Group testing is a method that can be used to estimate the prevalence of rare infectious diseases,which can effectively save time and reduce costs compared to the method of random sampling.However,previous literature ...Group testing is a method that can be used to estimate the prevalence of rare infectious diseases,which can effectively save time and reduce costs compared to the method of random sampling.However,previous literature only demonstrated the optimality of group testing strategy while estimating prevalence under some strong assumptions.This article weakens the assumption of misclassification rate in the previous literature,considers the misclassification rate of the infected samples as a differentiable function of the pool size,and explores some optimal properties of group testing for estimating prevalence in the presence of differential misclassification conforming to this assumption.This article theoretically demonstrates that the group testing strategy performs better than the sample by sample procedure in estimating disease prevalence when the total number of sample pools is given or the size of the test population is determined.Numerical simulation experiments were conducted to evaluate the performance of group tests in estimating prevalence in the presence of dilution effect.展开更多
To correct for misclassification error in registering causes of death in Iran death registry using Bayesian method. METHODSNational death statistic from 2006 to 2010 for gastric cancer which reported annually by the M...To correct for misclassification error in registering causes of death in Iran death registry using Bayesian method. METHODSNational death statistic from 2006 to 2010 for gastric cancer which reported annually by the Ministry of Health and Medical Education included in this study. To correct the rate of gastric cancer mortality with reassigning the deaths due to gastric cancer that registered as cancer without detail, a Bayesian method was implemented with Poisson count regression and beta prior for misclassified parameter, assuming 20% misclassification in registering causes of death in Iran. RESULTSRegistered mortality due to gastric cancer from 2006 to 2010 was considered in this study. According to the Bayesian re-estimate, about 3%-7% of deaths due to gastric cancer have registered as cancer without mentioning details. It makes an undercount of gastric cancer mortality in Iranian population. The number and age standardized rate of gastric cancer death is estimated to be 5805 (10.17 per 100000 populations), 5862 (10.51 per 100000 populations), 5731 (10.23 per 100000 populations), 5946 (10.44 per 100000 populations), and 6002 (10.35 per 100000 populations), respectively for years 2006 to 2010. CONCLUSIONThere is an undercount in gastric cancer mortality in Iranian registered data that researchers and authorities should notice that in sequential estimations and policy making.展开更多
BACKGROUND Misclassification of smoking habits leads to underestimation of true relationships between diseases and active smoking, and overestimation of true relationships with passive smoking. Information on misclass...BACKGROUND Misclassification of smoking habits leads to underestimation of true relationships between diseases and active smoking, and overestimation of true relationships with passive smoking. Information on misclassification rates can be obtained from studies using cotinine as a marker.AIM To estimate overall misclassification rates based on a review and meta-analysis of the available evidence, and to investigate how misclassification rates depend on other factors.METHODS We searched for studies using cotinine as a marker which involved at least 200 participants and which provided information on high cotinine levels in selfreported non-, never, or ex-smokers or on low levels in self-reported smokers. We estimated overall misclassification rates weighted on sample size and investigated heterogeneity by various study characteristics. Misclassification rates were calculated for two cotinine cut points to distinguish smokers and nonsmokers, the higher cut point intended to distinguish regular smoking.RESULTS After avoiding double counting, 226 reports provided 294 results from 205 studies. A total of 115 results were from North America, 128 from Europe, 25 from Asia and 26 from other countries. A study on 6.2 million life insurance applicants was considered separately. Based on the lower cut point, true current smokers represented 4.96%(95% CI 4.32-5.60%) of reported non-smokers, 3.00%(2.45-3.54%) of reported never smokers, and 10.92%(9.23-12.61%) of reported exsmokers. As percentages of true current smokers, non-, never and ex-smokers formed, respectively, 14.50%(12.36-16.65%), 5.70%(3.20-8.20%), and 8.93%(6.57-11.29%). Reported current smokers represented 3.65%(2.84-4.45%) of true non-smokers. There was considerable heterogeneity between misclassification rates.Rates of claiming never smoking were very high in Asian women smokers, the individual studies reporting rates of 12.5%, 22.4%, 33.3%, 54.2% and 66.3%. False claims of quitting were relatively