Contribution of Modeling Differences to Systematic Errors of the Celestial Reference Frame: Modest/Calc/Gloria
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Imaging other planetary systems from the moon
This paper studies the problem of using a telescope like the HST, only larger and sensitive to a wider range of wavelengths, to image systems of planets like the solar system around other stars. Both reflected starlight and thermal radiation from the planets are treated. The instrumental effects of aperture diffraction, scattering due to the power spectral density of telescope mirror surface errors, and telescope thermal emission are included. The integration time required to achieve a signal-to-noise ratio is computed at 5 for photon-statistical random errors only, which is a necessary but not sufficient criterion for detection at a confidence level of five standard deviations. A cold telescope on the moon with 16m aperture and the optical quality of HST could detect and characterize planets around nearby stars.
Brown, Robert A.↗
Cosmic ray records in Antarctic meteorites
The cosmogenic radionuclides Be(10), Al(26), and Mn(53) and noble gases were determined in more than 28 meteorites from Antarctica by nuclear analytical techniques and static mass spectrometry, respectively. The summarized results are listed. The concentrations of Al(26) and Mn(53) are normalized to the repective main target elements and given in dpm/kg Si sub eq and dpm/kg Fe. The errors stated include statistical as well as systematical errors. For noble gas concentrations estimated errors are 5% and for isotopic ratios 1.5%. Cosmic ray exposure ages T sub 21 were calculated by the noble gas concentrations and the terrestrial residence time (T) on the basis of the spallogenic nuclide Al(26). The suggested pairing of the LL6 chondrite RKPA 80238 and RKPA 80248 and the eucrites ALHA 76005 and ALHA 79017 is confirmed not only by the noble gas data but also by the concentrations of the spallation produced radionuclides. Futhermore, ALHA 80122, clasified as an H6 chondrite, has a noble gas pattern which suggest that this meteorite belongs to the ALHA 80111 shower.
Vogt, S.↗
Method for Real-Time Model Based Structural Anomaly Detection
A system and methods for real-time model based vehicle structural anomaly detection are disclosed. A real-time measurement corresponding to a location on a vehicle structure during an operation of the vehicle is received, and the real-time measurement is compared to expected operation data for the location to provide a modeling error signal. A statistical significance of the modeling error signal to provide an error significance is calculated, and a persistence of the error significance is determined. A structural anomaly is indicated, if the persistence exceeds a persistence threshold value.
Smith, Timothy A.↗
Error Convergence Characterization for Stochastic Transport Methods
There has been increased interest in reliably and efficiently solving engineering systems involving uncertainty in recent years. Characterization of the convergence of errors within the problem, including statistical and bias errors, increases confidence that chosen solution methods are appropriate for a particular problem and quantity of interest (QoI), that implementation errors have not been made, and can aid users or algorithms in solving problems within a tolerance efficiently. We demonstrate a method for characterizing error convergence in a simple stochastic transport problem. Though the approach is applicable to problems with more complicated physics, our simple problem enables analytic QoI solutions so that error convergence behavior and the identification of limiting errors can be presented with high precision. A one-dimensional, two-material, neutral-particle, and absorption-only transport problem involving uniformly distributed uncertain total cross sections is presented. Random sampling (RS) and stochastic collocation (SC) are used as stochastic solvers which sample from the uncertain space and Monte Carlo (MC) transport is employed to solve transport results on the resulting realizations. Probability density functions (PDFs) are created using either RS solutions or samples taken from a polynomial chaos expansion (PCE) constructed with SC solutions. The convergence of each solver is characterized with respect to the QoI against analytic solutions, convergence behavior is used to efficiently solve a QoI within a tolerance, and convergence plots are used to identify dominant solution errors.
