Joint Confidence Research Articles

Real-time RT-PCR high-resolution melting curve analysis and multiplex RT-PCR to detect and differentiate grapevine leafroll-associated virus 3 variant groups I, II, III and VI

BackgroundGrapevine leafroll-associated virus 3 (GLRaV-3) is the main contributing agent of leafroll disease worldwide. Four of the six GLRaV-3 variant groups known have been found in South Africa, but their individual contribution to leafroll disease is unknown. In order to study the pathogenesis of leafroll disease, a sensitive and accurate diagnostic assay is required that can detect different variant groups of GLRaV-3.MethodsIn this study, a one-step real-time RT-PCR, followed by high-resolution melting (HRM) curve analysis for the simultaneous detection and identification of GLRaV-3 variants of groups I, II, III and VI, was developed. A melting point confidence interval for each variant group was calculated to include at least 90% of all melting points observed. A multiplex RT-PCR protocol was developed to these four variant groups in order to assess the efficacy of the real-time RT-PCR HRM assay.ResultsA universal primer set for GLRaV-3 targeting the heat shock protein 70 homologue (Hsp70h) gene of GLRaV-3 was designed that is able to detect GLRaV-3 variant groups I, II, III and VI and differentiate between them with high-resolution melting curve analysis. The real-time RT-PCR HRM and the multiplex RT-PCR were optimized using 121 GLRaV-3 positive samples. Due to a considerable variation in melting profile observed within each GLRaV-3 group, a confidence interval of above 90% was calculated for each variant group, based on the range and distribution of melting points. The intervals of groups I and II could not be distinguished and a 95% joint confidence interval was calculated for simultaneous detection of group I and II variants. An additional primer pair targeting GLRaV-3 ORF1a was developed that can be used in a subsequent real-time RT-PCR HRM to differentiate between variants of groups I and II. Additionally, the multiplex RT-PCR successfully validated 94.64% of the infections detected with the real-time RT-PCR HRM.ConclusionThe real-time RT-PCR HRM provides a sensitive, automated and rapid tool to detect and differentiate different variant groups in order to study the epidemiology of leafroll disease.

Evaluating the validity of spectral calibration models for quantitative analysis following signal preprocessing

When paired with high-powered chemometric analysis, spectrometric methods offer great promise for the high-throughput analysis of complex systems. Effective classification or quantification often relies on signal preprocessing to reduce spectral interference and optimize the apparent performance of a calibration model. However, less frequently addressed by systematic research is the affect of preprocessing on the statistical accuracy of a calibration result. The present work demonstrates the effectiveness of two criteria for validating the performance of signal preprocessing in multivariate models in the important dimensions of bias and precision. To assess the extent of bias, we explore the applicability of the elliptic joint confidence region (EJCR) test and devise a new means to evaluate precision by a bias-corrected root mean square error of prediction. We show how these criteria can effectively gauge the success of signal pretreatments in suppressing spectral interference while providing a straightforward means to determine the optimal level of model complexity. This methodology offers a graphical diagnostic by which to visualize the consequences of pretreatment on complex multivariate models, enabling optimization with greater confidence. To demonstrate the application of the EJCR criterion in this context, we evaluate the validity of representative calibration models using standard pretreatment strategies on three spectral data sets. The results indicate that the proposed methodology facilitates the reliable optimization of a well-validated calibration model, thus improving the capability of spectrophotometric analysis.

Application of a Bioenergetics Model for Hatchery Production: Largemouth Bass Fed Commercial Feeds

