Statistical Uncertainty Research Articles

The Dark Energy Survey Supernova Program: Cosmological Analysis and Systematic Uncertainties

We present the full Hubble diagram of photometrically classified Type Ia supernovae (SNe Ia) from the Dark Energy Survey supernova program (DES-SN). DES-SN discovered more than 20,000 SN candidates and obtained spectroscopic redshifts of 7000 host galaxies. Based on the light-curve quality, we select 1635 photometrically identified SNe Ia with spectroscopic redshift 0.10 < z < 1.13, which is the largest sample of supernovae from any single survey and increases the number of known z > 0.5 supernovae by a factor of 5. In a companion paper, we present cosmological results of the DES-SN sample combined with 194 spectroscopically classified SNe Ia at low redshift as an anchor for cosmological fits. Here we present extensive modeling of this combined sample and validate the entire analysis pipeline used to derive distances. We show that the statistical and systematic uncertainties on cosmological parameters are σΩM,stat+sysΛCDM= 0.017 in a flat ΛCDM model, and (σΩM,σw)stat+syswCDM = (0.082, 0.152) in a flat wCDM model. Combining the DES SN data with the highly complementary cosmic microwave background measurements by Planck Collaboration reduces by a factor of 4 uncertainties on cosmological parameters. In all cases, statistical uncertainties dominate over systematics. We show that uncertainties due to photometric classification make up less than 10% of the total systematic uncertainty budget. This result sets the stage for the next generation of SN cosmology surveys such as the Vera C. Rubin Observatory's Legacy Survey of Space and Time.

Modeling the oxygen effect in DNA strand break induced by gamma-rays with TOPAS-nBio

Objective.To present and validate a method to simulate from first principles the effect of oxygen on radiation-induced double-strand breaks (DSBs) using the Monte Carlo Track-structure code TOPAS-nBio.Approach.Two chemical models based on the oxygen fixation hypothesis (OFH) were developed in TOPAS-nBio by considering an oxygen adduct state of DNA and creating a competition kinetic mechanism between oxygen and the radioprotective molecule WR-1065. We named these models 'simple' and 'detailed' due to the way they handle the hydrogen abstraction pathways. We used the simple model to obtain additional information for the •OH-DNA hydrogen abstraction pathway probability for the detailed model. These models were calibrated and compared with published experimental data of linear and supercoiling fractions obtained with R6K plasmids, suspended in dioxane as a hydroxyl scavenger, and irradiated with137Cs gamma-rays. The reaction rates for WR-1065 and O2with DNA were taken from experimental works. Single-Strand Breaks (SSBs) and DSBs as a function of the dose for a range of oxygen concentrations [O2] (0.021%-21%) were obtained. Finally, the hypoxia reduction factor (HRF) was obtained from DSBs.Main Results.Validation results followed the trend of the experimental within 12% for the supercoiled and linear plasmid fractions for both models. The HRF agreed with measurements obtained with137Cs and 200-280 kVp x-ray within experimental uncertainties. However, the HRF at an oxygen concentration of 2.1% overestimated experimental results by a factor of 1.7 ± 0.1. Increasing the concentration of WR-1065 from 1 mM to 10-100 mM resulted in a HRF difference of 0.01, within the 8% statistical uncertainty between TOPAS-nBio and experimental data. This highlights the possibility of using these chemical models to recreate experimental HRF results.Significance.Results support the OFH as a leading cause of oxygen radio-sensitization effects given a competition between oxygen and chemical DNA repair molecules like WR-1065.

Context-Dependent Criteria for Dirichlet Process in Sequential Decision-Making Problems

In models with insufficient initial information, parameter estimation can be subject to statistical uncertainty, potentially resulting in suboptimal decision-making; however, delaying implementation to gather more information can also incur costs. This paper examines an extension of information-theoretic approaches designed to address this classical dilemma, focusing on balancing the expected profits and the information needed to be obtained about all of the possible outcomes. Initially utilized in binary outcome scenarios, these methods leverage information measures to harmonize competing objectives efficiently. Building upon the foundations laid by existing research, this methodology is expanded to encompass experiments with multiple outcome categories using Dirichlet processes. The core of our approach is centered around weighted entropy measures, particularly in scenarios dictated by Dirichlet distributions, which have not been extensively explored previously. We innovatively adapt the technique initially applied to binary case to Dirichlet distributions/processes. The primary contribution of our work is the formulation of a sequential minimization strategy for the main term of an asymptotic expansion of differential entropy, which scales with sample size, for non-binary outcomes. This paper provides a theoretical grounding, extended empirical applications, and comprehensive proofs, setting a robust framework for further interdisciplinary applications of information-theoretic paradigms in sequential decision-making.

