Sampling Uncertainty Research Articles

The Importance of Measurement Uncertainty Arising from the Sampling Process in Conformity Assessment: The Case of Fuel Quality

There is growing concern regarding the environmental and operational safety aspects of fuel. The result of a physicochemical measurement is the outcome of a series of steps that begin with the sampling process. The information obtained from this step and the contribution from the analytical process define the measurement uncertainty, although most laboratories consider only the analytical contribution as a quality parameter. On the other hand, this variability can be used as vital information to evaluate conformity to a specification. This study aimed to use uncertainty information considering only the analytical uncertainty and, next, the analytical and sampling uncertainties in compliance assessment, taking physicochemical measurements of fuel as case studies. The first scenario, which is traditional and focused solely on analytical uncertainty, showed to be less rigorous than the second scenario, which combined sampling uncertainty with analytical uncertainty. The results indicated that for the flash point in jet fuel, the sulfur mass fraction in gasoline-ethanol blends, and the kinematic viscosity in diesel, the risks to consumers—first considering only analytical uncertainty and then combining analytical uncertainty with sampling uncertainty—were the following: 2.6% and 5.6%; 4.4% and 7.1%; and 1.6% and 18.9%, respectively. Since the initial result of each pair was below 5%, compliance with the specification is suggested. However, when accounting for sampling uncertainty, there is an indication of potential non-compliance with the specification. Therefore, it is concluded that the contribution of uncertainty arising from sampling must be considered in a conformity assessment.

Rethinking learning difficulty and uncertainty of samples with a target perturbation-aware bias-variance decomposition

Rethinking learning difficulty and uncertainty of samples with a target perturbation-aware bias-variance decomposition

Comparison of active learning algorithms in classifying head computed tomography reports using bidirectional encoder representations from transformers.

Systems equipped with natural language (NLP) processing can reduce missed radiological findings by physicians, but the annotation costs are burden in the development. This study aimed to compare the effects of active learning (AL) algorithms in NLP for estimating the significance of head computed tomography (CT) reports using bidirectional encoder representations from transformers (BERT). A total of 3728 head CT reports annotated with five categories of importance were used and UTH-BERT was adopted as the pre-trained BERT model. We assumed that 64% (2385 reports) of the data were initially in the unlabeled data pool (UDP), while the labeled data set (LD) used to train the model was empty. Twenty-five reports were repeatedly selected from the UDP and added to the LD, based on seven metrices: random sampling (RS: control), four uncertainty sampling (US) methods (least confidence (LC), margin sampling (MS), ratio of confidence (RC), and entropy sampling (ES)), and two distance-based sampling (DS) methods (cosine distance (CD) and Euclidian distance (ED)). The transition of accuracy of the model was evaluated using the test dataset. The accuracy of the models with US was significantly higher than RS when reports in LD were < 1800, whereas DS methods were significantly lower than RS. Among the US methods, MS and RC were even better than the others. With the US methods, the required labeled data decreased by 15.4-40.5%, and most efficient in RC. In addition, in the US methods, data for minor categories tended to be added to LD earlier than RS and DS. In the classification task for the importance of head CT reports, US methods, especially RC and MS can lead to the effective fine-tuning of BERT models and reduce the imbalance of categories. AL can contribute to other studies on larger datasets by providing effective annotation.

Impact of sample heterogeneity on the evaluation of uncertainty from sampling and analytical steps in pharmaceutical analysis.

Measurement uncertainty is a critical factor in the reliability of pharmaceutical analyses, since it directly affects batch acceptance and regulatory compliance. While analytical uncertainty has been extensively studied, uncertainty arising from sampling remains less explored. This study aims to address this gap by evaluating the contributions of sampling and analytical uncertainties to the overall uncertainty for acetaminophen tablets and oral solution. The duplicate method and analysis of variance (ANOVA) were used to assess the uncertainty from sampling and analytical steps. Ten different batches of acetaminophen tablets and oral solution were analyzed, and the combined uncertainties were calculated. For tablets, uncertainty from sampling accounted for 89 % of the overall uncertainty, highlighting the critical role of sample heterogeneity. In contrast, for oral solutions, analytical uncertainty dominated (90 % of the total), reflecting the homogeneous nature of the solution. Considering the uncertainty from sampling can be important to ensure a reduced risk of false acceptance or false rejection, particularly for heterogeneous dosage forms. In conclusion, incorporating sampling uncertainty into uncertainty budgets can significantly improve decision-making in pharmaceutical quality control.