42 ENGINEERING↗
A search for the dipole anisotropy of the Cosmic x ray background
X ray data was analyzed which was obtained by the HEAO-1 A2 satellite in order to look for large scale structure in the Cosmic X ray Background. The dipole moment of the x ray background is deltaI/I = (1.87 + or - .34)x 10(exp -2) in a direction, declination = 3.6 + or - 9.4 deg and right ascension = 15.9 + or - .2 hr. This implies a velocity of the Earth with respect to the background of 409.2 + or - 74.4 km/s in the same direction. Comparatively, measurements of the dipole anisotropy of the Cosmic Microwave Background imply a velocity of 369.2 + or - 4 km/s in a direction, declination = 6 + or - 1 deg and right ascension = 11.2 + or - .1 hr. Quoted errors are statistical only. The disparity between the velocities of the x ray dipole and microwave dipole may be due to residual structure in the x ray sky or as yet undiscovered systematic errors.
Evans, Tom↗
How Well do Multisatellite Products Capture the Space-Time Dynamics of Precipitation? Part II: Building an Error Model Through Spectral System Identification
Satellite precipitation products, as all quantitative estimates, come with some inherent degree of uncertainty. To associate a quantitative value of the uncertainty to each individual estimate, error modeling is necessary. Most of the error models proposed so far compute the uncertainty as a function of precipitation intensity only, and only at one specific spatio-temporal scale. We propose a spectral error model which accounts for the neighboring space-time dynamics of precipitation into the uncertainty quantification. Systematic distortions of the precipitation signal and random errors are characterized distinctively in every frequency-wavenumber band in the Fourier domain, to accurately characterize error across scales. The systematic distortions are represented as a deterministic space-time linear filtering term. The random errors are represented as a non-stationary additive noise. The spectral error model is applied to the IMERG multi satellite precipitation product and its parameters are estimated empirically through a system identification approach using the GV-MRMS gauge-radar measurements as reference (“truth”) over the eastern United States. The filtering term is found to be essentially low-pass. While traditional error models attribute most of the error variance to random errors, it is found here that the systematic filtering term explains 48% of the error variance at the native resolution of IMERG. This fact confirms that, at high resolution, filtering effects in satellite precipitation products cannot be ignored, and that the error cannot be represented as a purely random additive or multiplicative term. An important consequence is that precipitation estimates derived from totally different sources shall not be expected to automatically have statistically independent errors.
Precipitation↗
Methods for injection-error analysis and their comparison.
Statistical techniques for missile injection error analysis, discussing direct and adjoint methods
STATISTICAL ANALYSIS↗
Axial, scalar, and tensor charges of the nucleon from 2+1+1-flavor Lattice QCD
We present results for the isovector axial, scalar, and tensor charges 𝑔$^{𝑢−𝑑}_{𝐴}$, 𝑔$^{𝑢−𝑑}_{𝑆}$, and 𝑔$^{𝑢−𝑑}_{𝑇}$ of the nucleon needed to probe the Standard Model and novel physics. The axial charge is a fundamental parameter describing the weak interactions of nucleons. The scalar and tensor charges probe novel interactions at the TeV scale in neutron and nuclear 𝛽-decays, and the flavor-diagonal tensor charges 𝑔$^{𝑢}_{𝑇}$, 𝑔$^{𝑑}_{𝑇}$, and 𝑔$^{𝑠}_{𝑇}$ are needed to quantify the contribution of the quark electric dipole moment (EDM) to the neutron EDM. The lattice-QCD calculations were done using nine ensembles of gauge configurations generated by the MILC Collaboration using the highly improved staggered quarks action with 2+1+1 dynamical flavors. These ensembles span three lattice spacings 𝑎 ≈0.06,0.09, and 0.12 fm and light-quark masses corresponding to the pion masses 𝑀 𝜋 ≈ 135,225, and 315 MeV. High-statistics estimates on five ensembles using the all-mode-averaging method allow us to quantify all systematic uncertainties and perform a simultaneous extrapolation in the lattice spacing, lattice volume, and light-quark masses for the connected contributions. Our final estimates, in the $\overline{MS}$ scheme at 2 GeV, of the isovector charges are 𝑔$^{𝑢−𝑑}_{𝐴}$ = 1.195(33)(20), 𝑔$^{𝑢−𝑑}_{𝑆}$ = 0.97(12)(6), and 𝑔$^{𝑢−𝑑}_{𝑇}$ = 0.987(51)(20). The first error includes statistical and all systematic uncertainties except that due to the extrapolation Ansatz, which is given by the second error estimate. Combining our estimate for 𝑔$^{𝑢−𝑑}_{𝑆}$ with the difference of light quarks masses (𝑚 𝑑 − 𝑚 𝑢 ) QCD = 2.67(35) MeV given by the Flavor Lattice Average Group, we obtain (𝑀 𝑁 − 𝑀 𝑃 ) QCD = 2.59(49) MeV.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
