Statistical Uncertainty Analysis Research Articles

Statistical uncertainty and sensitivity analysis of intracellular signaling models - through approximate Bayesian computation and variance based global sensitivity analysis

Statistical uncertainty and sensitivity analysis of intracellular signaling models - through approximate Bayesian computation and variance based global sensitivity analysis

The Falsification of Nuclear Forces

We review our work on the statistical uncertainty analysis of the NN force. This is based on the Granada-2013 database where a statistically meaningful partial wave analysis comprising a total of 6713 np and pp published scattering data from 1950 till 2013 below pion production threshold has been made. We stress the necessary conditions required for a correct and self-consistent statistical interpretation of the discrepancies between theory and experiment which enable a subsequent statistical error propagation and correlation analysis

Uncertainty quantification and propagation in nuclear density functional theory

Nuclear density functional theory (DFT) is one of the main theoretical tools used to study the properties of heavy and superheavy elements, or to describe the structure of nuclei far from stability. While on-going efforts seek to better root nuclear DFT in the theory of nuclear forces [see Duguet et al., this issue], energy functionals remain semi-phenomenological constructions that depend on a set of parameters adjusted to experimental data in finite nuclei. In this paper, we review recent efforts to quantify the related uncertainties, and propagate them to model predictions. In particular, we cover the topics of parameter estimation for inverse problems, statistical analysis of model uncertainties and Bayesian inference methods. Illustrative examples are taken from the literature.

Structural investigation of mM Ni(II) complex isomers using transmission XAFS: the significance of model development.

High-accuracy transmission XAFS determined using the hybrid technique has been used to refine the geometries of bis(N-n-propyl-salicylaldiminato) nickel(II) (n-pr Ni) and bis(N-i-propyl-salicylaldiminato) nickel(II) (i-pr Ni) complexes which have approximately square planar and tetrahedral metal coordination. Multiple-scattering formalisms embedded in FEFF were used for XAFS modelling of the complexes. Here it is shown that an IFEFFIT-like package using weighting from experimental uncertainty converges to a well defined XAFS model. Structural refinement of (i-pr Ni) was found to yield a distorted tetrahedral geometry providing an excellent fit, χr(2) = 2.94. The structure of (n-pr Ni) is best modelled with a distorted square planar geometry, χr(2) = 3.27. This study demonstrates the insight that can be obtained from the propagation of uncertainty in XAFS analysis and the consequent confidence which can be obtained in hypothesis testing and in analysis of alternate structures ab initio. It also demonstrates the limitations of this (or any other) data set by defining the point at which signal becomes embedded in noise or amplified uncertainty, and hence can justify the use of a particular k-range for one data set or a different range for another. It is demonstrated that, with careful attention to data collection, including the correction of systematic errors with statistical analysis of uncertainty (the hybrid method), it is possible to obtain reliable structural information from dilute solutions using transmission XAFS data.

An Assessment of the Expected Cost-Effectiveness of Quadrivalent Influenza Vaccines in Ontario, Canada Using a Static Model.

Ontario, Canada, immunizes against influenza using a trivalent inactivated influenza vaccine (IIV3) under a Universal Influenza Immunization Program (UIIP). The UIIP offers IIV3 free-of-charge to all Ontarians over 6 months of age. A newly approved quadrivalent inactivated influenza vaccine (IIV4) offers wider protection against influenza B disease. We explored the expected cost-utility and budget impact of replacing IIV3 with IIV4, within the context of Ontario’s UIIP, using a probabilistic and static cost-utility model. Wherever possible, epidemiological and cost data were obtained from Ontario sources. Canadian or U.S. sources were used when Ontario data were not available. Vaccine efficacy for IIV3 was obtained from the literature. IIV4 efficacy was derived from meta-analysis of strain-specific vaccine efficacy. Conservatively, herd protection was not considered. In the base case, we used IIV3 and IIV4 prices of $5.5/dose and $7/dose, respectively. We conducted a sensitivity analysis on the price of IIV4, as well as standard univariate and multivariate statistical uncertainty analyses. Over a typical influenza season, relative to IIV3, IIV4 is expected to avert an additional 2,516 influenza cases, 1,683 influenza-associated medical visits, 27 influenza-associated hospitalizations, and 5 influenza-associated deaths. From a societal perspective, IIV4 would generate 76 more Quality Adjusted Life Years (QALYs) and a net societal budget impact of $4,784,112. The incremental cost effectiveness ratio for this comparison was $63,773/QALY. IIV4 remains cost-effective up to a 53% price premium over IIV3. A probabilistic sensitivity analysis showed that IIV4 was cost-effective with a probability of 65% for a threshold of $100,000/QALY gained. IIV4 is expected to achieve reductions in influenza-related morbidity and mortality compared to IIV3. Despite not accounting for herd protection, IIV4 is still expected to be a cost-effective alternative to IIV3 up to a price premium of 53%. Our conclusions were robust in the face of sensitivity analyses.