The international trial of nasal oxygen therapy after cardiac surgery (NOTACS) in patients at high risk of postoperative pulmonary complications: Economic evaluation protocol and analysis plan.

High-Flow Nasal Therapy (HFNT) is an innovative non-invasive form of respiratory support. Compared to standard oxygen therapy (SOT), there is an equipoise regarding the effect of HFNT on patient-centred outcomes among those at high risk of developing postoperative pulmonary complications after undergoing cardiac surgery. The NOTACS trial aims to determine the clinical and cost-effectiveness of HFNT compared to SOT within 90 days of surgery in the United Kingdom, Australia, and New Zealand. This protocol describes the methods and analyses planned for economic evaluation embedded within the ongoing NOTACS trial. The economic evaluation will identify, measure and value resources and health outcomes in both trial arms and compare changes in costs with 'days alive and at home' and EQ-5D-5L quality adjusted life years (QALYs) from the perspective most relevant to the decision-making country. Results from pooling data across the trial will use health and social care sector perspective. All patient-specific data including hospital/community care and health outcomes will be collected prospectively. Unit costs will be sourced from national, published or local data. Missing data will be assessed, with values replaced depending on assumed mechanism of missingness, and impact of replacement on cost-effectiveness assessed. Costs and outcomes by trial arm will be presented as components and totals per patient using a range of descriptive statistics. Regression models for costs and effects will account for patient characteristics, quality of life and health service utilization at baseline. Uncertainty in parameters, sampling and heterogeneity will be addressed through deterministic, probabilistic and subgroup analyses to assess the impact of varying methods and assumptions for costs, outcomes and approaches used in base-case analysis. Results will be interpreted using recommended national cost-effectiveness thresholds. The study is registered with ISRCTN (ISRCTN14092678) on 13/05/2020. ISRCTN is a primary registry of the WHO ICTRP network and includes all items from the WHO Trial Registration data set.

Robustness assessment of regressions using cluster analysis typologies: a bootstrap procedure with application in state sequence analysis

BackgroundIn standard Sequence Analysis, similar trajectories are clustered together to create a typology of trajectories, which is then often used to evaluate the association between sequence patterns and covariates inside regression models. The sampling uncertainty, which affects both the derivation of the typology and the associated regressions, is typically ignored in this analysis, an oversight that may lead to wrong statistical conclusions. We propose utilising sampling variation to derive new estimates that further inform on the association of interest.MethodsWe introduce a novel procedure to assess the robustness of regression results obtained from the standard analysis. Bootstrap samples are drawn from the data, and for each bootstrap, a new typology replicating the original one is constructed, followed by the estimation of the corresponding regression models. The bootstrap estimates are then combined using a multilevel modelling framework that mimics a meta-analysis. The fitted values from this multilevel model allow to account for the sampling uncertainty in the inferential analysis. We illustrate the methodology by applying it to the study of healthcare utilisation trajectories in a Swiss cohort of diabetic patients.ResultsThe procedure provides robust estimates for an association of interest, along with 95% prediction intervals, representing the range of expected values if the clustering and associated regressions were performed on a new sample from the same underlying distribution. It also identifies central and borderline trajectories within each cluster. Regarding the illustrative application, while there was evidence of an association between regular lipid testing and subsequent healthcare utilisation patterns in the original analysis, this is not supported in the robustness assessment.ConclusionsInvestigating the relationship between trajectory patterns and covariates is of interest in many situations. However, it is a challenging task with potential pitfalls. Our Robustness Assessment of Regression using Cluster Analysis Typologies (RARCAT) may assist in ensuring the robustness of such association studies. The method is applicable wherever clustering is combined with regression analysis, so its relevance goes beyond State Sequence Analysis.

