Residual Error Distribution Research Articles

Absolute Calibration of ATMS Upper Level Temperature Sounding Channels Using GPS RO Observations

The absolute accuracy of antenna brightness temperatures (TDR) from the Advanced Technology Microwave Sounder (ATMS) onboard the Suomi National Polar-orbiting Partnership satellite is estimated using the Constellation Observing System for Meteorology, Ionosphere, and Climate radio occultation (RO) data as input to the U.S. Joint Center of Satellite Data Assimilation community radiative transfer model (RTF). It is found that the mean differences (e.g., biases) of observed TDR observations to GPS RO simulations are positive for channels 6, 10-13 with values smaller than 0.5 K and negative for channels 5, 7-9 with values greater than -0.7 K. The bias distribution is slightly asymmetric across the scan line. A line-by-line RTF is used to further understand the sources of errors in forward calculations. It is found that, for some channels, the bias can be further reduced in a magnitude of 0.3 K if the accurate line-by-line simulations are used. With the high quality of GPS RO observations and the accurate RTF, ATMS upper level temperature sounding channels are calibrated with known absolute accuracy. After the bias removal in ATMS TDR data, it is shown that the distribution of residual errors for ATMS channels 5-13 is close to a normal Gaussian one. Thus, for these channels, the ATMS antenna brightness temperature can be absolutely calibrated to the sensor brightness temperature without a systematic bias.

Combining input uncertainty and residual error in crop model predictions: A case study on vineyards

As crop modelling has matured and been proposed as a tool for many practical applications, there is increased need to evaluate the uncertainty in model predictions. A particular case of interest that has not been treated before is that where one takes into account both uncertainty in the model explanatory variables and model residual error (the uncertainty in model predictions even when the explanatory variables are perfectly known). The specific case we consider is that of a model for predicting water stress of a vineyard. For many of the model explanatory variables, the vine grower (or the farmer advisor) has a choice between approximate values which are easily obtainable and more precise values that are more difficult (and more expensive) to obtain. We specifically discuss the explanatory variable “initial water stress” which is directly based on the initial soil water content and can be estimated or measured (precise but expensive). The vine grower is interested in the decrease in uncertainty that would result from measuring initial water stress, but it is the decrease in total uncertainty, including model residual error, that is of importance.We propose using accurate measurements of water stress over time in multiple vineyards, to estimate model residual error. The uncertainty in initial water stress can be estimated if one has approximate and precise values of initial water stress in several vineyards. We then combine the two sources of error by simulation thanks to an independence hypothesis; the model is run multiple times with a distribution of values for initial water stress, and on each day a distribution of model residual errors is added to the result.The results show that the resulting uncertainty is quite different in different fields. In some cases, uncertainty in initial water stress becomes negligible a short time after the start of simulations, in other cases that uncertainty remains important, compared to model residual error, throughout the growing season. In all cases, residual error is a substantial percentage of overall error and thus should be taken into account.

AVO inversion based on generalized extreme value distribution with adaptive parameter estimation

Amplitude Variation with Offset (AVO) inversion is very sensitive to noise and other uncertainties which are often far from Gaussian in the actual pre-stack seismic data, sometimes causing AVO inversion to give poor results. Since the generalized extreme value (GEV) distribution can efficiently fit any distribution with different parameters, to obtain steady and rational AVO inversion results, we use GEV distribution to model the distribution of the iterative residual error in the AVO inversion. The maximum likelihood method is used to re-evaluate the GEV distribution parameters of each iterative residual error to efficiently fit its non-Gaussian property and reduce the sensitivity of AVO inversion to non-Gaussian residual error. Quasi-Newton based Conjugate Gradient (QCG) AVO algorithm is derived from adaptive adjusted parameters GEV distribution to make sure the direction is always a descent direction for the objective function. Finally, a new choice of adaptive variable step length obtained by the Taylor expression of the residual vector can adaptively adjust the step length to accelerate the convergent speed. Both the synthetic and real seismic data tests illustrate the effectiveness of the proposed method.

