Sources Of Systematic Error Research Articles

Non-singlet quark helicity PDFs of the nucleon from pseudo-distributions

The non-singlet helicity quark parton distribution functions (PDFs) of the nucleon are determined from lattice QCD, by jointly leveraging pseudo-distributions and the distillation spatial smearing paradigm. A Lorentz decomposition of appropriately isolated space-like matrix elements reveals pseudo-distributions that contain information on the leading-twist helicity PDFs, as well as an invariant amplitude that induces an additional z2 contamination of the leading-twist signal. An analysis of the short-distance behavior of the space-like matrix elements using matching coefficients computed to next-to-leading order (NLO) exposes the desired PDF up to this additional z2 contamination. Due to the non-conservation of the axial current, we elect to isolate the helicity PDFs normalized by the nucleon axial charge at the same scale μ2. The leading-twist helicity PDFs as well as several sources of systematic error, including higher-twist effects, discretization errors, and the aforementioned z2 contaminating amplitude are jointly determined by characterizing the computed pseudo-distribution in a basis of Jacobi polynomials. The Akaike Information Criterion is exploited to effectively average over distinct model parameterizations and cuts on the pseudo-distribution. Encouraging agreement is observed with recent global analyses of each non-singlet quark helicity PDF, notably a rather small non-singlet anti-quark helicity PDF for all quark momentum fractions.

Addressing Systematics in the Traceback Age of the β Pictoris Moving Group

We characterize the impact of several sources of systematic errors on the computation of the traceback age of the β Pictoris moving group (βPMG). We find that uncorrected gravitational redshift and convective blueshift bias absolute radial velocity measurements by ∼0.6 km s−1, which leads to erroneously younger traceback ages by ∼2 Myr. Random errors on parallax, proper motion, and radial velocity measurements lead to an additional bias of ∼0.6 Myr on traceback ages. Contamination of astrometric and kinematic data by kinematic outliers and unresolved multiple systems in the full input sample of 76 members and candidates of βPMG also erroneously lowers traceback ages by ∼3 Myr. We apply our new numerical traceback analysis tool to a core sample of 25 carefully vetted members of βPMG using Gaia Data Release 3 data products and other kinematic surveys. Our method yields a corrected age of 20.4 ± 2.5 Myr, bridging the gap between kinematic ages (11–19 Myr) and other age-dating methods, such as isochrones and lithium depletion boundary (20–26 Myr). We explore several association size metrics that can track the spatial extent of βPMG over time, and we determine that minimizing the variance along the heliocentric curvilinear coordinate (i.e., toward the Galactic Center) offers the least random and systematic errors, due to the wider UVW space velocity dispersion of members of βPMG along the U-axis, which tends to maximize the spatial growth of the association along the -axis over time.

Filaments in the OMC-3 cloud and uncertainties in estimates of filament profiles

Context.Filamentary structures are an important part of star-forming interstellar clouds. The properties of filaments hold clues to their formation mechanisms and their role in the star-formation process.Aims.We compare the properties of filaments in the Orion Molecular Cloud 3 (OMC-3), as seen in mid-infrared (MIR) absorption and far-infrared (FIR) dust emission. We also wish to characterise some potential sources of systematic errors in filament studies.Methods.We calculated optical depth maps of the OMC-3 filaments based on the MIR absorption seen inSpitzerdata and FIR dust emission observed withBerscheland the ArTéMiS instrument. We then compared the filament properties extracted from the data. Potential sources of error were investigated more generally with the help of radiative transfer models.Results.The widths of the selected OMC-3 filament segments are in the range 0.03–0.1 pc, with similar average values seen in both MIR and FIR analyses. Compared to the widths, the individual parameters of the fitted Plummer functions are much more uncertain. The asymptotic power-law index has typically valuesp ~3 but with a large scatter. Modelling shows that the FIR observations can systematically overestimate the filament widths. The effect is potentially tens of per cent at column densities aboveN(H2) ~ 1022cm–2but is reduced in more intense radiation fields, such as the Orion region. Spatial variations in dust properties could cause errors of similar magnitude. In the MIR analysis, dust scattering should generally not be a significant factor, unless there are high-mass stars nearby or the dust MIR scattering efficiency is higher than in the tested dust models. Thermal MIR dust emission can be a more significant source of error, especially close to embedded sources.Conclusions.The analysis of interstellar filaments can be affected by several sources of systematic error, but mainly at high column densities and, in the case of FIR observations, in weak radiation fields. The widths of the OMC-3 filaments were consistent between the MIR and FIR analyses and did not reveal any systematic dependence on the angular resolution of the observations.