Sampling the diurnal and annual cycles of the Earth's energy imbalance with constellations of satellite-borne radiometers

Abstract. The Earth's energy imbalance, i.e. the difference between incoming solar radiation and outgoing reflected and emitted radiation, is the one quantity that ultimately controls the evolution of our climate system. However, despite its importance, there is limited knowledge of the exact magnitude of the energy imbalance, and the small net difference of about 1 W m−2 between two large fluxes (approximately 340 W m−2) makes it challenging to measure directly. There has recently been renewed interest in using wide-field-of-view radiometers on board satellites to measure the outgoing radiation, as a possible method for deducing the global annual mean energy imbalance. Here we investigate how to sample in order to correctly determine the global annual mean imbalance and interannual trends, using a limited number of satellites. We simulate satellites in polar (90° inclination), sun-synchronous (98°) and precessing orbits (73, 82°), as well as constellations of these types of satellite orbits. We find that no single satellite provides sufficient sampling, both globally and of the diurnal and annual cycles, to reliably determine the global annual mean. If sun-synchronous satellites are used, at least six satellites are required for an uncertainty below 1 W m−2. One precessing satellite combined with one polar satellite results in root-mean-square errors of 0.08 to 0.10 W m−2, and a combination of two or three polar satellites results in root-mean-square errors of 0.10 or 0.04 W m−2, respectively. In conclusion, at least two satellites that complement each other are necessary to ensure global coverage and achieve a sampling uncertainty well below the current estimate of the energy imbalance.

Online Active Continual Learning for Robotic Lifelong Object Recognition.

In real-world applications, robotic systems collect vast amounts of new data from ever-changing environments over time. They need to continually interact and learn new knowledge from the external world to adapt to the environment. Particularly, lifelong object recognition in an online and interactive manner is a crucial and fundamental capability for robotic systems. To meet this realistic demand, in this article, we propose an online active continual learning (OACL) framework for robotic lifelong object recognition, in the scenario of both classes and domains changing with dynamic environments. First, to reduce the labeling cost as much as possible while maximizing the performance, a new online active learning (OAL) strategy is designed by taking both the uncertainty and diversity of samples into account to protect the information volume and distribution of data. In addition, to prevent catastrophic forgetting and reduce memory costs, a novel online continual learning (OCL) algorithm is proposed based on the deep feature semantic augmentation and a new loss-based deep model and replay buffer update, which can mitigate the class imbalance between the old and new classes and alleviate confusion between two similar classes. Moreover, the mistake bound of the proposed method is analyzed in theory. OACL allows robots to select the most representative new samples to query labels and continually learn new objects and new variants of previously learned objects from a nonindependent and identically distributed (i.i.d.) data stream without catastrophic forgetting. Extensive experiments conducted on real lifelong robotic vision datasets demonstrate that our algorithm, even trained with fewer labeled samples and replay exemplars, can achieve state-of-the-art performance on OCL tasks.

Boosting one-class transfer learning for multiple view uncertain data

Transfer learning can leverage knowledge from source tasks to improve learning on a target task, even when training samples are limited. However, most previous transfer learning approaches focus on a single view of the data and assume no uncertainty in the training samples. To address these limitations, we propose a novel method called boosting one-class transfer learning for multi-view uncertain data (UMTO-SVMs), which handles one-class classification in multi-view data with uncertain information. Our method transfers knowledge containing uncertainty from multiple source tasks to the target task and constrains complementary information across different views to improve consistency. By combining basic classifiers using the Adaboost algorithm, we build a robust classifier. We also design an iterative framework to optimize the method and prove the convergence of the algorithm. Experimental results on three benchmark datasets show that UMTO-SVMs outperform previous one-class classification methods.

Tutorial on Molecular Latent Space Simulators (LSSs): Spatially and Temporally Continuous Data-Driven Surrogate Dynamical Models of Molecular Systems.

The inherently serial nature and requirement for short integration time steps in the numerical integration of molecular dynamics (MD) calculations place strong limitations on the accessible simulation time scales and statistical uncertainties in sampling slowly relaxing dynamical modes and rare events. Molecular latent space simulators (LSSs) are a data-driven approach to learning a surrogate dynamical model of the molecular system from modest MD training trajectories that can generate synthetic trajectories at a fraction of the computational cost. The training data may comprise single long trajectories or multiple short, discontinuous trajectories collected over, for example, distributed computing resources. Provided the training data provide sufficient sampling of the relevant thermodynamic states and dynamical transitions to robustly learn the underlying microscopic propagator, an LSS furnishes a global model of the dynamics capable of producing temporally and spatially continuous molecular trajectories. Trained LSS models have produced simulation trajectories at up to 6 orders of magnitude lower cost than standard MD to enable dense sampling of molecular phase space and large reduction of the statistical errors in structural, thermodynamic, and kinetic observables. The LSS employs three deep learning architectures to solve three independent learning problems over the training data: (i) an encoding of the high-dimensional MD into a low-dimensional slow latent space using state-free reversible VAMPnets (SRVs), (ii) a propagator of the microscopic dynamics within the low-dimensional latent space using mixture density networks (MDNs), and (iii) a generative decoding of the low-dimensional latent coordinates back to the original high-dimensional molecular configuration space using conditional Wasserstein generative adversarial networks (cWGANs) or denoising diffusion probability models (DDPMs). In this software tutorial, we introduce the mathematical and numerical background and theory of LSS and present example applications of a user-friendly Python package software implementation to alanine dipeptide and a 28-residue beta-beta-alpha (BBA) protein within simple Google Colab notebooks.