AbstractFish bioenergetics models based on natural prey items have been widely used to address research and management questions. However, few attempts have been made to evaluate and apply bioenergetics models to hatchery‐reared fish receiving commercial feeds that contain substantially higher energy densities than natural prey. In this study, we evaluated a bioenergetics model for age‐0 largemouth bass Micropterus salmoides reared on four commercial feeds. Largemouth bass (n ≈ 3,504) were reared for 70 d at 25°C in sixteen 833‐L circular tanks connected in parallel to a recirculation system. Model performance was evaluated using error components (mean, slope, and random) derived from decomposition of the mean square error obtained from regression of observed on predicted values. Mean predicted consumption was only 8.9% lower than mean observed consumption and was similar to error rates observed for largemouth bass consuming natural prey. Model evaluation showed that the 97.5% joint confidence region included the intercept of 0 (−0.43 ± 3.65) and slope of 1 (1.08 ± 0.20), which indicates the model accurately predicted consumption. Moreover model error was similar among feeds (P = 0.98), and most error was probably attributable to sampling error (unconsumed feed), underestimated predator energy densities, or consumption‐dependent error, which is common in bioenergetics models. This bioenergetics model could provide a valuable tool in hatchery production of largemouth bass. Furthermore, we believe that bioenergetics modeling could be useful in aquaculture production, particularly for species lacking historical hatchery constants or conventional growth models.

Probing cosmology with weak lensing Minkowski functionals

In this paper, we show that Minkowski functionals (MFs) of weak gravitational lensing (WL) convergence maps contain significant non-Gaussian, cosmology-dependent information. To do this, we run a large suite of cosmological ray-tracing N-body simulations to create mock WL convergence maps, and study the cosmological information content of MFs derived from these maps. Our suite consists of 80 independent ${512}^{3}$ N-body runs, covering seven different cosmologies, varying three cosmological parameters ${\ensuremath{\Omega}}_{m}$, $w$, and ${\ensuremath{\sigma}}_{8}$ one at a time, around a fiducial lambda cold dark matter model. In each cosmology, we use ray tracing to create a thousand pseudoindependent $12\text{ }\text{ }{\mathrm{deg}}^{2}$ convergence maps, and use these in a Monte Carlo procedure to estimate the joint confidence contours on the above three parameters. We include redshift tomography at three different source redshifts ${z}_{s}=1$, 1.5, 2, explore five different smoothing scales ${\ensuremath{\theta}}_{G}=1,2,3,5,10\text{ }\text{ }\mathrm{arcmin}$, and explicitly compare and combine the MFs with the WL power spectrum. We find that the MFs capture a substantial amount of information from non-Gaussian features of convergence maps, i.e. beyond the power spectrum. The MFs are particularly well suited to break degeneracies and to constrain the dark energy equation of state parameter $w$ (by a factor of $\ensuremath{\approx}\mathrm{\text{three}}$ better than from the power spectrum alone). The non-Gaussian information derives partly from the one-point function of the convergence (through ${V}_{0}$, the ``area'' MF), and partly through nonlinear spatial information (through combining different smoothing scales for ${V}_{0}$, and through ${V}_{1}$ and ${V}_{2}$, the boundary length and genus MFs, respectively). In contrast to the power spectrum, the best constraints from the MFs are obtained only when multiple smoothing scales are combined.

A Study of Process Quality Assessment for Golf Club-Shaft in Leisure Sport Industries

Abstract Effective management of process quality is crucial for attracting customers and maintaining their loyalty, and the quantification of quality for processes with multiple characteristics has recently been receiving considerable attention. This paper proposes a comprehensive process quality index to provide numerical measures for the precision, accuracy, and performance of processes in the manufacturing of golf club-shafts, using both smaller-the-better type and symmetric nominal-the-best type characteristics. The point estimates of these indices were replaced with joint confidence blocks in order to overcome a lack of reliability. Based on this index, we developed a control chart with process capability zones describing joint confidence blocks of all characteristics related to golf club-shafts within a single chart. Finally, we present an assessment procedure and illustrated examples with which to evaluate the process quality for the manufacture of golf club-shaft. The results reveal that the straightness and torsion of the club-shaft are “out of control” and unqualified, whereas the length, tip outer circumference, and butt outer circumference of the club-shaft are categorized as “excessive.” The application of this chart enables engineers involved in the manufacturing of golf equipment to simultaneously monitor and control the quality characteristics of golf club-shafts.