A cross-correlation analysis of CMB lensing and radio galaxy maps

Aims. The goal of this work is to clarify the origin of the seemingly anomalously large clustering signal detected at large angular separation in the wide TGSS radio survey and, in so doing, to investigate the nature and the clustering properties of the sources that populate the radio sky in the [0.15, 1.4] GHz frequency range. Methods. To achieve this goal, we cross-correlated the angular position of the radio sources in the TGSS and NVSS samples with the cosmic microwave background (CMB) lensing maps from the Planck satellite. A cross-correlation between two different tracers of the underlying mass density field has the advantage of being quite insensitive to possible systematic errors that may affect the two observables, provided that they are not correlated, which seems unlikely in our case. The cross-correlation analysis was performed in harmonic space and limited to relatively modest multipoles. These choices, together with that of binning the measured spectra, minimize the correlation among the errors in the measured spectra and allowed us to adopt the Gaussian hypothesis to perform the statistical analysis. Finally, we decided to consider the auto-angular power spectrum on top of the cross-spectrum since a joint analysis has the potential to improve the constraints on the radio source properties by lifting the degeneracy between the redshift distribution, N(z), and the bias evolution, b(z). Results. The angular cross-correlation analysis does not present the power excess at large scales for TGSS and provides a TGSS–CMB lensing cross-spectrum that is in agreement with the one measured using the NVSS catalog. This result strongly suggests that the excess found in TGSS clustering analyses can be due to uncorrected systematic effects in the data. However, we considered several cross-spectra models that rely on physically motivated combinations of N(z) and b(z) prescriptions for the radio sources and find that they all underestimate the amplitude of the measured cross-spectra on the largest angular scales considered in our analysis, ∼10°. This result is robust to the various potential sources of systematic errors, both of observational and theoretical nature, that may affect our analysis, including the uncertainties in the N(z) model. Having assessed the robustness of the results to the choice of N(z), we repeated the analysis using simpler bias models specified by a single free parameter, bg, namely, the value of the effective bias of the radio sources at redshift zero. This improves the goodness of the fit, although not even the best model, which assumes a non-evolving bias, quite matches the amplitude of the cross-spectrum at small multipoles. Moreover, the best fitting bias parameter, bg = 2.53 ± 0.11, appears to be somewhat large considering that it represents the effective bias of a sample that is locally dominated by mildly clustered star-forming galaxies and Fanaroff-Riley class I sources. Interestingly, it is the addition of the angular auto-spectrum that favors the constant bias model over the evolving one. Conclusions. The nature of the large cross-correlation signal between the radio sources and the CMB lensing maps found in our analysis at large angular scales is not clear. It probably indicates some limitation in the modeling of the radio sources, namely the relative abundance of the various populations, their clustering properties, and how these evolve with redshift. What our analysis does show is the importance of combining the auto-spectrum with the cross-spectrum, preferably obtained with unbiased tracers of the large-scale structure, such as CMB lensing, for answering these questions.

Measurement of Telescope Transmission Using a Collimated Beam Projector

With the increasingly large number of Type Ia supernova being detected by current-generation survey telescopes, and even more expected with the upcoming Rubin Observatory Legacy Survey of Space and Time, the precision of cosmological measurements will become limited by systematic uncertainties in flux calibration rather than statistical noise. One major source of systematic error in determining SNe Ia color evolution (needed for distance estimation) is uncertainty in telescope transmission, both within and between surveys. We introduce here the Collimated Beam Projector (CBP), which is meant to measure a telescope transmission with collimated light. The collimated beam more closely mimics a stellar wave front as compared to flat-field-based instruments, allowing for more precise handling of systematic errors such as those from ghosting and filter angle-of-incidence dependence. As a proof of concept, we present CBP measurements of the StarDICE prototype telescope, achieving a standard (1σ) uncertainty of 3% on average over the full wavelength range measured with a single beam illumination.