A Bayesian-Based Credible and Reliable Control Method for Active Vibration Suppression of Structures with Uncertain Parameters

As a classical design method for addressing uncertainty in control systems, robust control is designed with the goal of complete reliability of the control system. Nevertheless, the pursuit of robustness can inadvertently give rise to considerable performance degradation, rendering the resultant closed-loop control system excessively conservative in its design. Reliability-based design methods serve as an effective approach for managing uncertainties, which will achieve a balance between the robustness and performance of the active control system by taking advantage of the characteristic of reliability that allows for a certain level of permissible failure probability. The accurate quantification of uncertainty is the key to achieving reliable control, but common uncertainty quantification methods cannot achieve credible quantification of uncertainty in small samples and update the distribution of new samples. In this paper, a nonprobabilistic Bayesian inference based interval uncertainty quantification method is proposed. This method updates the distribution of interval boundaries and radii by introducing a small number of samples, and obtains interval parameters under a given confidence level. On the basis of uncertainty quantification, the dynamic reliability of the vibration system is derived, and nonprobabilistic reliability is introduced into the design of active controllers through optimization strategies. The reliable control strategy aims to select the optimal controller parameters on a reliable path with a given credibility, in order to solve the problem of overly conservative robust control theory. Two numerical examples were used to verify the feasibility and applicability of this method.

A novel framework for debris flow susceptibility assessment considering the uncertainty of sample selection

The uncertainty arising from random sampling of non-debris flow samples significantly impacts the accuracy of debris flow susceptibility assessments (DFSA). This study introduces a novel uncertainty elimination method, Kernel Density Estimation (KDE), and compares it with Mean and Maximum Probability Analysis (MPA) methods. Furthermore, we investigate the responses of four commonly used machine learning models to sampling uncertainty, comparing two structurally similar models (Random Forest (RF) and Extremely Randomized Trees (ERT)) with two structurally different models (Support Vector Machine (SVM) and Multilayer Perceptron (MLP)). The results indicate that the application of these uncertainty elimination methods can significantly enhance AUC values and zoning accuracy, with the KDE method outperforming the others. Specifically, the AUC values based on KDE for RF, ERT, SVM, and MLP are 0.995, 0.999, 0.999, and 0.853, respectively. The corresponding zoning accuracy for these models is 1.00, 1.00, 1.00, and 0.78, respectively. The study further reveals that the responses to sampling uncertainty vary by model architecture: RF, ERT, and SVM typically exhibit bimodal normal distributions, while the MLP model shows a unimodal distribution. Additionally, MLP is more sensitive to variations in negative samples, whereas RF and ERT are less affected due to the ensemble structure.

An integrated quantitative systems pharmacology virtual population approach for calibration with oncology efficacy endpoints.

In drug development, quantitative systems pharmacology (QSP) models are becoming an increasingly important mathematical tool for understanding response variability and for generating predictions to inform development decisions. Virtual populations are essential for sampling uncertainty and potential variability in QSP model predictions, but many clinical efficacy endpoints can be difficult to capture with QSP models that typically rely on mechanistic biomarkers. In oncology, challenges are particularly significant when connecting tumor size with time-to-event endpoints like progression-free survival while also accounting for censoring due to consent withdrawal, loss in follow-up, or safety criteria. Here, we expand on our prior work and propose an extended virtual population selection algorithm that can jointly match tumor burden dynamics and progression-free survival times in the presence of censoring. We illustrate the core components of our algorithm through simulation and calibration of a signaling pathway model that was fitted to clinical data for a small molecule targeted inhibitor. This methodology provides an approach that can be tailored to other virtual population simulations aiming to match survival endpoints for solid-tumor clinical datasets.