Multivalley effective mass theory simulation of donors in silicon

Last year, Salfi et al. made the first direct measurements of a donor wave function and found extremely good theoretical agreement with atomistic tight-binding [Salfi et al., Nat. Mater. 13, 605 (2014)]. Here, we show that multi-valley effective mass theory, applied properly, does achieve close agreement with tight-binding and hence gives reliable predictions. To demonstrate this, we variationally solve the coupled six-valley Shindo-Nara equations, including silicon's full Bloch functions. Surprisingly, we find that including the full Bloch functions necessitates a tetrahedral, rather than spherical, donor central cell correction to accurately reproduce the experimental energy spectrum of a phosphorus impurity in silicon. We cross-validate this method against atomistic tight-binding calculations, showing that the two theories agree well for the calculation of donor-donor tunnel coupling. Further, we benchmark our results by performing a statistical uncertainty analysis, confirming that derived quantities such as the wave function profile and tunnel couplings are robust with respect to variational energy fluctuations. Finally, we apply this method to exhaustively enumerate the tunnel coupling for all donor-donor configurations within a large search volume, demonstrating conclusively that the tunnel coupling has no spatially stable regions. Though this instability is problematic for reliably coupling donor pairs for two-qubit operations, we identify specific target locations where donor qubits can be placed with scanning tunneling microscopy technology to achieve reliably large tunnel couplings.

Error Reduction in Spatial Robots Based on the Statistical Uncertainty Analysis

ABSTRACT Kinematic accuracy of the robot end-effector is decreased by many uncertainties. In order to design and manufacture robots with high accuracy, it is essential to know the effects of these uncertainties on the motion of robots. Uncertainty analysis is a useful method which can estimate deviations from desired path in robots caused by uncertainties. This paper presents an applied formulation based on Direct Linearization Method (DLM), for 3D statistical uncertainty analysis of open- loop mechanisms and robots. The maximum normal and parallel components of the position error on the end-effector path are introduced. In this paper, uncertainty effects of both linear and angular variations in performance of spatial open-loop mechanisms and robots are considered. Based on the relations for the percent contributions of manufacturing variables, for the position error reduction, the tolerances that have the most significant effects on the commutated uncertainty zone of the end-effector position can be modified. The proposed method is illustrated using a spatial manipulator with three-revolute joints and verified with a Monte Carlo simulation method. Finally, normal and parallel distances to end-effector path are determined as error bands for all over range of motion. The results of applying this method demonstrate that estimating the position error in mechanisms and robots can be done efficiently and precisely.

Uncertainties in nuclear matrix elements for neutrinoless double-beta decay

I briefly review calculations of the matrix elements governing neutrinoless double-beta decay, focusing on attempts to assign uncertainties. At present, systematic error dominates statistical error and assigning uncertainty is difficult. For some purposes, however, statistical assessment of uncertainty is profitable and, after describing the nuclear models in which matrix elements are commonly calculated, I highlight some statistical uncertainty analysis within the quasiparticle random-phase approximation. I also propose, in broad terms, strategies for reducing both systematic and statistical error.

Statistical Matching and Uncertainty Analysis in Combining Household Income and Expenditure Data

Statistical Matching and Uncertainty Analysis in Combining Household Income and Expenditure Data

Optimal design for parameter estimation in EEG problems in a 3D multilayered domain.