Tool wear monitoring based on cointegration modelling of multisensory information

A new method based on the cointegration theory is presented in this article to realise tool wear monitoring based on multisensory information. The main characteristic of cointegration modelling is that it can reflect the long-run equilibrium relationship of non-stationary time series, thereby avoiding the appearance of spurious regression. Monitoring of milling process was carried out by installing two dynamic force sensors in different directions. The cointegration model is constructed to describe the relationship between the tool wear value and the relevant features extracted from the sensory signal. For comparison, the root mean square error (RMSE), mean error (ME) and residual error distribution are utilised to evaluate the prediction accuracy of the cointegration model and the multiple linear regression (MLR) method. The monitoring and comparison results show that the proposed method can avoid the spurious regression effectively and predict the tool wear more accurately. This method casts new light on the accurate prediction of tool wear in the industrial environment.

Population pharmacokinetics of valnemulin in swine

This study was carried out in 121 pigs to develop a population pharmacokinetic (PPK) model by oral (p.o.) administration of valnemulin at a single dose of 10 mg/kg. Serum biochemistry parameters of each pig were determined prior to drug administration. Three to five blood samples were collected at random time points, but uniformly distributed in the absorption, distribution, and elimination phases of drug disposition. Plasma concentrations of valnemulin were determined by high-performance liquid chromatography-tandem mass spectrometry (HPLC-MS/MS). The concentration-time data were fitted to PPK models using nonlinear mixed effect modeling (NONMEM) with G77 FORTRAN compiler. NONMEM runs were executed using Wings for NONMEM. Fixed effects of weight, age, sex as well as biochemistry parameters, which may influence the PK of valnemulin, were investigated. The drug concentration-time data were adequately described by a one-compartmental model with first-order absorption. A random effect model of valnemulin revealed a pattern of log-normal distribution, and it satisfactorily characterized the observed interindividual variability. The distribution of random residual errors, however, suggested an additive model for the initial phase (<12 h) followed by a combined model that consists of both proportional and additive features (≥ 12 h), so that the intra-individual variability could be sufficiently characterized. Covariate analysis indicated that body weight had a conspicuous effect on valnemulin clearance (CL/F). The featured population PK values of Ka , V/F and CL/F were 0.292/h, 63.0 L and 41.3 L/h, respectively.

Extreme value theory-based integrity monitoring of global navigation satellite systems

Measurements consistency-based Receiver Autonomous Integrity Monitoring (RAIM) is the main technique for monitoring the integrity of global satellite navigation systems at the user-level. Existing RAIM algorithms utilize two tests, in the position domain a test for RAIM availability and in the measurement domain a test for failure detection. These tests involve the computation of three parameters: test statistic, decision threshold, and protection level. The test statistic is based on the actual measurements in the form of the sum of the squared errors (SSE). The decision threshold is chosen on the basis of the statistical characteristics of the SSE including the assumption that the errors are normally distributed. However, in practice residual, error distributions exhibit heavier tails than predicted by the Gaussian model. Therefore, this paper challenges the normality assumption of the residual navigation errors in three ways. First, real data are used to assess its impact on the traditional RAIM algorithm. Second, extreme value theory is applied to the tails, and the generalized extreme value (GEV) distribution is derived to capture residual navigation errors. Third, the performance of the traditional RAIM approach is compared with that employing the GEV distribution. The results demonstrate that the GEV model is a more accurate representation of the distribution of residual navigation errors than the conventional Gaussian model and should be used in the development of integrity monitoring algorithms.

