Total Estimation Error Research Articles

Setting Performance Goals and Evaluating Total Analytical Error for Diagnostic Assays

Total analytical error has been a useful metric both to assess laboratory assay quality and to set goals. It is often estimated by combining imprecision (SD) and average bias in the equation: total analytical error = bias + 1.65 x imprecision. This indirect estimation model (referred to as the simple combination model) leads to different estimates of total analytical error than that of a direct estimation method (referred to as the distribution-of-differences method) or of simulation. A review of the literature was undertaken to reconcile the different estimation approaches. The simple combination model can underestimate total analytical error by neglecting random interference bias and by not properly treating other error sources such as linear drift and outliers. A simulation method to estimate total analytical error is outlined, based on the estimation and combination of total analytical error source distributions. Goals for each total analytical error source can be established by allocation of the total analytical error goal. Typically, the allocation is cost-based and uses the probability of combinations of error sources. The distribution-of-differences method, simple combination model, and simulation method to evaluate total analytical error are compared. Outlier results can profoundly influence quality, but their rates are seldom reported. Total analytical error should be estimated either directly by the distribution-of-differences method or by simulation. A systems engineering approach that uses allocation of the total analytical error goal into error source goals provides a cost-effective approach to meeting total analytical error. Because outliers can cause serious laboratory error, the inclusion of outlier rate estimates from large studies (e.g., those conducted by manufacturers) would be helpful in assessing assay quality.

Open‐path Fourier transform infrared spectroscopy of SO2: An empirical error budget analysis, with implications for volcano monitoring

Fourier transform infrared (FTIR) spectroscopy is increasingly used as a tool for volcano monitoring, allowing measurement of a range of gases including SO2, HCl, and HF. Retrievals are complicated, since the open‐path spectra are typically pressure broadened and contaminated hy atmospheric H2O, CO2, etc., and the field instruments employed have low spectral resolution (∼0.5 cm−1). We present a detailed analysis of 0.5 cm−1 resolution infrared spectra of certified SO2 mixtures in order to assess the sensitivity of such instruments and the retrieval procedures used for field spectra. We investigate the effects on retrievals of the SO2 V1+v3 band (centered at 2499.87 cm−1) of varying the retrieval spectral window and background fit, and of errors in the instrument line shape (ILS), temperature, and pressure. Largest deviations in retrieved amounts result from errors in the ILS (1.5–2.1%) and temperature (2.9–3.0% for a 10 K change). The total error estimate associated with these factors is similar to the uncertainty in line parameter data. Overall, the retrieval accuracy was better than 5%, except for the lowest concentration spectra. Errors calculated in the retrieval algorithm were conservative enough to cover these accuracy limits. We estimate that in field spectra, SO2 concentrations above 2.5 × 1017 molecules cm−2 (100 ppm m at room temperature and pressure) should be measurable with high accuracy. These results are encouraging in the context of deployment of open‐path FTIR spectrometers for surveillance of active volcanoes, and the findings are equally applicable to other open‐path measurements of SO2, for example from anthropogenic sources.

Systematic errors in multi-frequency EIT

Systematic errors have been measured with a multi-frequency data-collection system operating between 10.24 and 81.92 kHz. The errors were present even though a conventional background measurement on a uniform saline phantom had already been subtracted. Errors due to changes in transimpedance between the calibration and the tissue measurements, cable movement and electrode-skin contact impedance were simulated giving a total systematic error estimate equivalent to a 9% change in tissue conductivity. It was shown that more than 89% of the image was above the total error magnitude, indicating that most of the image revealed true changes in tissue conductivity. In three human subjects, the largest conductivity changes were in two regions, located posteriorly on either side of the midline, and were interpreted as due to the erector spinae muscles. These regions showed increases in conductivity of 73-104%. Identification of other anatomical features was difficult because of the poor spatial resolution of the images.