A comprehensive inventory of Australia's critical minerals: Simplifying the complexity of critical resources

National inventories of mineral resources invariably exclude critical minerals produced as smelter-refinery by-products due to insufficient data. This study addresses this gap through the development of a comprehensive database of Australia's critical minerals resources in mines and mineral deposits combined with extensive geochemical data analysis. We provide a description of how such a database can be constructed for any country using publicly available information and consider a range of uncertainties arising from the use of proxy data to estimate critical mineral grades. A detailed analysis of Australian critical mineral resource endowments is presented alongside a review and discussion of reporting mechanisms and transparency. Our results show that despite statistical uncertainties, data complexities and limited prior accounting, estimated Australian endowments of a range of critical metals which currently remain unreported are likely to be substantial (e.g., an additional 4.2 Mt Co). This Australian case study suggests that the global development of similar databases is likely to reveal substantially greater endowments of critical metals than previously recognised, providing confidence in the ability to simplify the previously complex assessment of critical minerals required for the modern world's technological needs.

Search for X(3872)→π0π0χc1,2

Using 10.1 fb−1 of e+e− collision data collected by the BESIII detector with center-of-mass energies between 4.15 GeV and 4.30 GeV, we search for the decays X(3872)→π0π0χc1,2, where the X(3872) is produced in e+e−→γX(3872). No evidence above 3σ is found for either decay. Upper limits at the 90% CL on the branching fractions of X(3872)→π0π0χc1,2 normalized to the branching fraction of X(3872)→π+π−J/ψ are set to be B(X(3872)→π0π0χc1)/B(X(3872)→π+π−J/ψ)&lt;1.1 and B(X(3872)→π0π0χc2)/B(X(3872)→π+π−J/ψ)&lt;0.5, taking into account both statistical and systematic uncertainties. Published by the American Physical Society 2024

Methodical evaluation of Boyle temperatures using Mayer sampling Monte Carlo with application to polymers in implicit solvent.

The Boyle temperature, TB, for an n-segment polymer in solution is the temperature where the second osmotic virial coefficient, A2, is zero. This characteristic is of interest for its connection to the polymer condensation critical temperature, particularly for n → ∞. TB can be measured experimentally or computed for a given model macromolecule. For the latter, we present and examine two approaches, both based on the Mayer-sampling Monte Carlo (MSMC) method, to calculate Boyle temperatures as a function of model parameters. In one approach, we use MSMC calculations to search for TB, as guided by the evaluation of temperature derivatives of A2. The second approach involves numerical integration of an ordinary differential equation describing how TB varies with a model parameter, starting from a known TB. Unlike general MSMC calculations, these adaptations are appealing because they neither invoke a reference for the calculation nor use special averages needed to avoid bias when computing A2 directly. We demonstrate these methods by computing TB lines for off-lattice linear Lennard-Jones polymers as a function of chain stiffness, considering chains of length n ranging from 2 to 512 monomers. We additionally perform calculations of single-molecule radius of gyration Rg and determine the temperatures Tθ, where linear scaling of Rg2 with n is observed, as if the polymers were long random-walk chains. We find that Tθ and TB seem to differ by 6% in the n → ∞ limit, which is beyond the statistical uncertainties of our computational methodology. However, we cannot rule out systematic error relating to our extrapolation procedure as being the source of this discrepancy.

Cross Section Evaluation for Exclusive Channels of K+Λ and K+Σ0 Electroproduction off Protons using CLAS Detector Data