The fundamental problem of collecting data in the ``best way'' in order to assure statistically efficient estimation of parameters is known as Optimal Experimental Design. Many inverse problems consist in selecting best parameter values of a given mathematical model based on fits to measured data. These are usually formulated as optimization problems and the accuracy of their solutions depends not only on the chosen optimization scheme but also on the given data. We consider an electromagnetic interrogation problem, specifically one arising in an electroencephalography (EEG) problem, of finding optimal number and locations for sensors for source identification in a 3D unit sphere from data on its boundary. In this effort we compare the use of the classical D-optimal criterion for observation points as opposed to that for a uniform observation mesh. We consider location and best number of sensors and report results based on statistical uncertainty analysis of the resulting estimated parameters.

Harmonic analysis for the characterization and correction of geometric distortion in MRI.

Magnetic resonance imaging (MRI) is gaining widespread use in radiation therapy planning, patient setup verification, and real-time guidance of radiation delivery. Successful implementation of these technologies relies on the development of simple and efficient methods to characterize and monitor the geometric distortions arising due to system imperfections and gradient nonlinearities. To this end, the authors present the theory and validation of a novel harmonic approach to the quantification of system-related distortions in MRI. The theory of spatial encoding in MRI is applied to demonstrate that the 3D distortion vector field (DVF) is given by the solution of a second-order boundary value problem (BVP). This BVP is comprised of Laplace's equation and a limited measurement of the distortion on the boundary of a specified region of interest (ROI). An analytical series expansion solving this BVP within a spherical ROI is obtained, and a statistical uncertainty analysis is performed to determine how random errors in the boundary measurements propagate to the ROI interior. This series expansion is then evaluated to obtain volumetric DVF mappings that are compared to reference data obtained on a 3 T full-body scanner. This validation is performed within two spheres of 20 cm diameter (one centered at the scanner origin and the other offset +3 cm along each of the transverse directions). Initially, a high-order mapping requiring measurements at 5810 boundary points is used. Then, after exploring the impact of the boundary sampling density and the effect of series truncation, a reduced-order mapping requiring measurements at 302 boundary points is evaluated. The volumetric DVF mappings obtained from the harmonic analysis are in good agreement with the reference data. Following distortion correction using the high-order mapping, the authors estimate a reduction in the mean distortion magnitude from 0.86 to 0.42 mm and from 0.93 to 0.39 mm within the central and offset ROIs, respectively. In addition, the fraction of points with a distortion magnitude greater than 1 mm is reduced from 35.6% to 2.8% and from 40.4% to 1.5%, respectively. Similarly, following correction using the reduced-order mapping, the mean distortion magnitude reduces to 0.45-0.42 mm within the central and offset ROIs, and the fraction of points with a distortion magnitude greater than 1 mm is reduced to 2.8% and 1.5%, respectively. A novel harmonic approach to the characterization of system-related distortions in MRI is presented. This method permits a complete and accurate mapping of the DVF within a specified ROI using a limited measurement of the distortion on the ROI boundary. This technique eliminates the requirement to exhaustively sample the DVF at a dense 3D array of points, thereby permitting the design of simple, inexpensive phantoms that may incorporate additional modules for auxiliary quality assurance objectives.

Statistical Analysis of Uncertainties in Deterministic Computational Modeling – Application to Composite Process Resin Infusion Flow Model

Deterministic physics-based flow modeling provides an effective way to simulate and understand the resin flow infusion process in liquid composite molding processes and its variants. These are effective to provide optimal injection time and locations prior to gelation for given process parameters of resin viscosity and preform permeability. However, there could be significant variations in these two parameters during actual manufacturing. This paper presents simulation-based statistical analysis of uncertainties of these process parameters involved in the resin flow infusion. Two key process parameters, viscosity and permeability, and their statistical variations are examined individually and subsequently in combination for their impact on the associated injection time. Values from statistical probability distribution of the process parameters were employed to find the solution space for this engineering application through deterministic physics-based process flow modeling simulations. A bivariate confidence envelope was developed using the appropriate Cumulative Density Function for a 95% probability of successfully completing resin infusion prior to physical resin gelation time. A logistic regression model for the influence of resin viscosity and permeability on the binary response of successful resin infusion is presented and conforms well to the sensitivity analysis inferences.