Estimating Traffic Accident Rates While Accounting for Traffic-Volume Estimation Error: A Gibbs Sampling Approach

Traffic-accident rates that are estimated for individual roadway sites are often used to identify potentially hazardous locations. Occasionally they are used to test whether an accident countermeasure is associated with a statistically significant change in accident rate. In assessing the uncertainty attached to estimated accident rates, it is often implicitly assumed that the total traffic at a site is known with certainty, when in actuality the total traffic almost always must be estimated from a short sample of traffic counts. This introduces estimation error, which, if ignored, can lead one to overstate the accuracy of an accident-rate estimate. An explanation is provided about how Bayes estimates of accident rates, which explicitly account for total traffic estimation error, can be computed readily using a (relatively) new estimation method called “Gibbs sampling.” A model of how traffic-count samples are related to total traffic is incorporated from earlier work done by the author and his students. In tests conducted using accident counts and traffic data from 17 automatic traffic-recorder sites in Minnesota, it was found that, when using a 2-day traffic-count sample, the traditional method for estimating accidents rates understated the likely error of these estimates by 12 to 40 percent, depending on the site.

Introduction au procédé d'échantillonnage

People is more and more affected by heterogeneous materials, with complex spatial distribution (biology, ecology, quality for use). Qualitative as well as quantitative measurement efficacy depends on both the relevance of the measured dimension, and the representativeness of the nanalysed fraction. Sampling and sample adaptation to on-line analyser, or to laboratory analysis, concerning application testing or sample storage, must agree with correction rules, in order to reduce bias risk, to decrease non-systematic errors, and to allow total error estimation. Every case needs a particular treatment. Critical factors are the actual objective, the heterogeneity of both constitution and distribution scales, the lot size, and the spatial disposition of the lot to be handled. Particulate materials are discussed and compared with molecular materials, to enlighten some fundamental notions such as: .Sampling by number or by weight. Liberation parameter. .Weight to be sampled (M E ). Increments to be collected (N). .Sampling design. Static or dynamic lot presentation. . Analytical result conversion into lot estimation. The eminent multidisciplinary character of the sampling process is highlighted. The Analyst has to certify correct methods for the entire process and to assume responsability. Sampling is easier to realize when early designed, during the engineering conception. The sampling practice is nowadays impossible to be appreciated as entirely satisfactory. Improvements are necessary, not only with gases and natural materials, but specially with particulate materials, but specially with particulate materials, concerning theoretical bases as well as reglementation and apparatus performance

Use of a priori information in estimating tissue resistivities - application to measured data

A statistically constrained minimum mean squares error estimator (MiMSEE) has been shown to be useful in estimating internal resistivity distribution by the use of simulated data. In this study, the performance of the MiMSEE algorithm is tested by using measured data from resistor phantoms. The MiMSEE uses a priori information on body geometry, electrode position, statistical properties of tissue resistivities, instrumentation noise and linearization error to calculate the optimum inverse matrix which maps the surface potentials to unknown regional resistivities. In this study, the MiMSEE is also constrained with the variance-covariance of the modelling error to improve the estimation accuracy. The data are obtained from two different phantom geometries, namely five-region and thorax. Using the measured data, the estimations are realized and errors are calculated. Then, the results are compared with the results obtained by using a conventional least squares error estimator (LSEE). The five-region model results show similarity with the simulation study results of Baysal and Eyüboglu. On the thorax model, the total estimation error is 34.2% with the MiMSEE compared with 856% with the LSEE. It is concluded that the MiMSEE is more robust than the LSEE and applicable to measured data.

Minimum Permeance Estimation of Variable Reluctance Machines by Using Neural Networks

A new approach was studied in this paper to calculate minimum permeance (Pmin) of variable reluctance machines (VRM). Finite element method (FEM) and neural network (NN) were employed together for estimation. The data collected by an electromagnetic finite element software (Flux 2D) were used to train NN. Trained NN was tested by another data set which are not in the training data set. Total estimation error in the test set was observed less than 2.5%. A similar study was performed with the data set collected using flux tube analysis (FTA). In this case, much larger data set was constructed by FTA since this method allows to generate larger data set. After training NN by this data set, it was tested by a test set generated by FTA. The total estimation error was observed less than 5%.

Study of the acoustic‐to‐articulatory transformation for vowels and fricatives.