Reaction Kinetics of Ethylene Combustion in a Carbon Dioxide Stream over a Cu–Mn–O Hopcalite Catalyst in Low Temperature Range

The intrinsic kinetics of the catalytic combustion of a trace amount of ethylene in a CO2 stream over a Cu–Mn–O catalyst prepared with a coprecipitation method is investigated. The experiments are carried out in a fixed-bed reactor with 0.3 g of catalyst in a low temperature range (470 to 620 K) and varying the concentration of C2H4 and O2 in the feed stream. The power rate law, Langmuir–Hinshelwood (LH), Eley–Rideal (ER), and Mars–van Krevelen (MVK) models are compared. The residual error distribution of the ethylene conversion is employed to optimize the model equations. The extended MVK model containing desorption terms of the combustion products fit the data well. The pilot test with a fixed-bed reactor and a commercial feed stream is carried out, and the macro kinetic equations are obtained. Combined with the extended MVK model equations of the intrinsic kinetics, the effectiveness factor is calculated, which gives further prediction of the performance of the extruded catalyst under commercial condit...

Spatial Bias in Multi-Atlas Based Segmentation.

Multi-atlas segmentation has been widely applied in medical image analysis. With deformable registration, this technique realizes label transfer from pre-labeled atlases to unknown images. When deformable registration produces error, label fusion that combines results produced by multiple atlases is an effective way for reducing segmentation errors. Among the existing label fusion strategies, similarity-weighted voting strategies with spatially varying weight distributions have been particularly successful. We show that, weighted voting based label fusion produces a spatial bias that under-segments structures with convex shapes. The bias can be approximated as applying spatial convolution to the ground truth spatial label probability maps, where the convolution kernel combines the distribution of residual registration errors and the function producing similarity-based voting weights. To reduce this bias, we apply a standard spatial deconvolution to the spatial probability maps obtained from weighted voting. In a brain image segmentation experiment, we demonstrate the spatial bias and show that our technique substantially reduces this spatial bias.

Prediction of body composition by total body electrical conductivity technique is affected by fat reserves of Japanese quail

The effect of fat accumulation on the prediction of in vivo body composition by a total body electrical conductivity (TOBEC) technique was evaluated using Japanese quail at 2 life periods (0 to 21 d and 28 to 70 d of age) that differ significantly in the fatness of birds. In total, 119 quail of 14 age categories were weighed and scanned by the TOBEC analyzer, and their carcasses were subjected to chemical analysis. The prediction equations for chemical composition (percentage of water, lipids, and lean tissue) and body masses (weight of body, water, lipids, and lean tissue) were obtained by linear regression analysis. The equations involved the E-value as the independent variable. In both growth phases, a high accuracy of estimation was found for the total body, lean, and water masses (0.85 ≤ R(2) ≤ 0.98), whereas a low accuracy of estimation was observed for percentages of lipids, lean tissue, and water (0.27 ≤ R(2) ≤ 0.64). Most of the variables showed a worse estimation in the late than in the early growth phase; the maximum difference was observed for the lipid mass (R(2) = 0.35 vs. 0.90, respectively). The correlations between analyzed variables and the residual error distributions of regression models demonstrated that the lower power of the models in the late versus early growth phase may be attributed to an enhanced fat accumulation in sexually mature birds. Their high fat reserves considerably decrease body hydration, which negatively influences the estimation of body composition based upon the TOBEC procedure.

Effects of large-scale nonstationarity on parametric maps. A study of rest perfusion CASL data

This study investigates the emergence of characteristic patterns in clusters thresholded at uncorrected significance levels, using as a case study rest perfusion images obtained with the continuous arterial spin labelling technique (CASL). The origin of these patterns is traced back to the existence of large-scale spatial covariance, a violation of the stationarity assumption on the spatial distribution of residual errors. It is shown that in the presence of large-scale covariance, several principles or intuitions common among experimenters when evaluating the inferential strength of their analyses are not applicable. Thresholded maps and clusters are confounded by the spatial patterns of large-scale covariance, irrespective of the existence of a true effect, as shown in t maps constructed by resampling groups at random from a large pool of volumes. Filtering clusters according to their size made the problem worse, and corrections on cluster size based on random field theory models of smoothness had only a minor impact on their tendency to appear in characteristic locations. A formal analysis shows that the large-scale covariance at the origin of these problems is retained in the parametric map irrespective of sample size. Therefore, neither sample independence nor sample size protect from replications of effects being confounded by replications of the spatial covariance of residual errors. In contrast, cluster peaks were not affected by large-scale covariance but only by local differences in smoothness levels, as predicted by random field theory for the distribution of maxima, highlighting the different inferential robustness of cluster-based and maxima-based statistics. A framework is provided to generalize these results to mixed effects models with nested random effects, applicable also to activation studies. Large-scale nonstationarity is most problematic when the variance source at the origin of the characteristic patterns is not specific to a function or variable involved in the inferential process, as typically in observational studies of individual differences. These results raise the question of the existence and impact of large-scale nonstationarity in studies with data obtained with other techniques.