A simple trick to improve the accuracy of PIV/PTV data

Particle Image Velocimetry (PIV) estimates velocities through correlations of particle images within interrogation windows, leading to a spatial modulation of the velocity field. Although in principle Particle Tracking Velocimetry (PTV) estimates locally non-modulated particle displacements, to exploit the scattered data from PTV it is necessary to interpolate these data on a structured grid, which implies a spatial modulation effect that biases the resulting velocity field. This systematic error due to finite spatial resolution inevitably depends on the interrogation window size and on the interparticle spacing. It must be observed that all these operations (cross-correlation, direct interpolation or averaging in windows) induce modulation on both the mean and the fluctuating part. We introduce a simple trick to reduce this systematic error source of PIV/PTV measurements exploiting ensemble statistics. Ensemble Particle Tracking Velocimetry (EPTV) can be leveraged to obtain the high-resolution mean flow by merging the different instantaneous realisations. The mean flow can be estimated with EPTV, and the fluctuating part can be measured from PIV/PTV. The high-resolution mean can then be superposed to the instantaneous fluctuating part to obtain velocity fields with lower systematic error. The methodology is validated against datasets with a progressively increasing level of complexity: two virtual experiments based on direct numerical simulations (DNS) of the wake of a fluidic pinball and a channel flow and the experimental data of a turbulent boundary layer. For all the cases both PTV and PIV are analysed.

Systematic Errors of Electric Field Measurements in Ferroelectrics by Unit Cell Averaged Momentum Transfers in STEM.

When using the unit cell average of first moment data from four-dimensional scanning transmission electron microscopy (4D-STEM) to characterize ferroelectric materials, a variety of sources of systematic errors needs to be taken into account. In particular, these are the magnitude of the acceleration voltage, STEM probe semi-convergence angle, sample thickness, and sample tilt out of zone axis. Simulations show that a systematic error of calculated electric fields using the unit cell averaged momentum transfer originates from violation of point symmetry within the unit cells. Thus, values can easily exceed those of potential polarization-induced electric fields in ferroelectrics. Importantly, this systematic error produces deflection gradients between different domains seemingly representing measured fields. However, it could be shown that for PbZr0.2Ti0.8O3, many adjacent domains exhibit a relative crystallographic mistilt and in-plane rotation. The experimental results show that the method gives qualitative domain contrast. Comparison of the calculated electric field with the systematic error showed that the domain contrast of the unit cell averaged electric fields is mainly caused by dynamical scattering effects and the electric field plays only a minor role, if present at all.

Calibration of machine platform nonlinearity in Instrumented Indentation Test in the macro range

Instrumented Indentation Test (IIT) is a non-conventional mechanical characterization technique to evaluate hardness, Young modulus, creep and relaxation of materials. In the macro range, it represents a cheaper and faster alternative to conventional tensile-based tests. IIT is a metrological scale; thus, to establish traceability, calibration is essential. Frame compliance calibration is critical because it is a major contribution to the measurement uncertainty. This work discusses the limits of the current state-of-the-art and proposes a novel methodology for frame compliance calibration. The introduced approach demonstrates the source of common systematic errors in the mechanical characterization reported in the literature, i.e. edge effect, while first highlighting a relevant frame compliance nonlinearity. The proposed procedure is cost-effective and relies upon constitutive spring modelling of IIT and calibration of reference block by nanoindentation. Results show that the novel approach corrects systematic trends in the characterization and yields a relative measurement uncertainty of 5%.

Sources of systematic errors in human path integration.

Triangle completion is a task widely used to study human path integration, an important navigation method relying on idiothetic cues. Systematic biases (compression patterns in the inbound responses) have been well documented in human triangle completion. However, the sources of systematic biases remain controversial. We used cross-validation modeling to compare three plausible theoretical models that assume that systematic errors occur in the encoding outbound path solely (encoding-error model), executing the inbound responses solely (execution-error model), and both (bicomponent model), respectively. The data for cross-validation modeling are from a previous study (Qi et al., 2021), in which participants learned three objects' locations (one at the path origin, that is, home) very well before walking each outbound path and then pointed to the objects' original locations after walking the outbound path. The modeling algorithm used one inbound response (i.e., response to the home) or multiple inbound responses (i.e., responses to two nonhome locations and the home) for each outbound path. The algorithm of using multiple inbound responses demonstrated that the bicomponent model outperformed the other models in accounting for the systematic errors. This finding suggests that both encoding the outbound path and executing the inbound responses contribute to the systematic biases in human path integration. In addition, the results showed that the algorithm using only the home response could not distinguish among these 3 models, suggesting that the typical triangle-completion task with only the home response for each outbound path cannot determine the sources of the systematic biases. (PsycInfo Database Record (c) 2022 APA, all rights reserved).