Using synthetic speech from an articulatory speech synthesizer, statistics are generated of the error between actual articulatory configurations and those estimated by an acoustic‐to‐articulatory mapping routine. Based solely on acoustics, neglecting aerodynamic and perceptual issues, histograms of total estimation error suggest that the inverse problem is no more ambiguous for fricatives than for vowels. By examining the error covariance, dominant articulatory dimensions are identified in the fricative model that have the greatest effect on the acoustic transfer function and, as a result, are better estimated by the acoustic‐to‐articulatory mapping routine. Weak articulatory dimensions are also found that the acoustic‐to‐articulatory mapping routine can barely estimate better than simply guessing. Suggestions are made for ways in which these error statistics, and specifically the knowledge of the unequal importance of different articulatory dimensions, can be used to motivate improved techniques for the acoustic‐to‐articulatory mapping of speech. Demonstrations of some of these ideas will be given on real and synthetic speech. [Work supported by the AFOSR.]

An error covariance model for sea surface topography and velocity derived from TOPEX/POSEIDON Altimetry

In order to facilitate the use of satellite altimeter‐derived sea surface topography and velocity in oceanographic models, a methodology is presented for deriving the total error covariance and its geographic distribution from TOPEX/POSEIDON measurements. The model is formulated using a parametric model fit to the altimeter range observations. The topography and velocity are modeled with spherical harmonic expansions whose coefficients are found through optimal adjustment to the altimeter range residuals using Bayesian statistics. All other parameters, including the orbit, geoid, surface models, and range corrections are provided as unadjusted parameters. The maximum likelihood estimates and errors are derived from the probability density function of the altimeter range residuals conditioned with a priori information. Estimates of model errors for the unadjusted parameters are obtained from the TOPEX/POSEIDON postlaunch verification results and the error covariances for the orbit and the geoid, except for the ocean tides. The error in the ocean tides is modeled, first, as the difference between two global tide models and, second, as the correction to the present tide model, the correction derived from TOPEX/POSEIDON data. A formal error covariance propagation scheme is used to derive the total error. Our global total error estimate for the TOPEX/POSEIDON topography relative to the geoid for one 10‐day period is found to be 11 cm RMS. When the error in the geoid is removed, thereby providing an estimate of the time dependent error, the uncertainty in the topography is 3.5 cm RMS. This level of accuracy is consistent with direct comparisons of TOPEX/POSEIDON altimeter heights with tide gauge measurements at 28 stations. In addition, the error correlation length scales are derived globally in both east‐west and north‐south directions, which should prove useful for data assimilation. The largest error correlation length scales are found in the tropics. Errors in the velocity field are smallest in midlatitude regions; they are less than 2 cm/s over most of the Southern Ocean. For both variables the largest errors are caused by uncertainty in the geoid. More accurate representations of the geoid await a dedicated geopotential satellite mission. Substantial improvements in the accuracy of ocean tide models are expected in the very near future from research with TOPEX/POSEIDON data. Consequently, estimates of the time dependent sea surface topography from TOPEX/POSEIDON could achieve a total uncertainty of less than 3 cm RMS. This level of accuracy from a spaceborne sensor represents a remarkable engineering achievement and a major contribution to ocean science.

Approximate method for solving an elliptic problem with discontinuous coefficients

The paper deals with an elliptic problem with coefficients discontinuous along a certain surface. An approximate method for solving this problem is constructed. It is based on extrapolation of solutions of problems which contain a small parameter in the boundary condition. For solving the latter problems an effective iterative method is proposed. An estimate of total error of the approximate solution of the problem is obtained.

Evaluating test methods by estimating total error

A common procedure for evaluating a test method by comparison with another, well-accepted method has been to use a repeated measurements design, in which several individual subjects' specimens are assayed with both methods. We propose the use of the intrasubject relative mean square error, which is a function of the intrasubject relative bias and the coefficient of variation of the test method, as a measure of total error. We construct for each individual subject a score that is based on how well an individual's estimate of total error compares with a maximum allowable value. If the individual's score is > 100%, then that individual's estimate of total error exceeds the maximum allowable value. We present a distribution-free statistical methodology for evaluating the sample of scores. This involves the construction of an upper tolerance limit to determine whether the test method yields values of the total error that are acceptable for most of the population with some level of confidence. Our definition of total error is very different from that defined in the National Cholesterol Education Program (NCEP) guidelines. The NCEP bound for total error has three main problems: (a) it incorrectly assumes that the standard error of the estimated relative bias is the test coefficient of variation; (b) it incorrectly assumes that the individual estimated relative biases follow gaussian distributions; (c) it is based on requiring the relative bias of the average individual in the population to lie within prescribed limits, whereas we believe it is more important to require the total error for most of the individuals in the population, say 95%, to lie within prescribed limits.