A formal likelihood function for parameter and predictive inference of hydrologic models with correlated, heteroscedastic, and non‐Gaussian errors

Estimation of parameter and predictive uncertainty of hydrologic models has traditionally relied on several simplifying assumptions. Residual errors are often assumed to be independent and to be adequately described by a Gaussian probability distribution with a mean of zero and a constant variance. Here we investigate to what extent estimates of parameter and predictive uncertainty are affected when these assumptions are relaxed. A formal generalized likelihood function is presented, which extends the applicability of previously used likelihood functions to situations where residual errors are correlated, heteroscedastic, and non‐Gaussian with varying degrees of kurtosis and skewness. The approach focuses on a correct statistical description of the data and the total model residuals, without separating out various error sources. Application to Bayesian uncertainty analysis of a conceptual rainfall‐runoff model simultaneously identifies the hydrologic model parameters and the appropriate statistical distribution of the residual errors. When applied to daily rainfall‐runoff data from a humid basin we find that (1) residual errors are much better described by a heteroscedastic, first‐order, auto‐correlated error model with a Laplacian distribution function characterized by heavier tails than a Gaussian distribution; and (2) compared to a standard least‐squares approach, proper representation of the statistical distribution of residual errors yields tighter predictive uncertainty bands and different parameter uncertainty estimates that are less sensitive to the particular time period used for inference. Application to daily rainfall‐runoff data from a semiarid basin with more significant residual errors and systematic underprediction of peak flows shows that (1) multiplicative bias factors can be used to compensate for some of the largest errors and (2) a skewed error distribution yields improved estimates of predictive uncertainty in this semiarid basin with near‐zero flows. We conclude that the presented methodology provides improved estimates of parameter and total prediction uncertainty and should be useful for handling complex residual errors in other hydrologic regression models as well.

Multi-criterion Optimization Approach to Ill-posed Inverse Problem with Visual Feature’s Recovery

Ill-posed inverse problem is commonly existed in signal processing such as image reconstruction from projection, parameter estimation on e lectromagnetic field, and path optimization in IP network. Usually, the solution of an inverse problem is unstable, not uniqu e or does not exi t. Traditional approach to solve this problem is to estimate the solution by optimizing a regularized objective function. In some cases, recovery of visual features is most emphasized in that solution; thereof the distribution of residual errors has distinct influence on the quality of solution. This paper analyzes ill-posed inverse problem with the case of image reconstruction from projections and discusses its fidelity based on various visual features in the estimated solution. Multi -criterion Optimization Approac h , a new approach to solve the ill-posed inverse problems with good recovery of visual features, is presented with its theory basis and the experiment results. The solution stability and accuracy are analyzed using singular value decomposition (SVD), and main factors affecting the reconstruction quality are also discussed.

