scale well in terms of computational speed compared to Integrated Nested Laplace Approximations. Based on our simulation study, we recommend that Integrated Nested Laplace Approximations is used for inference in cluster trials with binary outcomes and large (n> 500) cluster trials with continuous outcomes, and that Markov chain Monte Carlo is used in smaller (n≤500) cluster trials with continuous outcomes. Our case study demonstrated how to incorporate the uncertainty of trial clinicians into the sample size calculation to give an overall assessment of the likelihood of success of the trial. A fully Bayesian design can be used for two-arm cluster trials with both continuous and binary outcomes. Integrated Nested Laplace Approximations can allow for more efficient assessment of the assurance for cluster trials with binary outcomes and large cluster trials with continuous outcomes, without loss of accuracy in inference. A fully Bayesian design of a cluster randomised trial provides a coherent design and analysis framework and incorporates uncertainty in model parameters when choosing the sample size.

Time-division broadcast positioning systems offer advantages such as low implementation complexity and support for an unlimited number of passive receivers. However, most existing joint localization and synchronization (JLAS) methods for moving terminals rely on the assumption of pre-synchronized base stations (BSs), which restricts their flexibility and scalability in ad-hoc or large-scale deployments. This paper proposes a Fully Asynchronous JLAS (FA-JLAS) framework that operates without any prior inter-BS synchronization. We derive a new set of composite observables, the Symmetric Asynchronous TDOA (SA-TDOA) and the Inter-Frame Differencing Observable (IFDO), from timestamp measurements shared among BSs. These observables are designed to analytically eliminate nuisance parameters, including clock offsets and static non-line-of-sight (NLOS) delays. Based on these observables, a MAP-based estimation framework is developed that incorporates motion priors and jointly estimates the user equipment’s (UE) kinematic state and network synchronization parameters, thereby improving robustness in challenging 3D environments. Theoretical performance bounds are derived using the Cramér-Rao Lower Bound (CRLB), and simulation results demonstrate that the FA-JLAS framework achieves near-CRLB accuracy across various scenarios.

Non-proportional hazards cases are frequently expected in clinical trials with time-to-event endpoints (e.g., cardiology, oncology). The relevance of hazard ratios to quantify the treatment effect is questionable and potentially misleading in this context. Hence, alternative methods comparing restricted mean survival times are increasingly promoted. Specific challenges arise when planning clinical trials for comparing restricted mean survival times, as several nuisance parameter estimates are needed for calculating the sample size. Precise estimates might be difficult to obtain at the planning stage and might lead to underpowered trials. One way of dealing with this insecurity is to apply adaptive group sequential study designs with the option to adapt the sample size during an ongoing trial. Within this work, we consider such sample size adaptations, with a specific focus on the context of delayed treatment effects. We compare the performance of an adaptive design with the restricted mean survival time as the primary endpoint with other commonly chosen endpoints in this scenario by means of an extensive simulation study. With our proposed method, adaptive designs with the restricted mean survival time as the primary endpoint are now thoroughly explained. The combination test that we describe can also be useful for other adaptations than sample sizes.

Inference on a scalar parameter in the presence of high-dimensional nuisance parameters is challenging, especially when their dimension increases with the sample size. This issue is exacerbated in models with crossed fixed effects and sparse discrete data. In this scenario, we show that standard likelihood-based methods, such as the signed likelihood root or profile likelihood, often fail to provide reliable results due to limited information. Parametric bootstrap offers an alternative to analytical corrections but it has been less explored in the context of sparse discrete data and crossed fixed effects, and its theoretical properties have yet to be fully demonstrated. For these settings, this study shows that hybrid approaches combining analytical corrections with parametric bootstrap yield superior inferential accuracy. Simulation studies indicate that constrained bootstrap from penalized estimates outperforms standard bootstrap approaches, particularly in logistic regression models with severe sparsity.