Total variation and error estimates for spectral viscosity approximations

We study the behavior of spectral viscosity approximations to non-linear scalar conservation laws. We show how the spectral viscosity method compromises between the total-variation bounded viscosity approximations— which are restricted to first-order accuracy—and the spectrally accurate, yet unstable, Fourier method. In particular, we prove that the spectral viscosity method is L 1 {L^1} -stable and hence total-variation bounded. Moreover, the spectral viscosity solutions are shown to be Lip + {\text {Lip}^ + } -stable, in agreement with Oleinik’s E-entropy condition. This essentially nonoscillatory behavior of the spectral viscosity method implies convergence to the exact entropy solution, and we provide convergence rate estimates of both global and local types.

Multi-factor designs. IV. How multi-factor designs improve the estimate of total error by accounting for protocol-specific biases

Total error is often calculated as a combination of random error and fixed bias. However, the specific protocols used to estimate random error and fixed bias are themselves variable factors that can affect the estimate of total error. We refer to biases such as assay drift, sample-to-sample carryover, and reagent carryover as examples of fixed biases that are protocol-specific and distinguish them from other fixed biases. Failing to account for protocol-specific biases that are present will lead to incorrect estimates of total error when routine use of the assay involves a protocol different from that used to estimate total error. Multi-factor protocols are recommended to determine protocol-specific biases, which, if present, should be included in the estimate of total error.

On estimating the amplitude of harmonic vibration from the Doppler spectrum of reflected signals

The Doppler spectrum of echoes from a sinusoidally vibrating scatterer has discrete spectral lines weighted by Bessel functions of the first kind. Because the signal and spectrum are complicated functions of the vibration amplitude, a number of different approaches have been tried in the past to estimate the vibration amplitude, given a received signal. Here, a new and simple relationship between the spread (or variance) of the Doppler spectrum and the vibration amplitude is derived. A method of estimating the vibration amplitude is proposed based on this relation and a noise compensation procedure is also demonstrated. The performance of the estimators is studied through simulations. High accuracy is predicted under proper sampling conditions even when the signal-to-noise ratio is poor. Slight deviations from single-frequency oscillation, as would be caused by nonlinear or nonideal medium or source effects, are found to have little contribution to the total estimation error.

Sounding rocket measurement of the absolute solar EUV flux utilizing a silicon photodiode

A newly developed stable and high quantum efficiency silicon photodiode was used to obtain an accurate measurement of the integrated absolute magnitude of the solar extreme ultraviolet photon flux in the spectral region between 50 and 800 Å. The detector was flown aboard a solar pointing sounding rocket launched from White Sands Missile Range in New Mexico on October 24, 1988. The adjusted daily 10.7‐cm solar radio flux and sunspot number were 168.4 and 121, respectively. The unattenuated absolute value of the solar EUV flux at 1 AU in the specified wavelength region was 6.81×1010 photons cm−2 s−1. Based on a nominal probable error of 7% for National Institute of Standards and Technology detector efficiency measurements in the 50‐ to 500‐Å region (5% on longer wavelength measurements between 500 and 1216 Å), and based on experimental errors associated with our rocket instrumentation and analysis, a conservative total error estimate of ∼14% is assigned to the absolute integral solar flux obtained.

Lead in bone. IV. Distribution of lead in the human skeleton.