Optimum Design of Experiments for Statistical Inference

SummaryOne attractive feature of optimum design criteria, such as D- and A-optimality, is that they are directly related to statistically interpretable properties of the designs that are obtained, such as minimizing the volume of a joint confidence region for the parameters. However, the assumed relationships with inferential procedures are valid only if the variance of experimental units is assumed to be known. If the variance is estimated, then the properties of the inferences depend also on the number of degrees of freedom that are available for estimating the error variance. Modified optimality criteria are defined, which correctly reflect the utility of designs with respect to some common types of inference. For fractional factorial and response surface experiments, the designs that are obtained are quite different from those which are optimal under the standard criteria, with many more replicate points required to estimate error. The optimality of these designs assumes that inference is the only purpose of running the experiment, but in practice interpretation of the point estimates of parameters and checking for lack of fit of the treatment model assumed are also usually important. Thus, a compromise between the new criteria and others is likely to be more relevant to many practical situations. Compound criteria are developed, which take account of multiple objectives, and are applied to fractional factorial and response surface experiments. The resulting designs are more similar to standard designs but still have sufficient residual degrees of freedom to allow effective inferences to be carried out. The new procedures developed are applied to three experiments from the food industry to see how the designs used could have been improved and to several illustrative examples. The design optimization is implemented through a simple exchange algorithm.

Determination of the joint confidence region of the optimal operating conditions in robust design by the bootstrap technique

Robust design is widely recognised as a leading method for reducing variability and improving quality. Most of the engineering statistics literature focuses on finding point estimates of the optimum operating conditions for robust design. Various procedures have been considered for calculating point estimates of the optimum operating conditions. Although the point estimation procedure is important for continuous quality improvement, the immediate question is ‘‘how accurate are these optimum operating conditions?” The answer is to consider interval estimation for a single variable or joint confidence regions for multiple variables. In this paper, using the bootstrap technique, we develop procedures for obtaining joint confidence regions for the optimum operating conditions. Two different procedures, using Bonferroni and multivariate normal approximation, are introduced. The proposed methods are illustrated and substantiated using a numerical example.

Joint Confidence Region for the Tuning Parameters of the PID Controller

The aim of this paper is to estimate the joint confidence region for the tuning parameters of the PID controller. Considerations on the statistical independence and the linear relationship between the tuning parameters for a more realistic scenario are taken into account. In order to capture the data necessary for the simulation, an appropriate structure was implemented, consisting of a process-model-based controller. By using the data resulting from the simulations, it was also possible to find the probability density function for each tuning parameter, as well the region of joint confidence of such parameters, which indicates a contraction of the region when compared with the standard level of significance. What is also shown is how to restore the joint confidence region by means of the Principal Components Technique.

A generalized model for estimating the energy density of invertebrates

Invertebrate energy density (ED) values are traditionally measured using bomb calorimetry. However, many researchers rely on a few published literature sources to obtain ED values because of time and sampling constraints on measuring ED with bomb calorimetry. Literature values often do not account for spatial or temporal variability associated with invertebrate ED. Thus, these values can be unreliable for use in models and other ecological applications. We evaluated the generality of the relationship between invertebrate ED and proportion of dry-to-wet mass (pDM). We then developed and tested a regression model to predict ED from pDM based on a taxonomically, spatially, and temporally diverse sample of invertebrates representing 28 orders in aquatic (freshwater, estuarine, and marine) and terrestrial (temperate and arid) habitats from 4 continents and 2 oceans. Samples included invertebrates collected in all seasons over the last 19 y. Evaluation of these data revealed a significant relationship between ED and pDM (r2 = 0.96, p < 0.0001), where ED (as J/g wet mass) was estimated from pDM as ED = 22,960pDM − 174.2. Model evaluation showed that nearly all (98.8%) of the variability between observed and predicted values for invertebrate ED could be attributed to residual error in the model. Regression of observed on predicted values revealed that the 97.5% joint confidence region included the intercept of 0 (−103.0 ± 707.9) and slope of 1 (1.01 ± 0.12). Use of this model requires that only dry and wet mass measurements be obtained, resulting in significant time, sample size, and cost savings compared to traditional bomb calorimetry approaches. This model should prove useful for a wide range of ecological studies because it is unaffected by taxonomic, seasonal, or spatial variability.