In this work, a method for evaluating the cross sections of electroproduction of K+Λ and K+Σ 0 off protons in the region of invariant masses of final hadrons MK + MY &lt; W &lt; 2.65 GeV (MK and MY being the masses of the kaon and hyperon, respectively) and squares of four-momentum transfers of virtual photons, i.e., photon virtualities 0 &lt; Q2 &lt; 5 GeV2 , is developed based on experimental data of these exclusive channels’ cross sections measured by the CLAS detector in Hall B at Jefferson Lab. A set of algorithms has been implemented to evaluate the differential cross sections of these channels, along with their statistical and systematic uncertainties. A program was developed for the evaluation of differential cross sections and structure functions using C++ and Python libraries. An interactive website was created for working with the program, enabling the analysis of one-dimensional and two-dimensional dependences of structure functions and differential cross sections. The evaluation of differential cross sections for the K+Λ and K+Σ 0 electroproduction channels is necessary for extracting the structure function σLT ′ from the data on the polarization asymmetry of electroproduction reactions of these final states with longitudinally polarized electrons. The obtained results are also important for the development of realistic Monte Carlo event generators in planning future experiments and for evaluating the efficiency of detecting final particles when extracting reaction cross sections from experimental data

An interpretable machine learning-based model for shear resistance prediction of CFRP-strengthened RC beams using experimental and synthetic dataset

Existing analytical models for predicting the shear resistance of RC beams strengthened with externally bonded CFRP reinforcements exhibit deficient performance due to their inability to accurately capture the complex resisting mechanisms. Combined with significant statistical uncertainties in shear failure, driven by its brittle nature, this further undermines the reliability of these models. To address these limitations, this study leverages Machine Learning (ML) to develop more robust and reliable predictive tool. A rigorous feature-selection process identified eight predictors as the most influential. Subsequently, nine ML-algorithms were trained on a refined experimental dataset comprising 239 beams, with XGBoost emerging as the top performer. This model also outperformed established models likefib Bulletin-90 and ACI 2023 models. However, the limited scope of the experimental dataset constrained the model’s predictive performance especially when separately evaluated on beams strengthened with U-wraps, full wraps or side-bonded FRP configurations. Therefore, to achieve a more reliable model a synthetic dataset was generated using Tabular Variational Auto-Encoder. The XGBoost model trained with the synthetic dataset significantly improved the performance of the former model and exhibited better predictions for all strengthening configurations. Finally, to ensure the physical consistency of predictions, values obtained from the SHapley Additive exPlanations method were analysed.

System size effects on the free energy landscapes from molecular dynamics of phase-separating bilayers.

The "lipid raft" hypothesis proposes that cell membranes contain distinct domains of varying lipid compositions, where "rafts" of ordered lipids and cholesterol coexist with disordered lipid regions. Experimental and theoretical phase diagrams of model membranes have revealed multiple coexisting phases. Molecular dynamics (MD) simulations can also capture spontaneous phase separation of bilayers. However, these methods merely determine the signof the free energy change upon phase separation-whether or not it is favorable-but not the amplitude. Recently, we developed a workflow to compute the free energy of phase separation from MD simulations using the weighted ensemble method. However, while theoretical treatments generally focus on infinite systems and experimental measurements on mesoscopic to macroscopic systems, MD simulations are comparatively small. Therefore, if we are to put the results of these calculations into the appropriate context, we need to understand the effects the finite size of the simulation has on the computed free energy landscapes. In this study, we investigate this phenomenon by computing free energy profiles for a model phase-separating system as a function of system size, ranging from 324 to 10 110 lipids. The results suggest that, within the limits of statistical uncertainty, bulk-like behavior emerges once the systems contain roughly 4000 lipids.

Statistical estimation of full-sky radio maps from 21cm array visibility data using Gaussian Constrained Realisations

Abstract An important application of next-generation wide-field radio interferometers is making high dynamic range maps of radio emission. Traditional deconvolution methods like CLEAN can give poor recovery of diffuse structure, prompting the development of wide-field alternatives like Direct Optimal Mapping and m-mode analysis. In this paper, we propose an alternative Bayesian method to infer the coefficients of a full-sky spherical harmonic basis for a drift-scan telescope with potentially thousands of baselines, that can precisely encode the uncertainties and correlations between the parameters used to build the recovered image. We use Gaussian Constrained Realisations (GCR) to efficiently draw samples of the spherical harmonic coefficients, despite the very large parameter space and extensive sky-regions of missing data. Each GCR solution provides a complete, statistically-consistent gap-free realisation of a full-sky map conditioned on the available data, even when the interferometer’s field of view is small. Many realisations can be generated and used for further analysis and robust propagation of statistical uncertainties. In this paper, we present the mathematical formalism of the spherical harmonic GCR-method for radio interferometers. We focus on the recovery of diffuse emission as a use case, along with validation of the method against simulations with a known diffuse emission component.