high in pregnant women, in diseased individuals who may recently have been advised to quit, and in studies considering cigarette smoking rather than any smoking. False claims of smoking were higher in younger populations. Misclassification rates were higher in more recently published studies. There was no clear evidence that rates varied by the body fluid used for the cotinine analysis, the assay method used, or whether the respondent was aware their statements would be validated by cotinine-though here many studies did not provide relevant information. There was only limited evidence that rates were lower in studies classified as being of good quality,based on the extent to which other sources of nicotine were accounted for.CONCLUSION It is important for epidemiologists to consider the possibility of bias due to misclassification of smoking habits, especially in circumstances where rates are likely to be high. The evidence of higher rates in more recent studies suggests that the extent of misclassification bias in studies relating passive smoking to smoking-related disease may have been underestimated.展开更多
Enterprises have vast amounts of customer behavior data in the era of big data. How to take advantage of these data to evaluate custom forfeit risks effectively is a common issue faced by enterprises. Most of traditio...Enterprises have vast amounts of customer behavior data in the era of big data. How to take advantage of these data to evaluate custom forfeit risks effectively is a common issue faced by enterprises. Most of traditional customer churn predicting models ignore customer segmentation and misclassification cost, which reduces the rationality of model. Dealing with these deficiencies, we established a research model of customer churn based on customer segmentation and misclassification cost. We utilized this model to analyze customer behavior data of a telecom company. The results show that this model is better than those models without customer segmentation and misclassification cost in terms of the performance, accuracy and coverage of model.展开更多
Discrimination and classification rules are based on different types of assumptions. Also, all most statistical methods are based on some necessary assumptions. Parametric methods are the best choice if it follows all...Discrimination and classification rules are based on different types of assumptions. Also, all most statistical methods are based on some necessary assumptions. Parametric methods are the best choice if it follows all the underlying assumptions. When assumptions are violated, parametric approaches do not provide a better solution and nonparametric techniques are preferred. After Box-Cox transformation, when assumptions are satisfied, parametric methods provide fewer misclassification rates. With this problem in mind, our concern is to compare the classification accuracy of parametric and non-parametric approaches with the aid of Box-Cox transformation and Bootstrapping. We carried Support Vector Machines (SVMs) and different discrimination and classification rules to classify objects. The attention is to critically compare the SVMs with Linear discrimination Analysis (LDA), and Quadratic discrimination Analysis (QDA) for measuring the performance of these techniques before and after Box-Cox transformation using misclassification rates. From the apparent error rates, we observe that before Box-Cox transformation, SVMs perform better than existing classification techniques, on the other hand, after Box-Cox transformation, parametric techniques provide fewer misclassification rates compared to nonparametric method. We also investigated the performances of classification techniques using the Bootstrap approach and observed that Bootstrap-based classification techniques significantly reduce the classification error rate than the usual techniques of small samples. Thus, this paper proposes to apply classification techniques under the Bootstrap approach for classifying objects in case of small sample. A real and simulated datasets application is carried out to see the performance.展开更多
In this work, we developed a theoretical framework leading to misclassification of the final size epidemic data for the stochastic SIR (Susceptible-In</span></span><span style="font-family:Verdana;...In this work, we developed a theoretical framework leading to misclassification of the final size epidemic data for the stochastic SIR (Susceptible-In</span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">fective</span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">-Removed), household epidemic model, with false negative and false positive misclassification probabilities. Maximum likelihood based algorithm is then employed for its inference. We then analyzed and compared the estimates of the two dimensional model with those of the three and four dimensional models associated with misclassified final size data over arrange of theoretical parameters, local and global infection rates and corresponding proportion infected in the permissible region, away from its boundaries and misclassification probabilities.</span></span></span><span><span><span style="font-family:""> </span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">The adequacies of the three models to the final size data are examined. The four and three-dimensional models are found to outperform the two dimensional model on misclassified final size data.展开更多