Main Geomagnetic Field Models from Oersted and Magsat Data Via a Rigorous General Inverse Theory with Error Bounds
The purpose of the grant was to study how prior information about the geomagnetic field can be used to interpret surface and satellite magnetic measurements, to generate quantitative descriptions of prior information that might be so used, and to use this prior information to obtain from satellite data a model of the core field with statistically justifiable error estimates. The need for prior information in geophysical inversion has long been recognized. Data sets are finite, and faithful descriptions of aspects of the earth almost always require infinite-dimensional model spaces. By themselves, the data can confine the correct earth model only to an infinite-dimensional subset of the model space. Earth properties other than direct functions of the observed data cannot be estimated from those data without prior information about the earth. Prior information is based on what the observer already knows before the data become available. Such information can be "hard" or "soft". Hard information is a belief that the real earth must lie in some known region of model space. For example, the total ohmic dissipation in the core is probably less that the total observed geothermal heat flow out of the earth's surface. (In principle, ohmic heat in the core can be recaptured to help drive the dynamo, but this effect is probably small.) "Soft" information is a probability distribution on the model space, a distribution that the observer accepts as a quantitative description of her/his beliefs about the earth. The probability distribution can be a subjective prior in the sense of Bayes or the objective result of a statistical study of previous data or relevant theories.
Backus, George E.↗
Error Estimation of An Ensemble Statistical Seasonal Precipitation Prediction Model
This NASA Technical Memorandum describes an optimal ensemble canonical correlation forecasting model for seasonal precipitation. Each individual forecast is based on the canonical correlation analysis (CCA) in the spectral spaces whose bases are empirical orthogonal functions (EOF). The optimal weights in the ensemble forecasting crucially depend on the mean square error of each individual forecast. An estimate of the mean square error of a CCA prediction is made also using the spectral method. The error is decomposed onto EOFs of the predictand and decreases linearly according to the correlation between the predictor and predictand. Since new CCA scheme is derived for continuous fields of predictor and predictand, an area-factor is automatically included. Thus our model is an improvement of the spectral CCA scheme of Barnett and Preisendorfer. The improvements include (1) the use of area-factor, (2) the estimation of prediction error, and (3) the optimal ensemble of multiple forecasts. The new CCA model is applied to the seasonal forecasting of the United States (US) precipitation field. The predictor is the sea surface temperature (SST). The US Climate Prediction Center's reconstructed SST is used as the predictor's historical data. The US National Center for Environmental Prediction's optimally interpolated precipitation (1951-2000) is used as the predictand's historical data. Our forecast experiments show that the new ensemble canonical correlation scheme renders a reasonable forecasting skill. For example, when using September-October-November SST to predict the next season December-January-February precipitation, the spatial pattern correlation between the observed and predicted are positive in 46 years among the 50 years of experiments. The positive correlations are close to or greater than 0.4 in 29 years, which indicates excellent performance of the forecasting model. The forecasting skill can be further enhanced when several predictors are used.