Validation of the OpenMC Code for Fusion Applications: The FNG-Streaming Benchmark Case

In this work, we benchmark OpenMC against the FNG-ITER streaming experiment. FNG-ITER streaming, a high-quality experiment carried out at the ENEA laboratories in Frascati, Italy, was initially included in SINBAD (Shielding Integral Benchmark Archive and Database). More recently, the benchmark was included in the Compilation of Nuclear Data Experiments for Radiation Characterization as well. It consists of a neutron shielding experiment with a rather complex geometry that constitutes an appropriate validation study for the use of weight windows within OpenMC. Measurements include flux detection via four different types of activation foils divided into three batches and a set of thermoluminescent detectors for nuclear heating. The OpenMC results are in very good agreement with those of MCNP and the experimental measurements, with the majority of the discrepancies within the combined statistical error and experimental uncertainty (less than 10% computed measured discrepancy).

Evaluation of aerial thermography for measuring the thermal transmittance (U-value) of a building façade

In efforts to mitigate greenhouse gas emissions in the construction sector, policies promoting energy efficiency improvements in existing buildings are being implemented. Accurately assessing the impact of energy retrofit strategies requires precise determination of thermal envelope performance through energy audits. Aerial thermography, employing unmanned aerial vehicles (UAVs) equipped with infrared thermal cameras (IRT), is an underused method overcoming limitations in energy audits of large buildings or complexes. This approach offers an elevated perspective, providing an overview of the building’s thermal patterns, aiding in the identification of thermal envelope defects. By measuring temperature distribution, even in inaccessible envelope areas, the severity of identified defects can be estimated. Beyond detecting thermal bridges, air leaks, and moisture, aerial thermography is valid for estimating thermal transmittance (U-value) of enclosures. The aim of this research is to evaluate this method to calculate the U-value of the façade of an university building located in a Subtropical Mediterranean climate, during a typical full day in different seasons of the year. Concurrently with aerial thermography, the thermometric method (THM) was applied to compare results and refine the operational conditions during U-value measurement using different statistical indices and uncertainty analysis. The results demonstrated the validation of airborne thermography as a method for U-value calculation under specific meteorological and operational conditions, overcoming the common physical limitations of traditional building audit methods.

Modeling movements improves capture–recapture estimates for mobile species with sparse data: Polar bears (Ursus maritimus) in Viscount Melville sound

AbstractWildlife management requires estimates of demographic parameters that are difficult to obtain for mobile species at low densities. Biased parameter estimates often result from capture–recapture (CR) studies due to small sample sizes and unequal recapture probabilities, the latter of which can be caused by animal movements with respect to the sampling area. We developed a multistate CR model designed to minimize biases by including multiple data types (capture, harvest, natural mortality, and telemetry) and accounting for temporary emigration. We applied the model to data collected intensively from 2012 to 2014, and intermittently since the 1970s, for the Viscount Melville (VM) subpopulation of polar bears (Ursus maritimus) in the Canadian Arctic. The number of bears within the VM subpopulation boundary likely increased from an average of 145 (Bayesian 95% credible interval [CRI] [109, 221]) in 1989–1992 to 235 (95% CRI [148, 569]) in 2012–2014. Survival probability increased for all sex and age classes except adult females, for which estimates declined due to unknown reasons. Polar bear movements exhibited Markovian dependence with approximately 28% of the subpopulation located outside of the sampling area each spring. This contributed to inaccurate parameter estimates when using a simpler, single‐state CR model that only included capture data. Although the interpretation of demographic status was complicated by statistical uncertainty and changes in study design, our findings suggest that—as of 2014—the VM polar bear subpopulation had likely recovered from an earlier period of overharvest, was stable, and had not exhibited detectable negative effects of climate warming.

Mitigating the Binary Viewing Angle Bias for Standard Sirens

The inconsistency between experiments in the measurements of the local Universe expansion rate, the Hubble constant, suggests unknown systematics in the existing experiments or new physics. Gravitational-wave standard sirens, a method to independently provide direct measurements of the Hubble constant, have the potential to address this tension. Before that, it is critical to ensure there are no substantial systematics in the standard siren method. A significant systematic has been identified when the viewing angle of the gravitational-wave sources, the compact binary coalescences, was inferred inaccurately from electromagnetic observations of the sources. Such a systematic has led to a more than 10% discrepancy in the standard siren Hubble constant measurements with the observations of binary neutron star merger, GW170817. In this Letter, we develop a new formalism to infer and mitigate this systematic. We demonstrate that the systematic uncertainty of the Hubble constant measurements can be reduced to a level smaller than their statistical uncertainty with 5, 10, and 20 binary neutron star merger observations. We show that our formalism successfully reduces the systematics even if the shape of the biased viewing angle distribution does not follow precisely the model we choose. Our formalism ensures unbiased standard siren Hubble constant measurements when the binary viewing angles are inferred from electromagnetic observations.