Context . Estimating properties of star clusters from unresolved broadband photometry is a challenging problem that is classically tackled using spectral energy distribution (SED) fitting methods that are based on simple stellar population models. However, grid-based methods suffer from computational limitations. Because of their exponential scaling, they can become intractable when the number of inference parameters grows. In addition, nuisance parameters in the model can make the computation of the likelihood function intractable. These limitations can be overcome by modern generative deep learning methods that offer flexible and powerful tools for modeling high-dimensional posterior distributions and fast inference from learned data. Aims . We present a normalizing flow approach for the inference of cluster age, mass, and reddening parameters from Hubble Space Telescope broadband photometry. In particular, we explore our network’s behavior when dealing with an inference problem that has been analyzed in previous works. Methods . We used the SED modeling code CIGALE to create a dataset of synthetic photometric observations for 5 × 10 6 mock star clusters. Subsequently, this dataset was used to train a coupling-based flow in the form of a conditional invertible neural network to predict posterior probability distributions for cluster age, mass, and reddening from photometric observations. Results . We predicted cluster parameters for the Physics at High Angular resolution in Nearby GalaxieS (PHANGS) Data Release 3 catalog. To evaluate the capabilities of the network, we compared our results to the publicly available PHANGS estimates and found that the estimates agree reasonably well. Conclusions . We demonstrate that normalizing flow methods can be a viable tool for the inference of cluster parameters, and argue that this approach is especially useful when nuisance parameters make the computation of the likelihood intractable and in scenarios that require efficient density estimation.

We compare cosmological parameters from different sky maps and likelihood pipelines, assessing the robustness of cosmological results with respect to the choice of the latest maps-likelihood combination. We show that, for the multipole range retained in combination with ground-based observations, different products give very similar cosmological solutions; small remaining differences are reduced by the addition of other CMB datasets to . In particular, constraints on extended cosmological models benefit from the addition of small-scale power from ground-based experiments and are completely insensitive to the choice of maps and likelihood. For this work, we derive and release a nuisance-marginalized dataset and likelihood for the NPIPE data injected into the likelihood—which are usually used to obtain the reference PR4 cosmology. Using the extracted CMB spectra, we show that the additional constraining power for cosmology is coming from polarization at all scales and from temperature at multipoles above 1500 when going from PR3 to PR4. We also show that full marginalization over the foreground nuisance parameters can impact parameter inference and model selections when truncating some scales; our new likelihood enables correct combinations with other CMB datasets.

In recent years, orthogonal statistical learning has been widely recognized for its ability to reduce sensitivity with respect to nuisance parameters to estimate the target parameter, making it an important tool in causal inference, particularly in the estimation of the conditional average treatment effect (CATE). However, its application on conditional quantile treatment effect (CQTE), which offers a more comprehensive perspective on treatment effects than CATE, has not yet been explored comprehensively. In this article, we propose a novel method for learning CQTE. This method shares Neyman-orthogonal property, which produces CQTE estimators that are insensitive to small perturbations of nuisance functions. We first model the CQTE nonparametrically and use deep learning to estimate it. We establish the convergence rate of the neural network estimator, demonstrating that it achieves the minimax optimal rate of convergence (up to a polylogarithmic factor). This highlights deep learning’s ability to identify low-dimensional structures in high-dimensional data. Additionally, we then model CQTE linearly to facilitate interpretation and statistical inference. We prove that the corresponding coefficient and CQTE estimators achieve root-n consistency and asymptotic normality, even if the estimators of the nuisance parameters converge at a slower rate. Through empirical evaluation for numerical studies, we demonstrate the superiority of our method compared to competing methods.

A bstract Effective Field Theory (EFT) is a general framework to parametrize the low-energy approximation to a UV model that is widely used in model-independent searches for new physics. The use of EFTs at the LHC can suffer from a ‘validity’ issue, since new physics amplitudes often grow with energy and the kinematic regions with the most sensitivity to new physics have the largest theoretical uncertainties. We propose a method to account for these uncertainties with the aim of producing robust model-independent results with a well-defined statistical interpretation. In this approach, one must specify the new operators being studied as well as the new physics cutoff M , the energy scale where the EFT approximation breaks down. At energies below M , the EFT uncertainties are accounted for by adding additional higher dimensional operators with coefficients that are treated as nuisance parameters. The size of the nuisances are governed by a prior likelihood function that incorporates information about dimensional analysis, naturalness, and the scale M . At energies above M , our method incorporates the lack of predictivity of the EFT, and we show that this is crucial to obtain consistent results. We perform a number of tests of this method in a simple toy model, illustrating its performance in analyses aimed at new physics exclusion as well as for discovery. The method is conveniently implemented by the technique of event reweighting and is easily ported to realistic LHC analyses. We find that the procedure converges quickly with the number of nuisance parameters and is conservative when compared to UV models. The paper gives a precise meaning and offers a principled and practical solution to the widely debated ‘EFT validity issue’.