Accuracy of Measurements of Thermophysical Parameters by Dual-Beam Thermal-Lens Spectrometry.

Thermal-lens spectrometry is a sensitive technique for determination of physicochemical properties and thermophysical parameters of various materials including heterogeneous systems and nanoparticles. In this paper, we consider the issues of the correctness (trueness) of measurements of the characteristic time of the thermal-lens effect and, thus, of the thermal diffusivity determined by dual-beam mode-mismatching thermal lensing. As sources of systematic errors, major factors-radiation sources, sample-cell and detector parameters, and general measurement parameters-are considered using several configurations of the thermal-lens setups, and their contributions are quantified or estimated. Furthermore, with aqueous ferroin and Sudan I in ethanol as inert colorants, the effects of the intermolecular distance of the absorbing substance on the correctness of finding the thermophysical parameters are considered. The recommendations for checking the operation of the thermal-lens setup to ensure the maximum accuracy are given. The results obtained help reducing the impact of each investigated factor on the value of systematic error and correctly measure the thermophysical parameters using thermal-lens spectrometry.

Skinfold calipers: which instrument to use?

The considerable amount of original and generic types of skinfold calipers available is a source of systematic measurement error. This study is a brief report that critically examines the original and illustrated structural configuration of the three main types of skinfold calipers. For more than half a century, the Harpenden®, Lange® and Slim Guide® skinfolds calipers have been widely used in clinical and research settings. It is well established that the physical, mechanical and functional specificity of each type of skinfold caliper makes its interchangeable use impossible. Our report suggests that commercially available technical specifications are insufficient to judiciously choose a skinfold caliper. The area of the jaws, the coefficient of spring and the static and dynamic downward pressure of each type of skinfold caliper must be determined in the metrological laboratory and added to the technical user manual. Choosing a type of skinfold caliper for regular use, without conflict of commercial interest, requires a critical understanding of the physical, mechanical and functional characteristics that configure it. Therefore, a new downward static calibration test and the first eligibility flowchart for a skinfold caliper have been proposed. Finally, the information gathered in this report may be useful for manufacturers of anthropometric instruments and health professionals who use the skinfold technique as a tool for diagnosis and nutritional control.

Probing Galactic variations in the fine-structure constant using solar twin stars: methodology and results

ABSTRACT The rich absorption spectra of Sun-like stars are enticing probes for variations in the fine-structure constant, α, which gauges the strength of electromagnetism. While individual line wavelengths are sensitive to α, they are also sensitive to physical processes in the stellar atmospheres, which has precluded their use so far. Here we demonstrate a new differential approach using solar twins: velocity separations between close pairs of transitions are compared across stars with very similar physical properties, strongly suppressing astrophysical and instrumental systematic errors. We utilize 423 archival exposures of 18 solar twins from the High-Accuracy Radial velocity Planetary Searcher (HARPS), in which calibration errors can be reduced to ≲3 m s−1. For stars with ≈10 high-signal-to-noise ratio spectra (≥200 per pixel), velocity separations between pairs are measured with ≈10 m s−1 statistical precision. A companion paper assesses a range of systematic error sources using 130 stars, with a greater range of stellar parameters, providing accurate corrections for astrophysical effects and a residual, intrinsic star-to-star scatter of 0–13 m s−1. Within these uncertainties, we find no evidence for velocity separation differences in 17 transition pairs between solar twins. In a second companion paper, this is found to limit local (≲50 pc) variations in α to ≈50 parts per billion, ∼2 orders of magnitude less than other Galactic constraints.