The human gastrointestinal(GI)tract is influenced by numerous disorders.If not detected in the early stages,they may result in severe consequences such as organ failure or the development of cancer,and in extreme case...The human gastrointestinal(GI)tract is influenced by numerous disorders.If not detected in the early stages,they may result in severe consequences such as organ failure or the development of cancer,and in extreme cases,become life-threatening.Endoscopy is a specialised imaging technique used to examine the GI tract.However,physicians might neglect certain irregular morphologies during the examination due to continuous monitoring of the video recording.Recent advancements in artificial intelligence have led to the development of high-performance AI-based systems,which are optimal for computer-assisted diagnosis.Due to numerous limitations in endoscopic image analysis,including visual similarities between infected and healthy areas,retrieval of irrelevant features,and imbalanced testing and training datasets,performance accuracy is reduced.To address these challenges,we proposed a framework for analysing gastrointestinal tract images that provides a more robust and secure model,thereby reducing the chances of misclassification.Compared to single model solutions,the proposed methodology improves performance by integrating diverse models and optimizing feature fusion using a dual-branch CNN transformer architecture.The proposed approach employs a dual-branch feature extraction mechanism,where in the first branch,features are extracted using Extended BEiT,and EfficientNet-B5 is utilized in the second branch.Additionally,crossentropy loss is used to measure the error of prediction at both branches,followed by model stacking.This multimodal framework outperforms existing approaches acrossmultiple metrics,achieving 94.12%accuracy,recall and F1-score,as well as 94.15%precision on the Kvasir dataset.Furthermore,the model successfully reduced the false negative rate to 5.88%,enhancing its ability to minimize misdiagnosis.These results highlight the adaptability of the proposed work in clinical practice,where it can provide fast and accurate diagnostic assistance crucial for improving the early diagnosis of diseases in the gastrointestinal tract.展开更多
Individual tree health plays a vital role in maintaining a forest's ecological functions,including resources for waterfowl and other wildlife.Seasonal flooding due to altered hydrology is a major stressor on indiv...Individual tree health plays a vital role in maintaining a forest's ecological functions,including resources for waterfowl and other wildlife.Seasonal flooding due to altered hydrology is a major stressor on individual tree health in Greentree reservoirs(GTR),impounded bottomland hardwood forests especially less water tolerant species like red oaks(Quercus spp.).We evaluated the health of individual red oak species(n=6,432)in 662 plots across elevation gradients in 12 GTRs within the lower Mississippi Alluvial Valley using two tree health assessment approaches.The first approach assigns tree conditions(i.e.,stressed,moderate,low)based on overall qualitative tree attributes,while the second approach ranks stress,assigning numerical value based on the severity of four distinct qualitative tree attributes(i.e.,tip dieback,epicormics branch,bark condition,basal swell).The result indicated that the highest mean stress rank and the highest proportion of stressed tree conditions were red oak species,nuttall oak(Q.texana;18.59,0.44),willow oak(Q.phellos;18.66,0.38)and cherrybark oak(Q.pagoda;18.90,0.37).Red oak stress is positively correlated to elevation across the landscape(τ=0.10,p<0.001),but is negatively correlated to relative elevation,topographical changes,within each GTR(τ=-0.11,p<0.001).Additionally,the two health assessments are significantly associated(χ^(2)=313.78,df=2,p<0.001)and had a 13.1%misclassification rate.By utilizing the stress rank method for better classification of tree conditions to understand the adverse effect of prolonged flooding on the health of desirable red oak and other native tree species,management practices can be adjusted to improve tree health in GTRs,benefiting both wildlife and economic value.展开更多
The purpose of this paper is to provide an error analysis for the multicategory support vector machine （MSVM） classificaton problems. We establish the uniform convergency approach for MSVMs and estimate the misclass...The purpose of this paper is to provide an error analysis for the multicategory support vector machine （MSVM） classificaton problems. We establish the uniform convergency approach for MSVMs and estimate the misclassification error. The main difficulty we overcome here is to bound the offset vector. As a result, we confirm that the MSVM classification algorithm with polynomial kernels is always efficient when the degree of the kernel polynomial is large enough. Finally the rate of convergence and examples are given to demonstrate the main results.展开更多