Simultaneous determination of pre-emergence herbicides in environmental samples using HPLC-DAD combined with second-order calibration based on self-weighted alternating trilinear decomposition algorithm

This work presents a novel strategy for simultaneous and rapid quantitative analysis of three pre-emergence herbicides in environmental samples using HPLC-DAD combined with second-order calibration based on the self-weighted alternating trilinear decomposition (SWATLD) algorithm. The sample preparation procedure was simplified only by using water as solvent and methanol as extractant and data were measured in less than 4.2 min by applying an isocratic mode. Although the elution and spectral profiles of the analytes, prometryne (PRO), napropamide (NAP) and alachlor (ALA), are heavily overlapped with each other and with matrix constitutes, the method not only extracts the profiles of the analytes, but also simultaneously determines the concentrations of them in actual complex systems, i.e., river sediment and wastewater samples. In the analysis of river sediment and wastewater samples, the obtained average recoveries were 99 ± 6% and 98 ± 5% for PRO, 108 ± 6% and 100 ± 4% for NAP and 98 ± 5% and 97 ± 4% for ALA, respectively. Furthermore, the accuracy and precision of the proposed method was also evaluated through elliptical joint confidence region tests as well as figures of merit. Such a chemometrics-based protocol may be a very promising tool for more analytical applications in environment monitoring, due to its advantages of easy sample pretreatment, green, sufficient spectral resolution and concentration prediction even in the presence of unknown interferences.

Comparison of the predictive ability of several second-order multivariate methods in the simultaneous determination of two therapeutic drugs in human urine

The aim of this paper is to study the applicability of second-order multivariate methods in the simultaneous determination of two therapeutic drugs in human urine samples. The studied drugs, irinotecan and thalidomide, are used in the treatment of malignant tumours. Irinotecan (CPT-11) is used to treat colon cancer; recent studies have shown the benefits of using thalidomide in combination with CPT-11 in the treatment of this disease. CPT-11 is highly fluorescent, but the native fluorescence of thalidomide is very weak. The second-order methods assayed were parallel factor analysis (PARAFAC), unfolded partial least-squares (U-PLS) and multidimensional partial least-squares (N-PLS), both combined with the residual bilinearization procedure (RBL). The excitation-emission matrices (EEMs) of the samples were recorded as analytical signal. The accuracy and precision of the algorithms were evaluated through the root mean square error of prediction (RMSEP) and the elliptical joint confidence region test (EJCR), obtaining better results with PARAFAC, which was successfully applied to the determination of thalidomide and CPT-11 in human urine samples, after a previous liquid–liquid extraction with chloroform.

Implementation of a genetic algorithm on MD-optimal designs for multivariate response surface models

This study presents a genetic algorithm (GA) for identifying the exact D-optimal design for multivariate response surface models (called MD-optimal design). The MD-optimal design minimizes the volume of joint confidence regions of model parameters. The covariance between any two responses is assumed to be identical in the two examples of four responses and biresponse problems considered in this study. We have also provided an example of covariance estimation. In order to obtain the initial candidate set, we first obtain a D-optimal design for each response model by using a conventional approach; then, the set of solutions obtained from the individual model is treated as the initial set in the GA. This shows that the MD-optimal designs converge toward the same D-optimal design in a single response linear model; however, the different variance–covariance matrices attain dissimilar objective values. The GA exhibits stable representation in multiple response design problems and performs better than the US algorithm, which is generated only near the MD-optimal design. It is possible for an experimenter to set a high crossover rate except full crossover, and estimate the variance–covariance matrix in the preprocess or set it as an identity matrix in the process of the GA.