Determining the confidence interval for non-probabilistic surveys: Method proposal and validation

This paper proposes a novel method for determining confidence intervals in non-probabilistic survey samples, addressing the challenge of statistically quantifying uncertainty in such samples. The method utilizes combinatorial calculations to assess the myriad combinations possible in the unsampled population, applying the symmetric property of binomial coefficients to optimize computational efficiency. The proposed approach offers a practical solution, making it feasible to calculate confidence intervals even with large sample sizes. This methodology represents a significant advancement in survey research, providing a tool to evaluate and generalize non-probabilistic data, particularly in contexts where probabilistic sampling is not viable. The paper also validates the method using extensive testing, demonstrating its applicability and effectiveness in real-world scenarios.

Intolerance of uncertainty and psychosis: A systematic review.

Intolerance of uncertainty, the tendency to interpret and react negatively to uncertainty, is a transdiagnostic risk factor for anxiety, depression and eating-related disorders. Given the high comorbidity between anxiety, depression and schizophrenia-spectrum diagnoses (SSDs), there is potential for intolerance of uncertainty to play a role in modulating psychosis symptoms. To address this gap in our understanding, we conducted the first prospectively registered systematic review on intolerance of uncertainty and psychotic symptoms in both people with SSDs and in the general population. Four databases were searched (PsycINFO, Medline, Web of Science and PubMed), which identified ten studies with a total of 1503 participants that measured intolerance of uncertainty and psychosis symptoms. Key findings suggest the following: (1) Intolerance of uncertainty was associated with total negative psychotic symptoms with small-medium effect sizes; (2) intolerance of uncertainty was higher in individuals with an 'at-risk' mental state for psychosis compared to controls; (3) higher intolerance of uncertainty was associated with more individual psychotic symptoms related to delusions and paranoia within clinical and nonclinical samples; and (4) there was mixed evidence for a relationship between intolerance of uncertainty and auditory hallucinations and intolerance of uncertainty and total positive symptoms in clinical samples. Overall, these findings highlight that intolerance of uncertainty may be an important transdiagnostic dimension and potential treatment target for psychotic symptoms such as delusions and paranoia in people with SSDs.

Prototype Relationship Optimization Network for Few‐Shot Learning

AbstractFew‐shot learning (FSL) aims to infer labels for new samples based on a few labeled samples. FSL based on prototype metrics emphasizes the distance between unlabeled sample features and prototypes generated from a few labeled samples. However, due to the limited number of samples and the uncertainty of samples, the discrepancy between prototypes and the center of the real features may lead to metric error. This paper proposes the Prototype Relationship Optimization Network (PRON) to alleviate the prototype bias issue by utilizing prototype relationship optimization. The PRON involves three fundamental processes: (i) Constructing a multi‐layer prototype through multi‐layer feature embedding to enhance prototype representation capabilities; (ii) Utilizing prototype relationship interaction network of multi‐layer prototype forms multi‐layer prototype relationships to weaken the influence of uncertainty and strengthen the discrimination; (iii) Introduces a prototype refinement mechanism in the cascade structure to optimize prototype relationship representation. The inductive standard experimental results on three popular benchmark datasets show that the performance of the proposed method is very competitive and comparable to the state‐of‐the‐art FSL methods. © 2024 Institute of Electrical Engineers of Japan and Wiley Periodicals LLC.

Label-noise learning via uncertainty-aware neighborhood sample selection

Existing deep learning methods often require a large amount of high-quality labeled data. Yet, the presence of noisy labels in the real-world training data seriously affects the generalization ability of the model. Sample selection techniques, the current dominant approach to mitigating the effects of noisy labels on models, use the consistency of sample predictions and observed labels to make clean selections. However, these methods rely heavily on the accuracy of the sample predictions and inevitably suffer when the model predictions are unstable. To address these issues, we propose an uncertainty-aware neighborhood sample selection method. Especially, it calibrates for sample prediction by neighbor prediction and reassigns model attention to the selected samples based on sample uncertainty. By alleviating the influence of prediction bias on sample selection and avoiding the occurrence of prediction bias, our proposed method achieves excellent performance in extensive experiments. In particular, we achieved an average of 5% improvement in asymmetric noise scenarios.