Correction strategies to manage deformations in head-and-neck radiotherapy

Background and purpose To optimize couch shifts based on multiple region-of-interest (ROI) registrations and derive criteria for adaptive replanning for management of deformations in head-and-neck (H&N) cancer patients. Materials and methods Eight ROIs containing bony structures were defined on the planning-CT and individually registered to daily cone-beam CTs for 19 H&N cancer patients. Online couch shifts were retrospectively optimized to correct the mean setup error over all ROIs ( mean correction) or to minimize the maximum error ( MiniMax correction). Residual error distributions were analyzed for both methods. The number of measurements before adaptive-intervention and corresponding action-level were optimized. Results Overall residual setup errors were smallest for the mean corrections, while MiniMax corrections reduced the largest errors. The percentage of fractions with residual errors >5 mm was 38% versus 19%. Reduction of deformations by single plan adaptation was most effective after eight fractions: systematic deformations reduced from 1.7 to 0.9 mm. Fifty percent of this reduction can already be achieved by replanning 1/3 of the patients. Conclusion Two correction methods based on multiple ROI registration were introduced to manage setup errors from deformations that either minimize overall geometrical uncertainties or maximum errors. Moreover, the registrations could be used to select patient with large deformations for replanning.

A Traffic Forecasting Method with Function to Control Residual Error Distribution for IP Access Networks

Since traffic in IP access networks is less aggregated than in backbone networks, its variance could be significant and its distribution may be long-tailed rather than Gaussian in nature. Such characteristics make it difficult to forecast traffic volume in IP access networks for appropriate capacity planning. This paper proposes a traffic forecasting method that includes a function to control residual error distribution in IP access networks. The objective of the proposed method is to grasp the statistical characteristics of peak traffic variations, while conventional methods focus on average rather than peak values. In the proposed method, a neural network model is built recursively while weighting residual errors around the peaks. This enables network operators to control the trade-off between underestimation and overestimation errors according to their planning policy. Evaluation with a total of 136 daily traffic volume data sequences measured in actual IP access networks demonstrates the performance of the proposed method.

Simulation of gas-solid fluidized bed reactor for F-T synthesis

Using the lumping method, CH4, C3H8, C10H22, and C22H44 were chosen as the model products, and CO as the key component. The mathematical model of a gas-solid fluidized bed reactor was established based on some hypotheses. The consumption kinetic model of CO was investigated, and the parameters were estimated by Universal Global Optimization with the Marquardt method. Residual error distribution and a statistical test show that the intrinsic kinetic models are reliable and acceptable. A model of carbon chain growth probability was established in terms of experiments. Coupled with the Ander-son-Schulz-Flory (ASF) distribution, the amount of specific product could be obtained. Large-scale cold model experiments were conducted to investigate the distribution of the gas (solid) phase and determine the function of the voidage with the location of the catalytic bed. The change tendencies of the components in the catalytic bed at different temperatures were computed and figured out. The calculated value computed by the model established for the Fe-based F-T synthesis catalyst fit the experimental value very well under the same operating conditions, and all the absolute values of the relative deviations are less than 5%.

Setup Reproducibility for Thoracic and Upper Gastrointestinal Radiation Therapy: Influence of Immobilization Method and On-Line Cone-Beam CT Guidance

We report the setup reproducibility of thoracic and upper gastrointestinal (UGI) radiotherapy (RT) patients for 2 immobilization methods evaluated through cone-beam computed tomography (CBCT) image guidance, and present planning target volume (PTV) margin calculations made on the basis of these observations. Daily CBCT images from 65 patients immobilized in a chestboard (CB) or evacuated cushion (EC) were registered to the planning CT using automatic bony anatomy registration. The standardized region-of-interest for matching was focused around vertebral bodies adjacent to tumor location. Discrepancies >3 mm between the CBCT and CT datasets were corrected before initiation of RT and verified with a second CBCT to assess residual error (usually taken after 90 s of the initial CBCT). Positional data were analyzed to evaluate the magnitude and frequencies of setup errors before and after correction. The setup distributions were slightly different for the CB (797 scans) and EC (757 scans) methods, and the probability of adjustment at a 3-mm action threshold was not significantly different ( p = 0.47). Setup displacements >10 mm in any direction were observed in 10% of CB fractions and 16% of EC fractions ( p = 0.0008). Residual error distributions after CBCT guidance were equivalent regardless of immobilization method. Using a published formula, the PTV margins for the CB were L/R, 3.3 mm; S/I, 3.5 mm; and A/P, 4.6 mm), and for EC they were L/R, 3.7 mm; S/I, 3.3 mm; and A/P, 4.6 mm. In the absence of image guidance, the CB slightly outperformed the EC in precision. CBCT allows reduction to a single immobilization system that can be chosen for efficiency, logistics, and cost. Image guidance allows for increased geometric precision and accuracy and supports a corresponding reduction in PTV margin.