Fast liquid chromatography-diode array detection assisted by chemometrics for quantification of seven ultraviolet filters in effluent wastewater

A fast chromatographic method is presented for simultaneous quantification of seven organic ultraviolet (UV) filters (benzophenone-3,4-methylbenzilidene camphor, octocrylene, 1-(4-tert-butylphenyl)-3-(4-methyoxyphenyl)1,3-propanedione), ethylhexyl methoxy cinnamate, ethylhexyl salicylate and homosalate) in effluent wastewater samples. The UV filters were pre-concentrated by Bond Elut-ENV cartridges and separated on an ODS column (15cm×0.46cm, 5μm) in less than 2.5min using a non-aqueous mobile phase of methanol–acetonitrile (50:50, v/v) with flow-rate of 1.5mLmin−1. Appropriate baseline correction through asymmetric least squares was applied to reduce the matrix of background signals in three way data. Then, second-order calibration based on multivariate curve resolution-alternating least squares (MCR-ALS) was implemented on the unfolded three-way data obtained from liquid chromatography with diode array detection (LC-DAD) through standard addition calibration method for handling co-eluted peaks, systematic and proportional errors. Recoveries ranging from 76% to 130% and %RSD values less than 11.2 for all UV filter shows the accuracy and precision of the proposed method in wastewater samples. In addition, statistical t-test as well as computed elliptical joint confidence region (EJCR) confirms the accuracy of the proposed method and indicates the absence of both constant and proportional errors in the predicted concentrations. This study demonstrates that coupling of the fast HPLC-DAD method with powerful algorithm of MCR-ALS can be considered as an efficient method for quantification of UV filters in highly contaminated samples of wastewaters where both time and cost per each analysis can be reduced significantly.

Uncertainty of variance component estimates in nested sampling: a case study on the field‐scale spatial variability of a restored soil

We studied the variation of soil properties on a 6‐ha artificial catchment constructed near Cottbus, Germany, to investigate processes of initial ecosystem genesis. We wanted to evaluate whether spatial auto‐correlation patterns could be identified 3 years after site construction. Topsoil was sampled at 192 locations using a balanced nested design involving six spatial scales (0.2 to 60 m) and analysed for particle size, organic matter content, pH, soluble P and various fractions of selected metals. Variance components were estimated by residual maximum likelihood. The uncertainty of variance estimates was characterized by the Fisher Information matrix and likelihood joint confidence regions. The latter approach was used for the first time to characterize uncertainties of variance estimates in spatial nested sampling. Likelihood ratio tests showed that all variables were spatially auto‐correlated but the allocation of the variance to specific spatial scales was highly uncertain. For most variables, at least one variance component could not be estimated precisely because the profile likelihood was either flat or the maximum lay on the boundary of the parameter space. Uncertainty estimates derived from the Fisher Information matrix either could not be computed or were unrealistic in these cases. Likelihood joint confidence regions gave more realistic uncertainty estimates. Joint confidence regions for accumulated variance components showed that the shape of the estimated variograms was poorly defined for most variables. Simulations indicated that poor identification of variance components might be a general problem of nested sampling surveys, which has been under‐estimated in the past. Hence, our work provides some incentive for re‐examining the statistical properties of the methodology.

Anthocyanin degradation kinetics during thermal and high pressure treatments of raspberries

The effect of combined high temperature and high pressure on the degradation of the four main cyanidin-3-glycosides in raspberries was investigated. Anthocyanin degradation accelerated with increasing temperature as well as with increasing pressure, revealing a synergistic effect of both process variables. Degradation rate constants were estimated using a first order kinetic model. Temperature and pressure dependence of the degradation rate constants were expressed as activation energies and activation volumes according to Arrhenius and Eyring equations, respectively. In search of statistical differences between the E a – k ref - and V a – k ref -parameters estimated simultaneously, 90% joint confidence regions were constructed. A combined Arrhenius–Eyring model was found suitable to describe the combined temperature–pressure dependence of the degradation rate constants. Cyanidin-3-glucorutinoside showed the slowest degradation in comparison to the other cyanidins. Cyanidin-3-rutinoside experienced the smallest effect of temperature and the strongest effect of pressure compared to the others.