A multi-scale uncertainty quantification model encompassing minimum-size unit cells for effective properties of plain woven composites

The uncertainty quantification is crucial to the high-precision prediction of composites’ effective properties. However, the unclear input uncertainties of multiscale parameters, complex uncertainty propagations of inter-scale correlations, and unaffordable computational cost of massive simulations are three primary problems at present. In this work, an innovative model with high accuracy and feasible cost for the mechanical property prediction of plain woven composites is developed encompassing minimum-size unit cells and multi-scale uncertainty quantification. For the accuracy holding, an uncertainty analysis process consists of the traceability description, inter-scale propagation and quantification is established. The uncertainties of geometry are described by uniform distributions for fiber, fiber bundle and composite scales, respectively; that of constituent properties is described by normal distributions for fiber and matrix, and its propagations to bundle and composite scales are realized by Nataf transformation methods with the consideration of parameter correlations. For the cost control, minimum-size unit cells are formulated by exhaustive analysis of structural symmetries to reduce the computational cost without accuracy compromising for the single simulation, and 1/8 and 1/16 unit cells compared with traditional full-size ones are obtained. The evolution convergence for statistical uncertainties of effective properties is finally obtained with totally reduced computational cost of 89%.

Realistic Uncertainties for Fundamental Properties of Asteroseismic Red Giants and the Interplay between Mixing Length, Metallicity, and νmax

Asteroseismic modeling is a powerful way to derive stellar properties. However, the derived quantities are limited by built-in assumptions used in stellar models. This work presents a detailed characterization of stellar model uncertainties in asteroseismic red giants, focusing on the mixing-length parameter α MLT, the initial helium fraction Y init, the solar abundance scale, and the overshoot parameters. First, we estimate error floors due to model uncertainties to be ≈0.4% in mass, ≈0.2% in radius, and ≈17% in age, primarily due to the uncertain state of α MLT and Y init. The systematic uncertainties in age exceed typical statistical uncertainties, suggesting the importance of their evaluation in asteroseismic applications. Second, we demonstrate that the uncertainties from α MLT can be entirely mitigated by direct radius measurements or partially through νmax . Utilizing radii from Kepler eclipsing binaries, we determined the α MLT values and calibrated the α MLT–[M/H] relation. The correlation observed between the two variables is positive, consistent with previous studies using 1D stellar models, but in contrast with outcomes from 3D simulations. Third, we explore the implications of using asteroseismic modeling to test the νmax scaling relation. We found that a perceived dependency of νmax on [M/H] from individual frequency modeling can be largely removed by incorporating the calibrated α MLT–[M/H] relation. Variations in Y init can also affect νmax predictions. These findings suggest that νmax conveys information not fully captured by individual frequencies, and that it should be carefully considered as an important observable for asteroseismic modeling.

A consistent terminology to communicate ground-related uncertainty

Engineering geology is highly affected by uncertainty related to geology, geotechnical parameters, models and methods. While the technical aspects of ground-related uncertainty are increasingly well investigated, the terminology to communicate uncertainty - e.g., “It is likely that X will happen.” - has not yet been unified and experts use it however they see fit. Due to varying experience, personal biases and societal backgrounds, people may understand uncertainty statements very differently, which is misleading and can even result in legal disputes. This contribution investigates the usage of uncertainty communicating terminology in ground-related disciplines and finds that there is a pronounced prevalence of uncertainty terminology in them. Furthermore, there is a special need to express uncertainty related to quantities (e.g. “most of the project area consists of…”). In response, we propose a framework to consistently communicate ground-related uncertainty encompassing three steps: 1. When you are certain about a statement, do not use uncertainty communicating language. 2. Assess and state the degree of confidence in a statement based on the quantity and quality of the available evidence vs. the agreement of the evidence. 3. If you have high or very high confidence in the statement, communicate the uncertainty in a consistent manner, otherwise elaborate how higher confidence can be achieved. The proposed approach feeds into new uncertainty-aware standards, such as Eurocode 7, and goes beyond them by addressing uncertainty in text and speech. This paper provides the premises for increased awareness of uncertainty communication and encourages further works on the topic.