Swarm Thermal Ion Imager measurement performance

We assess the performance of the thermal ion imaging (TII) technique as conceived for the Swarm Earth Explorer satellites. Analysis, simulation, and laboratory testing performed prior to flight provided estimates of systematic and random error sources of the electric field instrument’s vector ion drift, electric field, and ion kinetic temperature measurements. An end-to-end instrument simulator, consisting of models of the TIIs on a prototypical Swarm satellite orbiting Earth with ionospheric plasma, electric field, and magnetic field inputs, was used to generate TII sensor data (level 0 instrument data). These data were processed with a prototype processor (the level 1b processor) to characterize theoretical measurement performance. We describe the methodology used to assess TII measurement uncertainty and present the main findings of the end-to-end measurement performance study. In addition, we assess the measurement performance achieved during approximately eight years of orbital operations. Example measurements demonstrate the quality of ion drift velocity. Unprocessed TII imagery reveals spurious signals which can affect measurement performance. Availability of such imagery has proven vital for diagnosing measurement anomalies associated with sensor operation and spacecraft–plasma interactions.Graphical

Supplemental Material for Sources of Systematic Errors in Human Path Integration

Supplemental Material for Sources of Systematic Errors in Human Path Integration

Deblending Galaxies with Generative Adversarial Networks

Deep generative models including generative adversarial networks (GANs) are powerful unsupervised tools in learning the distributions of data sets. Building a simple GAN architecture in PyTorch and training on the CANDELS data set, we generate galaxy images with the Hubble Space Telescope (HST) resolution starting from a noise vector. We proceed by modifying the GAN architecture to improve Subaru Hyper Suprime-Cam (HSC) ground-based images by increasing their resolution to the HST resolution. We use the super-resolution GAN on a large sample of blended galaxies, which we create using CANDELS cutouts. In our simulated blend sample, ∼20% would unrecognizably be blended even in the HST-resolution cutouts. In the HSC-like cutouts this fraction rises to ∼90%. With our modified GAN we can lower this value to ∼50%. We quantify the blending fraction in the high, low, and GAN resolutions over the whole manifold of angular separation, flux ratios, sizes, and redshift difference between the two blended objects. The two peaks found by the GAN deblender result in improvement by a factor of 10 in the photometry measurement of the blended objects. Modifying the architecture of the GAN, we also train a multiwavelength GAN with HST cutouts in seven optical + near-infrared bands. This multiwavelength GAN improves the fraction of detected blends by another ∼10% compared to the single-band GAN. This is most beneficial to the current and future precision cosmology experiments (e.g., LSST, SPHEREx, Euclid, Roman), specifically those relying on weak gravitational lensing, where blending is a major source of systematic error.

Data-Driven Calibration Algorithm and Pre-Launch Performance Simulations for the SWOT Mission

The Surface Water and Ocean Topography (SWOT) mission will be affected by various sources of systematic errors, which are correlated in space and in time. Their amplitude before calibration might be as large as tens of centimeters, i.e., able to dominate the mission error budget. To reduce their magnitude, we developed so-called data-driven (or empirical) calibration algorithms. This paper provided a summary of the overall problem, and then presented the calibration framework used for SWOT, as well as the pre-launch performance simulations. We presented two complete algorithm sequences that use ocean measurements to calibrate KaRIN globally. The simple and robust Level-2 algorithm was implemented in the ground segment to control the main source of error of SWOT’s hydrology products. In contrast, the more sophisticated Level-3 (multi-mission) algorithm was developed to improve the accuracy of ocean products, as well as the one-day orbit of the SWOT mission. The Level-2 algorithm yielded a mean inland error of 3–6 cm, i.e., a margin of 25–80% (of the signal variance) with respect to the error budget requirements. The Level-3 algorithm yielded ocean residuals of 1 cm, i.e., a variance reduction of 60–80% with respect to the Level-2 algorithm.

TDCOSMO

The largest source of systematic errors in the time-delay cosmography method likely arises from the lens model mass distribution, where an inaccurate choice of model could in principle bias the value of H0. A Bayesian hierarchical framework has been proposed which combines lens systems with kinematic data, constraining the mass profile shape at a population level. The framework has been previously validated using a small sample of lensing galaxies drawn from hydro-simulations. The goal of this work is to expand the validation to a more general set of lenses consistent with observed systems, as well as confirm the capacity of the method to combine two lens populations: one which has time delay information and one which lacks time delays and has systematically different image radii. For this purpose, we generated samples of analytic lens mass distributions made of baryons+dark matter and fit the subsequent mock images with standard power-law models. Corresponding kinematics data were also emulated. The hierarchical framework applied to an ensemble of time-delay lenses allowed us to correct the H0 bias associated with model choice to find H0 within 1.5σ of the fiducial value. We then combined this set with a sample of corresponding lens systems which have no time delays and have a source at lower z, resulting in a systematically smaller image radius relative to their effective radius. The hierarchical framework has successfully accounted for this effect, recovering a value of H0 which is both more precise (σ ∼ 2%) and more accurate (0.7% median offset) than the time-delay set alone. This result confirms that non-time-delay lenses can nonetheless contribute valuable constraining power to the determination of H0 via their kinematic constraints, assuming they come from the same global population as the time-delay set.