Manufacturing yield and cost estimation of a MEMS accelerometer based on statistical uncertainty analysis

Manufacturing yield maximization to minimize the production cost is one of the most important objectives of manufacturing. The manufacturing yield is the probability to manufacture products that satisfy multiple performance requirements. For a given set of product performance requirements, its manufacturing yield can be estimated based on the system parameter uncertainties including manufacturing tolerances, which are related to the production cost. We employ three performance indices for the design of a MEMS accelerometer, and the manufacturing yield and cost are estimated using statistical uncertainty analysis methods. The effects of the MEMS accelerometer parameter uncertainties on the manufacturing yield and cost are investigated.

Evaluating the efficiency of environmental monitoring programs

Statistical uncertainty analyses can be used to improve the efficiency of environmental monitoring, allowing sampling designs to maximize information gained relative to resources required for data collection and analysis. In this paper, we illustrate four methods of data analysis appropriate to four types of environmental monitoring designs. To analyze a long-term record from a single site, we applied a general linear model to weekly stream chemistry data at Biscuit Brook, NY, to simulate the effects of reducing sampling effort and to evaluate statistical confidence in the detection of change over time. To illustrate a detectable difference analysis, we analyzed a one-time survey of mercury concentrations in loon tissues in lakes in the Adirondack Park, NY, demonstrating the effects of sampling intensity on statistical power and the selection of a resampling interval. To illustrate a bootstrapping method, we analyzed the plot-level sampling intensity of forest inventory at the Hubbard Brook Experimental Forest, NH, to quantify the sampling regime needed to achieve a desired confidence interval. Finally, to analyze time-series data from multiple sites, we assessed the number of lakes and the number of samples per year needed to monitor change over time in Adirondack lake chemistry using a repeated-measures mixed-effects model. Evaluations of time series and synoptic long-term monitoring data can help determine whether sampling should be re-allocated in space or time to optimize the use of financial and human resources.

Impacts of sea-level rise and urbanization on groundwater availability and sustainability of coastal communities in semi-arid South Texas

The sea levels along the semi-arid South Texas coast are noted to have risen by 3–5 mm/year over the last five decades. Data from General Circulation Models (GCMs) indicate that this trend will continue in the 21st century with projected sea level rise in the order of 1.8–5.9 mm/year due to the melting of glaciers and thermal ocean expansion. Furthermore, the temperature in South Texas is projected to increase by as much as 4 °C by the end of the 21st century creating a greater stress on scarce water resources of the region. Increased groundwater use hinterland due to urbanization as well as rising sea levels due to climate change impact the freshwater-saltwater interface in coastal aquifers and threaten the sustainability of coastal communities that primarily rely on groundwater resources. The primary goal of this study was to develop an integrated decision support framework to assist land and water planners in coastal communities to assess the impacts of climate change and urbanization. More specifically, the developed system was used to address whether coastal side (primarily controlled by climate change) or landward side processes (controlled by both climate change and urbanization) had a greater control on the saltwater intrusion phenomenon. The decision support system integrates a sharp-interface model with information from GCMs and observed data and couples them to statistical and information-theoretic uncertainty analysis techniques. The developed decision support system is applied to study saltwater intrusion characteristics at a small coastal community near Corpus Christi, TX. The intrusion characteristics under various plausible climate and urbanization scenarios were evaluated with consideration given to uncertainty and variability of hydrogeologic parameters. The results of the study indicate that low levels of climate change have a greater impact on the freshwater-saltwater interface when the level of urbanization is low. However, the rate of inward intrusion of the saltwater wedge is controlled more so by urbanization effects than climate change. On a local (near coast) scale, the freshwater-saltwater interface was affected by groundwater production locations more so than the volume produced by the community. On a regional-scale, the sea level rise at the coast was noted to have limited impact on saltwater intrusion which was primarily controlled by freshwater influx from the hinterlands towards the coast. These results indicate that coastal communities must work proactively with planners from the up-dip areas to ensure adequate freshwater flows to the coast. Field monitoring of this parameter is clearly warranted. The concordance analysis indicated that input parameter sensitivity did not change across modeled scenarios indicating that future data collection and groundwater monitoring efforts should not be hampered by noted divergences in projected climate and urbanization patterns.