Shen, Samuel S. P.↗
Direct CP violation and the ΔI=1/2 rule in K→ππ decay from the standard model
We present a lattice QCD calculation of the Δ I = 1 / 2 , K → π π decay amplitude A 0 and ϵ ' , the measure of direct C P violation in K → π π decay, improving our 2015 calculation [1] of these quantities. Both calculations were performed with physical kinematics on a 32 3 × 64 lattice with an inverse lattice spacing of a - 1 = 1.3784 ( 68 ) GeV . However, the current calculation includes nearly 4 times the statistics and numerous technical improvements allowing us to more reliably isolate the π π ground state and more accurately relate the lattice operators to those defined in the standard model. We find Re ( A 0 ) = 2.99 ( 0.32 ) ( 0.59 ) × 10 - 7 GeV and Im ( A 0 ) = - 6.98 ( 0.62 ) ( 1.44 ) × 10 - 11 GeV , where the errors are statistical and systematic, respectively. The former agrees well with the experimental result Re ( A 0 ) = 3.3201 ( 18 ) × 10 - 7 GeV . These results for A 0 can be combined with our earlier lattice calculation of A 2 [2] to obtain Re ( ϵ ' / ϵ ) = 21.7 ( 2.6 ) ( 6.2 ) ( 5.0 ) × 10 - 4 , where the third error represents omitted isospin breaking effects, and Re ( A 0 ) / Re ( A 2 ) = 19.9 ( 2.3 ) ( 4.4 ) . The first agrees well with the experimental result of Re ( ϵ ' / ϵ ) = 16.6 ( 2.3 ) × 10 - 4 . A comparison of the second with the observed ratio Re ( A 0 ) / Re ( A 2 ) = 22.45 ( 6 ) , demonstrates the standard model origin of this “ Δ I = 1 / 2 rule” enhancement.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
Multidimensional effects in nonadiabatic statistical theories of spin- forbidden kinetics. A case study of 3 O + CO → CO 2
The appropriateness of treating crossing seams of electronic states of different spins as nonadiabatic transition states in statistical calculations of spin-forbidden reaction rates is considered. We show that the spin-forbidden reaction coordinate, the nuclear coordinate perpendicular to the crossing seam, is coupled to the remaining nuclear degrees of freedom. We found that this coupling gives rise to multidimensional effects that are not typically included in statistical treatments of spin-forbidden kinetics. Three qualitative categories of multidimensional effects may be identified: static multidimensional effects due to the geometry-dependence of the local shape of the crossing seam and of the spin–orbit coupling, dynamical multidimensional effects due to energy exchange with the reaction coordinate during the seam crossing, and nonlocal(history-dependent) multidimensional effects due to interference of the electronic variables at second, third, and later seam crossings. Nonlocal multidimensional effects are intimately related to electronic decoherence, where electronic dephasing acts to erase the history of the system. A semiclassical model based on short-time full-dimensional trajectories that includes all three multidimensional effects as well as a model for electronic decoherence is presented. The results of this multidimensional nonadiabatic statistical theory (MNST) for the 3 O + CO → CO 2 reaction are compared with the results of statistical theories employing one-dimensional (Landau–Zener and weak coupling) models for the transition probability and with those calculated previously using multistate trajectories. The MNST method is shown to accurately reproduce the multistate decay-of-mixing trajectory results, so long as consistent thresholds are used. Furthermore, the MNST approach has several advantages over multistate trajectory approaches and is more suitable in chemical kinetics calculations at low temperatures and for complex systems. The error in statistical calculations that neglect multidimensional effects is shown to be as large as a factor of 2 for this system, with static multidimensional effects identified as the largest source of error.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Hadronic light-by-light contribution to the muon anomaly from lattice QCD with infinite volume QED at physical pion mass
The hadronic light-by-light scattering contribution to the muon anomalous magnetic moment, (g–2)/2, is computed in the infinite volume QED framework with lattice QCD. We report $a^{HLbL}_μ$ = 12.47(1.15)(0.95) ×10 –10 where the first error is statistical and the second systematic. The result is mainly based on the 2+1 flavor Möbius domain wall fermion ensemble with inverse lattice spacing a –1 = 1.73 GeV, lattice size L = 5.5 fm, and m π = 139 MeV, generated by the RBC-UKQCD collaborations. The leading systematic error of this result comes from the lattice discretization. This result is consistent with previous determinations.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
Sampling errors in the measurement of rain and hail parameters
Attention is given to a general derivation of the fractional standard deviation (FSD) of any integrated property X such that X(D) = cD to the n. This work extends that of Joss and Waldvogel (1969). The equation is applicable to measuring integrated properties of cloud, rain or hail populations (such as water content, precipitation rate, kinetic energy, or radar reflectivity) which are subject to statistical sampling errors due to the Poisson distributed fluctuations of particles sampled in each particle size interval and the weighted sum of the associated variances in proportion to their contribution to the integral parameter to be measured. Universal curves are presented which are applicable to the exponential size distribution permitting FSD estimation of any parameters from n = 0 to n = 6. The equations and curves also permit corrections for finite upper limits in the size spectrum and a realistic fall speed law.