Study on methanol synthesis from coal-based syngas

The intrinsic kinetic models of the Langmuir-Hinshelwood type were investigated in terms of the reaction rates of CO hydrogenation and CO2 hydrogenation in the form of reactant fugacity. The parameters were estimated by the Universal Global Optimization using the Marquardt method. Residual error distribution and statistic tests show that the intrinsic kinetic models are reliable and acceptable. The mathematic model of a combined converter formed by gas-cooled and water-cooled reactor was developed and the gas-cooled reactor and the water-cooled reactor were characterized with one-dimensional mathematic model. The distributions of temperature and concentration in the catalytic bed of the gas-cooled reactor and the water-cooled reactor in a combined converter with a yield of 1.2 Mt/a were simulated. The parallel cross linking pore model was used to describe the transfer process of multi-component diffusion system in the catalyst. The calculated value computed by the internal diffusion efficiency factor calculation model established for methanol synthesis catalyst fit the experimental value very well.

Intrinsic kinetics of methane aromatization under non-oxidative conditions over modified Mo/HZSM-5 catalysts

The intrinsic reaction kinetics of methane aromatization under non-oxidative conditions over modified Mo/HZSM-5 catalysts was studied in the quartz pipe-reactor under ordinary pressure with the temperature ranging from 913.15 to 973.15 K and the space velocity from 700 to 2100 ml/(g·h). The Langmuir-Hinshelwood model was chosen to describe the intrinsic kinetics while Levenberg-Marquardt method was selected to determine the parameters in the kinetic model. Statistical test and residual error distribution diagrams showed that experimental data were in good agreement with calculated data, and Langmuir-Hinshelwood model was suitable for the description of the intrinsic kinetics of methane aromatization under the reaction conditions discussed in this article.

Financial prediction with constrained tail risk

A new class of asymmetric loss functions derived from the least absolute deviations or least squares loss with a constraint on the mean of one tail of the residual error distribution, is introduced for analyzing financial data. Motivated by risk management principles, the primary intent is to provide “cautious” forecasts under uncertainty. The net effect on fitted models is to shape the residuals so that on average only a prespecified proportion of predictions tend to fall above or below a desired threshold. The loss functions are reformulated as objective functions in the context of parameter estimation for linear regression models, and it is demonstrated how optimization can be implemented via linear programming. The method is a competitor of quantile regression, but is more flexible and broader in scope. An application is illustrated on prediction of NDX and SPX index returns data, while controlling the magnitude of a fraction of worst losses.

On the performance of turbo codes-based hybrid ARQ with segment selective repeat in WCDMA

In this paper, a new turbo codes-based hybrid automatic repeat request (TC-HARQ) scheme with segment selective repeat (SSR) is proposed. The main strategy is, upon retransmission, to repeat the data that are most important for the next round of decoding based on the distribution of residual errors after current decoding. The performance in terms of reliability and throughput is analyzed. To adapt to correlated fading channels where an inter-leaver is always employed before transmission, we further modify the SSR strategy so that data having experienced correlated deep fading are selected for retransmission. Finally, this proposed scheme is applied to the wideband code division multiple access (WCDMA) system under frequency selective fading channels. Simulation results demonstrate that in all single and multiple user cases, SSR-based TC-HARQ leads to significant throughput improvement with similar bit error rate (BER) performance as compared to type-I TC-HARQ.