Anisotropic frequency-dependent spreading of seismic waves from first-arrival vertical seismic profile data analysis

A model of first-arrival amplitude decay combining geometric spreading, scattering, and inelastic dissipation is derived from a multioffset, 3D vertical seismic profile data set. Unlike the traditional approaches, the model is formulated in terms of path integrals over the rays and without relying on the quality factor ([Formula: see text]) for rocks. The inversion reveals variations of geometric attenuation (wavefront curvatures and scattering, [Formula: see text]) and the effective attenuation parameter ([Formula: see text]) with depth. Both of these properties are also found to be anisotropic. Scattering and geometric spreading (focusing and defocusing) significantly affect seismic amplitudes at lower frequencies and shallower depths. Statistical analysis of model uncertainties quantitatively measures the significance of these results. The model correctly predicts the observed frequency-dependent first-arrival amplitudes at all frequencies. This and similar models can be applied to other types of waves and should be useful for true-amplitude studies, including inversion, inverse [Formula: see text]-filtering, and amplitude variations with offset analysis. With further development of petrophysical models of internal friction and elastic scattering, attenuation parameters [Formula: see text] and [Formula: see text] should lead to constraints on local heterogeneity and intrinsic physical properties of the rock. These parameters can also be used to build models of the traditional frequency-dependent [Formula: see text] for forward and inverse numerical viscoelastic modeling.

Effect of system variables on the uncertainty of the mass point leak rate methodology using first-order regression

Advances in nondestructive testing for leak rate characterisation are rare because procedures are well accepted; however, for many critical applications, an understanding of the accuracy and reliability of a reported leak rate is equally as important as the leak rate itself (e.g., manned spacecraft and nuclear power industry). Although it is known that the mass point leak rate method can achieve high accuracies, the measurement uncertainty and limitations of the method are less understood. Using a least-squares regression on a mass–time population and a statistical analysis of regression uncertainty, this study investigated the influence of (1) differential pressure, (2) steady-state and transient temperature, (3) volume size, (4) gas type, (5) sampling time duration, and (6) sampling interval on the reported mass point leak rate value. The analyses accounted for all significant sources of error. An experimental evaluation and validation of the method were conducted on a capillary-type, National Institute of Standards and Technology traceable leak standard and, where appropriate, simultaneous measurements were taken using a helium leak detector for comparison. The mass point technique was shown to provide high-accuracy results for various gases and volume sizes. Across the range of temperatures and pressures, the uncertainty measurements of the mass point technique were between ± 0.34% and ± 0.72%. When the temperature of the test section was varied ± 5°C during the experiment, the mass point technique results deviated 2–4% from those of the standard.

Voxel-based statistical analysis of uncertainties associated with deformable image registration

Deformable image registration (DIR) algorithms have inherent uncertainties in their displacement vector fields (DVFs).The purpose of this study is to develop an optimal metric to estimate DIR uncertainties. Six computational phantoms have been developed from the CT images of lung cancer patients using a finite element method (FEM). The FEM generated DVFs were used as a standard for registrations performed on each of these phantoms. A mechanics-based metric, unbalanced energy (UE), was developed to evaluate these registration DVFs. The potential correlation between UE and DIR errors was explored using multivariate analysis, and the results were validated by landmark approach and compared with two other error metrics: DVF inverse consistency (IC) and image intensity difference (ID). Landmark-based validation was performed using the POPI-model. The results show that the Pearson correlation coefficient between UE and DIR error is rUE-error = 0.50. This is higher than rIC-error = 0.29 for IC and DIR error and rID-error = 0.37 for ID and DIR error. The Pearson correlation coefficient between UE and the product of the DIR displacements and errors is rUE-error × DVF = 0.62 for the six patients and rUE-error × DVF = 0.73 for the POPI-model data. It has been demonstrated that UE has a strong correlation with DIR errors, and the UE metric outperforms the IC and ID metrics in estimating DIR uncertainties. The quantified UE metric can be a useful tool for adaptive treatment strategies, including probability-based adaptive treatment planning.