A Structural Solution for Task Management in a Resident-Directed, Team-Based Radiotherapy Clinic

<h3>Purpose/Objective(s)</h3> The radiation oncology service at our urban safety net hospital is high volume and organized into a series of resident-directed Teams covering various disease sites. As configured in our OIS, task management was difficult, and OIS-related miscommunication led to rushed/excess work and risked patient impact. An initiative was started to reduce the incidence of such miscommunication and associated sequelae. <h3>Materials/Methods</h3> A root cause analysis was performed. Clinical and OIS processes were mapped and failure modes assessed. While the clinic was organized into Teams, the OIS was not, and manual assignment of users to tasks was required. This was time consuming and error prone, with errors most common after residents rotated, during cross coverage, and with long intervals between consultation and simulation. Scheduling therapists often scheduled the incorrect resident to at least one task. Multiple attendings had patients on any given Team, but each was unable to see the entire Team's tasks. Tasks associated to specific residents had to be accounted for after they switched rotations. OIS functionality was such that only attendings could be automatically assigned to tasks and that individual tasks could not be assigned to multiple user groups. An alternative solution was developed involving a specific naming schema for tasks, creation of virtual resources for task assignment representing Teams and key user groups, and procurement of Team-specific VOIP phones. <h3>Results</h3> The Team concept was integrated into the OIS, and missed tasks and other OIS-related miscommunication are no longer a common reason for process failure. A minimum set of actions necessary to meet needs was codified into a set of Team-based clinical pathways. Task naming used the convention "<responsible group> - <task>." Tasks assigned to Team resources allowed rapid Team-specific, user group-specific identification of rate-limiting actions when sorted alphabetically. This also allowed transparency into the status of key activities performed by all user groups. Attendings maintained an accurate personal list. The updated system was reliable, required fewer actions, and reduced cognitive demand for all users. For schedulers, the minimum number of clicks required went from 25 to 5 and the minimum number of choices went from 8 to 1. Work to determine which resident to schedule was eliminated as therapists could rely on the less variable Team concept. A forcing function detected likely failure modes of wrong attending and wrong Team. Team-specific VOIP phones allowed the correct resident to be contacted no matter their physical location while minimizing interruptions to co-residents. <h3>Conclusion</h3> A novel implementation of virtual task lists improved quality by eliminating systematic sources of error and excess work.

Static quark potential from center vortices in the presence of dynamical fermions

For the first time, center vortices are identified on SU(3) lattice ensembles that include dynamical fermions. Using a variational method, the static quark potential is calculated on untouched, vortex-removed, and vortex-only fields. Two dynamical ensembles and one pure gauge ensemble are studied, allowing for an exploration of the impact of dynamical fermions on the center-vortex vacuum. Novel modifications to the standard Coulomb term are introduced to describe the long range behavior of the vortex-removed potential. These modifications remove a source of systematic error in the fitted string tension on the original ensembles. Our pure Yang-Mills result is consistent with previous studies, where projected center-vortex fields only reproduce approximately two thirds of the string tension. Remarkably, we find that the vortex-only fields on both dynamical lattices are able to fully reproduce the respective untouched string tensions.

MICROSCOPE: systematic errors

The MICROSCOPE mission aims to test the weak equivalence principle (WEP) in orbit with an unprecedented precision of 10−15 on the Eötvös parameter thanks to electrostatic accelerometers on board a drag-free micro-satellite. The precision of the test is determined by statistical errors, due to the environment and instrument noises, and by systematic errors to which this paper is devoted. Systematic error sources can be divided into three categories: external perturbations, such as the residual atmospheric drag or the gravity gradient at the satellite altitude, perturbations linked to the satellite design, such as thermal or magnetic perturbations, and perturbations from the instrument internal sources. Each systematic error is evaluated or bounded in order to set a reliable upper bound on the WEP parameter estimation uncertainty.