Assessment of whole cartilage surface damage in an osteoarthritis rat model: The Cartilage Roughness Score (CRS) utilizing microcomputed tomography

ObjectiveThis study aims to establish an accurate and robust imaging biomarker for pre-clinical osteoarthritis (OA) research, focusing on early detection of cartilage surface degeneration. MethodUsing 50 male Wistar rats, this study aims to observe Collagenase Induced Osteoarthritis (CIOA) progression through microcomputed x-ray tomography (µCT), histopathological analysis, and gait analysis. A novel parameter, Cartilage Roughness Score (CRS), was developed for assessing cartilage structural damage from µCT data and was compared with histological OARSI Cartilage Degeneration Score (OARSI CDS). Additionally, as CRS maps the full surface, it was used to simulate the level of uncertainty in histological sampling. ResultsCRS and OARSI CDS have a linear relationship. CRS for healthy cartilage is 2.75 (95% CI: 1.14-4.36) and with every 1 unit increase in OARSI, CRS is expected to increase by 0.64 (95% CI: 0.35-0.92). Cartilage degeneration due to CIOA was evident in both histopathological scoring and CRS. However, only CRS was sensitive enough to show consistent damage progression from day 10 to day 60. Furthermore, our simulation for histological sampling suggested that up to 16 coronal slices with 200µm spacing would be needed to accurately represent the full extent of cartilage surface degeneration in a slice wise manner. Gait analysis showed changes solely at eight days post-collagenase injection, normalizing by day 60. ConclusionThe CRS analysis method emerges as a robust tool for cartilage surface damage assessment. This study demonstrates the potential of automatic 3D analysis over the traditional 2D histological approach when evaluating cartilage surface damage. Data statementMicro-computed tomography data is available via ida.fairdata.fi46 (https://doi.org/10.23729/f33d3ba8-01b8-47af-90dd-94b7c7861247)

Addressing multiple facets of bias and uncertainty in continental scale biodiversity databases

The availability of biodiversity databases is expanding at unprecedented rates. Nevertheless, species occurrence data can be intrinsically biased and contain uncertainties that impact the accuracy and reliability of biodiversity estimates. In this study, we developed a reproducible framework to assess three dimensions of bias—taxonomic, spatial, and temporal—as well as temporal uncertainty associated with data collections. We utilized the vegetation plot data located in Europe, from sPlotOpen, an open-access database, as a case study. The metrics proposed for estimating bias include completeness of the species richness for taxonomic bias, Nearest Neighbor Index for spatial bias, and Pielou’s index for temporal bias. Additionally, we introduced a new method based on a negative exponential curve to model the temporal decay in biodiversity data, aiming to quantify temporal uncertainty. Finally, we assessed the sampling bias considering the influence of various spatial variables (i.e, road density, human population count, Natura 2000 network and topographic roughness). We discovered that the facets of bias and the temporal uncertainty varied throughout Europe, as did the different roles played by spatial variables in determining biases. sPlotOpen showed a clustered distribution of the vegetation plots, and an uneven distribution in sampling completeness, year of sampling and temporal uncertainty. The facets of bias were significantly explained mainly by the presence of Natura 2000 network and marginally by the human population count. These results suggest that employing an efficient procedure to examine biases and uncertainties in data collections can enhance data quality and provide more reliable biodiversity estimates.

On the use of dioxane as reference for determination of the hydrodynamic radius by NMR spectroscopy

Measuring the compaction of a protein or complex is key to our understanding of the interactions within and between biomolecules. Experimentally, protein compaction is often probed either by estimating the radius of gyration (Rg) obtained from small-angle x-ray scattering (SAXS) experiments or the hydrodynamic radius (Rh) obtained, for example, by pulsed field gradient NMR (PFG NMR) spectroscopy. PFG NMR experiments generally report on the translational diffusion coefficient, which in turn can be used to estimate Rh using an internal standard to account for sample viscosity and uncertainty about the gradient strength. 1,4-Dioxane is one such commonly used internal standard, and the reference value of Rh is therefore important. We have revisited the basis for the commonly used reference value for the Rh of dioxane (2.12 Å) that is used to convert measured diffusion coefficients into a hydrodynamic radius. We followed the same approach that was used to establish the current reference value by measuring SAXS and PFG NMR data for a set of seven different proteins and using these as standards. Our analysis shows that the current Rh reference value for dioxane Rh is underestimated, and we instead suggest a new value of 2.27 ± 0.04 Å. Using this updated reference value results in a ∼7% increase in Rh values for proteins whose hydrodynamic radii have been measured by PFG NMR. These results are particularly important when the absolute value of Rh is of interest such as when determining or validating ensemble descriptions of intrinsically disordered proteins.