Flameless atomic absorption spectroscopy was used to measure lead concentrations in samples from 5 selected human skeletal sites (tibia, skull, rib, ilium, and vertebra) obtained from 134 hospital autopsies. Lead was distributed unequally among the different bones in distinct patterns that were age-, and to some extent, sex-dependent. To estimate lead concentration of the entire skeleton, all skeletal bones were divided into 5 groups based on their approximate compact/trabecular bone ratios, considering each of our 5 sampled sites to be the prototype for each such group. Regression analysis of the 10 possible bone site pair values at different ages yielded age-related constants. These constants were incorporated into an equation we developed that can be used both to estimate mean skeletal lead concentration (Pb) of the entire body skeleton and also to predict the lead concentration at any of the other 4 bone sites if any 1 of the 5 is measured. Applications of these data to in vivo bone lead measurements are detailed with respect to selection of the site to be measured, estimation of total skeletal lead burden, anticipated variations or error, and dependence of these factors on age and sex of the sampled population.

Method of turbulent flux measurement on a ship by using a stable platform system.

The tropical marine boundary layer is of fundamental importance to the whole of the atmospheric motion system by providing a large amount of water vapor into the free atmosphere. It is one of the important subjects for GARP to investigate the turbulent transport mechanism in this layer. In this paper a description is given of a stable platform system that was aimed for turbulent transport measurements on board. The system is designed primarily for turbulent flux measurements by the eddy correlation method on a ship. Various components of the system are briefly described and evaluation data obtained during the summer MONEX field program are also presented. It was found that this system is applicable to the turbulent flux measurement by the eddy correlation method on a ship during MONEX. By further estimation of total errors, it was also found that this system is applicable to the measurements under rougher sea surface conditions.

Prenatal diagnosis and outcome of pregnancy in 2036 women investigated by amniocentesis

The report presents the indications for prenatal diagnosis, the results from amniocentesis and details of outcome of pregnancy in 2036 women. Aneuploidy was found in 26 fetuses (1.3%) including 16 with trisomy 21 and 9 sex chromosome abnormalities. There were 38 balanced chromosomal rearrangements (1.9%): 23 of these (1.1%) were pericentric inversions of a number 9 chromosome. Only two of the chromosomal abnormalities were found in other than those mothers referred for maternal age of 35 or over. Concern is expressed at the low referral rate for older mothers in the population served (only 25% of those over 40 years). Failure of amniotic cell culture occurred in 2.8% of cultures. Maternal cell contamination was detected in 23 cultures (1.1%) with four errors in reported fetal sex. Total error estimate was 0.5%. There were 20 in vitro artefacts (1.0%) with no reporting errors. Neural tube defects were identified in 28 fetuses and there were three false-positive and one false-negative results. Data on outcome of pregnancy was available from 1805 pregnancies (96.5%): 1295 were normal (71.7%) and 510 (28.3%) showed some abnormality. Pregnancy was terminated for fetal abnormality in 53 cases (2.9%) and fetal loss occurred in 65 (3.7%). Methods, quality control, safety and service considerations are discussed. It is suggested that amniocentesis should be restricted to centres where the greatest expertise is available. The service should be improved to meet the needs of a greater number of patients. The series is compared with other studies of over 1500 cases.

Three-dimensional lithospheric modelling at NORSAR: linearity of the method and amplitude variations from the anomalies

A modification of the Aki et al. technique for three-dimensional lithospheric modelling is used to find smoothly varying models for the P-wave velocity structure beneath NORSAR. The method includes ray tracing and calculation of geometrical spreading in the anomalies. The results of linear inversion of the travel-time data compare well with those of previous investigators. The assumption of linearity, which removes the need to ray trace through the anomalies, is tested with iterative solutions for both synthetic and real data. A model with an rms velocity perturbation of 3 percent, extending to 120 km depth, is found to be reasonably linear. In fact the procedure leads to two models which satisfy the same amount of the real data but which differ by far more than the standard errors. However, these differences are not significant once the imperfect resolution is accounted for by using the total estimation error of the stochastic inverse. The depth of major anomalies appears to be greater than the array diameter and is therefore not well constrained. Comparing the geometrical spreading produced by these models with the amplitude variations observed at the array indicates that structure deeper than 120 km but shallower than 200 km makes an important contribution to the observations. None of the models used can produce variations as large as those in the amplitude data. For deep, essentially two-dimensional, anomalies the fit to these data is much better for sources to the NE of the array than for sources in other quadrants.

Estimation of total errors in software

To improve the reliability of software, any information about errors in computer programs is useful. A simple parametrization scheme to estimate the total errors during development phase is suggested. Estimated errors using available data are compared with the actual errors.