Shutdown dose rate calculation for fission reactors: An application of the MS-CADIS method to OPAL

There have been considerable advances of shutdown dose rate (SDDR) calculation methods for fusion related problems, however applications of these methods in the fission reactor field have hitherto been sparse. The present study attempts to bridge this gap by investigating the applicability of SDDR calculation methods for fission reactor problems. Specifically, we aim to assess and validate whether recent advances in SDDR methods can be successfully applied in fission research reactors. To this end, we estimate the shutdown dose rate distribution at the Open Pool Australian Light water reactor (OPAL) using the rigorous two step (R2S) computational method, and we compare the calculated results with the experimental data. This method utilizes a 3D reactor model implemented in the Monte Carlo N-Particle (MCNP) transport code, the AutomeD VAriaNce reduction Generator (ADVANTG) code for geometry discretization and variance reduction calculations, and the Oak Ridge Isotope GENeration (ORIGEN) inventory code for activation calculations. To ensure robustness, we employ two variance reduction techniques, Forward Weighted Consistent Adjoint Driven Importance Sampling (FW-CADIS) and Multi-Step Consistent Adjoint Driven Importance Sampling (MS-CADIS). To the best of our knowledge, this is the first MS-CADIS method implementation for fission reactor problems. The SDDR is estimated at ten locations within the experimental hall, all situated more than 4 m away from the reactor core.The paper shows that, the experimental observations are within the lower and upper bounds of the simulation results for 4 out of 10 locations, while the remaining observations are within a factor of 7, with one significant outlier. The calculated average dose rate is within 5% of the nominal values of the experimental observations for 3 locations. The computational results are within statistical uncertainty by using two different variance reduction techniques, with significant computational advantage of MS-CADIS over FW-CADIS for SDDR calculations. The results indicate that the combination of SDDR distribution maps, estimated dose rate energy dependance, and activation information are powerful tools in identifying the radioisotopes and reactor components dominating the SDDR. These results can contribute to better radiation safety practices in contaminated areas, by enabling the minimal dose path planning or by improving radiation shielding.

A comparison of some existing and novel methods for integrating historical models to improve estimation of coefficients in logistic regression

Abstract Model integration refers to the process of incorporating a fitted historical model into the estimation of a current study to increase statistical efficiency. Integration can be challenging when the current model includes new covariates, leading to potential model misspecification. We present and evaluate seven existing and novel model integration techniques, which employ both likelihood constraints and Bayesian informative priors. Using a simulation study of logistic regression, we quantify how efficiency—assessed by bias and variance—changes with the sample sizes of both historical and current studies and in response to violations to transportability assumptions. We also apply these methods to a case study in which the goal is to use novel predictors to update a risk prediction model for in-hospital mortality among pediatric extracorporeal membrane oxygenation patients. Our simulation study and case study suggest that (i) when historical sample size is small, accounting for this statistical uncertainty is more efficient; (ii) all methods lose efficiency when there exist differences between the historical and current data-generating mechanisms; (iii) additional shrinkage to zero can improve efficiency in higher-dimensional settings but at the cost of bias in estimation.

Uncertainty Propagation of Monte Carlo Cross-Section Generation for Graphite-Moderated Pebble Bed Reactors

Monte Carlo codes have become increasingly popular for generating homogenized few-group cross-section data, especially for advanced reactor designs that have complex geometries and nontraditional compositions. However, the stochastic nature of Monte Carlo processes has the potential to introduce additional statistical uncertainties in the overall uncertainty in the prediction of core behavior. The work performed in this research quantified the additional uncertainty introduced by the use of Monte Carlo multigroup cross sections into the analysis of graphite-moderated pebble bed reactors. In this research, the objective was achieved by performing uncertainty quantification for the key output parameters in deterministic steady-state and transient safety calculations. The results show that when the homogenized multigroup cross sections are generated with a sufficient number of neutron histories in the Monte Carlo calculation, the uncertainties in the subsequent deterministic simulations caused by the Monte Carlo cross-section uncertainty are negligible compared to the contributions from the uncertainties of other input parameters.