Dosimetric characterization of the GammaClip™169Yb low dose rate permanent implant brachytherapy source for the treatment of nonsmall cell lung cancer postwedge resection

A novel (169)Yb low dose rate permanent implant brachytherapy source, the GammaClip™, was developed by Source Production & Equipment Co. (New Orleans, LA) which is designed similar to a surgical staple while delivering therapeutic radiation. In this report, the brachytherapy source was characterized in terms of "Dose calculation for photon-emitting brachytherapy sources with average energy higher than 50 keV: Report of the AAPM and ESTRO" by Perez-Calatayud et al. [Med. Phys. 39, 2904-2929 (2012)] using the updated AAPM Task Group Report No. 43 formalism. Monte Carlo calculations were performed using Monte Carlo N-Particle 5, version 1.6 in water and air, the in-air photon spectrum filtered to remove photon energies below 10 keV in accordance with TG-43U1 recommendations and previously reviewed (169)Yb energy cutoff levels [D. C. Medich, M. A. Tries, and J. M. Munro, "Monte Carlo characterization of an Ytterbium-169 high dose rate brachytherapy source with analysis of statistical uncertainty," Med. Phys. 33, 163-172 (2006)]. TG-43U1 dosimetric data, including SK, Ḋ(r,θ), Λ, gL(r), F(r, θ), φan(r), and φan were calculated along with their statistical uncertainties. Since the source is not axially symmetric, an additional set of calculations were performed to assess the resulting axial anisotropy. The brachytherapy source's dose rate constant was calculated to be (1.22±0.03) cGy h(-1) U(-1). The uncertainty in the dose to water calculations, Ḋ(r,θ), was determined to be 2.5%, dominated by the uncertainties in the cross sections. The anisotropy constant, φan, was calculated to be 0.960±0.011 and was obtained by integrating the anisotropy factor between 1 and 10 cm using a weighting factor proportional to r(-2). The radial dose function was calculated at distances between 0.5 and 12 cm, with a maximum value of 1.20 at 5.15±0.03 cm. Radial dose values were fit to a fifth order polynomial and dual exponential regression. Since the source is not axially symmetric, angular Monte Carlo calculations were performed at 1 cm which determined that the maximum azimuthal anisotropy was less than 8%. With a higher photon energy, shorter half-life and higher initial dose rate 169Yb is an interesting alternative to 125I for the treatment of nonsmall cell lung cancer.

TU‐G‐134‐02: A Harmonic Field Approach to Quantifying MRI Spatial Accuracy for MRIgRT

Purpose: An outstanding problem in the clinical implementation of MRIgRT is the development of simple and efficient methods for the measurement, characterization, and monitoring of geometrical accuracy in MRI. This study presents the theory, implementation, and validation of a novel harmonic field approach to the quantification of spatial accuracy in MRI. Methods: A harmonic field description of the 3D distortion vector field in MRI is derived as the solution of a second‐order boundary value problem comprised of the Laplace equation and a limited measurement of the distortion at a sparse distribution of points. Harmonic representations of the distortion field were calculated for spherical, cylindrical, and irregular regions of interest (ROIs). These representations were then used to derive volumetric mappings of the distortion field that were compared against reference data obtained on a 3 T full‐body scanner. The effects of sampling density were explored and a statistical uncertainty analysis was performed. Results: The volumetric mappings of the distortion field derived from the harmonic analysis were found to be in excellent agreement with the reference data. For all ROI geometries and distortion vector components, the 1 mm3 voxel size of the images used to acquire the reference data was greater than at least two standard deviations in all discrepancies. The statistical uncertainty analysis demonstrated the robustness of the harmonic approach, as the uncertainties in the volumetric mappings were calculated to be less than or equal to the input reference data. Conclusion: A novel harmonic approach has been proposed for quantifying MRI spatial accuracy in large imaging volumes for MRIgRT using only limited measurement data. This technique abates the requirement to directly measure the distortion at a dense 3D array of points and thus permits the design of simple, inexpensive phantoms that may feature additional modules for supplementary imaging and dosimetry QA objectives.