Functional Data Analysis in Ecosystem Research: The Decline of Oweekeno Lake Sockeye Salmon and Wannock River Flow

Functional regression is a natural tool for exploring the potential impact of the physical environment (continuously monitored) on biological processes (often only assessed annually). This paper explores the potential use of functional regression analysis and the closely related functional principal component analysis for studying the relationship between river flow (continuously monitored) and salmon abundance (measured annually). The specific example involves a depressed sockeye salmon population in Rivers Inlet, BC. Particular attention is given to (i) the role of subject matter expertise and cross-validation techniques in guiding decisions on basis functions and smoothing parameters, and (ii) the importance of restricting the time domain for the continuously monitored variable to a scientifically meaningful period of time. In addition, we derive a joint confidence region for the functional regression coefficient function and discuss its use relative to the more commonly used pointwise confidence intervals. The analysis points to a substantial negative correlation between early spring river flow and marine survival of the sockeye salmon that subsequently migrate down the inlet.

Confidence Intervals and Joint Confidence Regions for the Two-Parameter Exponential Distribution based on Records

Exponential distribution is widely adopted as a lifetime model. Many authors have considered the interval estimation of the parameters of two-parameter exponential distribution based on complete and censored samples. In this paper, we consider the interval estimation of the location and scale parameters and the joint confidence region of the parameters of two-parameter exponential distribution based on upper records. A simulation study is done for the performance of all proposed confidence intervals and regions. We also propose the predictive intervals of the future records. Finally, a numerical example is given to illustrate the proposed methods.

Optimal sampling in retrospective logistic regression via two-stage method

Case-control sampling is popular in epidemiological research because of its cost and time saving. In a logistic regression model, with limited knowledge on the covariance matrix of the point estimator of the regression coefficients a priori, there exists no fixed sample size analysis. In this study, we propose a two-stage sequential analysis, in which the optimal sample fraction and the required sample size to achieve a predetermined volume of a joint confidence set are estimated in an interim analysis. Additionally required observations are collected in the second stage according to the estimated optimal sample fraction. At the end of the experiment, data from these two stages are combined and analyzed for statistical inference. Simulation studies are conducted to justify the proposed two-stage procedure and an example is presented for illustration. It is found that the proposed two-stage procedure performs adequately in the sense that the resultant joint confidence set has a well-controlled volume and achieves the required coverage probability. Furthermore, the optimal sample fractions among all the selected scenarios are close to one. Hence, the proposed procedure can be simplified by always considering a balance design.

Errors of Estimating Near-Surface Q-A statistical Approach

Although various estimating methods have been developed for measuring Q from near-surface seismic data, less thought has been given to the accuracy of Q obtained. The errors of Q depend on the ways of measuring Q and the computation techniques used in estimating. The main purpose of this paper is to give a compre- hensive evaluation for the accuracy of measuring near-surface Q. We discuss the possible origins from which errors may develop, and provide a statistical guide to the accuracy that can be expected. A set of real data based on the improved spectral ratio method for near-surface Q was used as an example of validation and sensitivity analysis. The Bonferroni procedure was adopted for deriving the joint confidence intervals for k and n of the power law model. The same approach with modest modification may be applied to analyze the accuracy of Q estimated by other methods.

Simultaneous Determination of Dextromethorphan and Quinidine Contents in Biological Fluid Samples Using Excitation-Emission Matrix Fluorescence Coupled with Second-Order Calibration Methods

This paper presents a novel method for simultaneous determination of dextromethorphan and quinidine contents in biological fluid samples using excitation–emission matrix fluorescence (EEM) coupled with second-order calibration methods. The adopted calibration methods, i.e., parallel factor analysis (PARAFAC), self-weighted alternating tri-linear decomposition (SWATLD), and alternating penalty trilinear decomposition (APTLD), could adequately exploit the second-order advantage. The accuracy of the three methods was evaluated through figures of merit and elliptical joint confidence region (EJCR) tests. It has been found that all the methods could give good results. But, with correct number of factors, the PARAFAC model performed slightly better than the others.