Gertzman, H. S.↗
A Bayesian Approach for Characterizing and Mitigating Gate and Measurement Errors
Various noise models have been developed in quantum computing study to describe the propagation and effect of the noise that is caused by imperfect implementation of hardware. Identifying parameters such as gate and readout error rates is critical to these models. We use a Bayesian inference approach to identify posterior distributions of these parameters such that they can be characterized more elaborately. By characterizing the device errors in this way, we can further improve the accuracy of quantum error mitigation. Experiments conducted on IBM’s quantum computing devices suggest that our approach provides better error mitigation performance than existing techniques used by the vendor. Also, our approach outperforms the standard Bayesian inference method in some scenarios.
97 MATHEMATICS AND COMPUTING↗
Multi-fidelity stochastic collocation method for computation of statistical moments
We present an efficient numerical algorithm to approximate the statistical moments of stochastic problems, in the presence of models with different fidelities. The method extends the multi-fidelity approximation method developed in . By combining the efficiency of low-fidelity models and the accuracy of high-fidelity models, our method exhibits fast convergence with a limited number of high-fidelity simulations. We establish an error bound of the method and present several numerical examples to demonstrate the efficiency and applicability of the multi-fidelity algorithm.
97 MATHEMATICS AND COMPUTING↗
SU-D-BRD-07: Evaluation of the Effectiveness of Statistical Process Control Methods to Detect Systematic Errors For Routine Electron Energy Verification
Purpose: To evaluate the ability of statistical process control methods to detect systematic errors when using a two dimensional (2D) detector array for routine electron beam energy verification. Methods: Electron beam energy constancy was measured using an aluminum wedge and a 2D diode array on four linear accelerators. Process control limits were established. Measurements were recorded in control charts and compared with both calculated process control limits and TG-142 recommended specification limits. The data was tested for normality, process capability and process acceptability. Additional measurements were recorded while systematic errors were intentionally introduced. Systematic errors included shifts in the alignment of the wedge, incorrect orientation of the wedge, and incorrect array calibration. Results: Control limits calculated for each beam were smaller than the recommended specification limits. Process capability and process acceptability ratios were greater than one in all cases. All data was normally distributed. Shifts in the alignment of the wedge were most apparent for low energies. The smallest shift (0.5 mm) was detectable using process control limits in some cases, while the largest shift (2 mm) was detectable using specification limits in only one case. The wedge orientation tested did not affect the measurements as this did not affect the thickness of aluminum over the detectors of interest. Array calibration dependence varied with energy and selected array calibration. 6 MeV was the least sensitive to array calibration selection while 16 MeV was the most sensitive. Conclusion: Statistical process control methods demonstrated that the data distribution was normally distributed, the process was capable of meeting specifications, and that the process was centered within the specification limits. Though not all systematic errors were distinguishable from random errors, process control limits increased the ability to detect systematic errors using routine measurement of electron beam energy constancy.
07 ISOTOPE AND RADIATION SOURCES↗