AIM To correct the misclassification in registered gastric cancer incidence across Iranian provinces in cancer registry data. METHODS Gastric cancer data is extracted from Iranian annual of national cancer registratio...AIM To correct the misclassification in registered gastric cancer incidence across Iranian provinces in cancer registry data. METHODS Gastric cancer data is extracted from Iranian annual of national cancer registration report 2008. A Bayesian method with beta prior is implemented to estimate the rate of misclassification in registering patient'spermanent residence in neighboring province. Each time two neighboring provinces with lower and higher than 100% expected coverage of cancer cases are selected to be entered in the model. The expected coverage of cancerous patient is reported by medical university of each province. It is assumed that some cancer cases from a province with a lower than 100% expected coverage are registered in their neighboring province with more than 100% expected coverage. RESULTS The condition was true for 21 provinces from a total of 30 provinces of Iran. It was estimated that 43% of gastric cancer cases of North and South Khorasan provinces in north-east of Iran was registered in Razavi Khorasan as the neighboring facilitate province; also 72% misclassification was estimated between Sistan and balochestan province and Razavi Khorasan. The misclassification rate was estimated to be 36% between West Azerbaijan province and East Azerbaijan province, 21% between Ardebil province and East Azerbaijan, 63% between Hormozgan province and Fars province, 8% between Chaharmahal and bakhtyari province and Isfahan province, 8% between Kogiloye and boyerahmad province and Isfahan, 43% Golestan province and Mazandaran province, 54% between Bushehr province and Khozestan province, 26% between Ilam province and Khuzestan province, 32% between Qazvin province and Tehran province(capital of Iran), 43% between Markazi province and Tehran, and 37% between Qom province and Tehran. CONCLUSION Policy makers should consider the regional misclassification in the time of programming for cancer control, prevention and resource allocation.展开更多
Object:To determine the extent and impact of upgrading and downgrading among men who underwent radical prostatectomy(RP)according to new grade groupings and to identify predictors of upgrading from biopsy grade Group ...Object:To determine the extent and impact of upgrading and downgrading among men who underwent radical prostatectomy(RP)according to new grade groupings and to identify predictors of upgrading from biopsy grade Group Ⅰ and Ⅱ,and downgrading to grade Group I,in a community setting.Methods:Study participants included 2279 men with non-metastatic prostate cancer diagnosed 2006-2015 who underwent prostatectomy,from the multi-institutional South Australia Prostate Cancer Clinical Outcomes Collaborative registry.Extent of up-or down-grading was assessed by comparing biopsy and prostatectomy grade groupings.Risk of biochemical recurrence(BCR)with upgrading was assessed using multivariable competing risk regression.Binomial logistic regression was used to identify pre-treatment predictors of upgrading from grade Groups Ⅰ and Ⅱ,and risk group reclassification among men with low risk disease.Results:Upgrading occurred in 35%of cases,while downgrading occurred in 13%of cases.Sixty percent with grade Group I disease were upgraded following prostatectomy.Upgrading from grade Group I was associated with greater risk of BCR compared with concordant grading(Hazard ratio:3.1,95%confidence interval:1.7-6.0).Older age,higher prostate-specific antigen levels(PSA),fewer biopsy cores,higher number of positive cores and more recent diagnosis predicted upgrading from grade Group Ⅰ,while higher PSA and clinical stage predicted upgrading from grade Group Ⅱ.No clinical risk factors for reclassification were identified.Conclusion:Biopsy sampling errors may play an important role in upgrading from grade Group I.Improved clinical assessment of grade is needed to encourage greater uptake of active surveillance.展开更多
In medical diagnosis, the problem of class imbalance is popular. Though there are abundant unlabeled data, it is very difficult and expensive to get labeled ones. In this paper, an ensemble-based active learning algor...In medical diagnosis, the problem of class imbalance is popular. Though there are abundant unlabeled data, it is very difficult and expensive to get labeled ones. In this paper, an ensemble-based active learning algorithm is proposed to address the class imbalance problem. The artificial data are created according to the distribution of the training dataset to make the ensemble diverse, and the random subspace re-sampling method is used to reduce the data dimension. In selecting member classifiers based on misclassification cost estimation, the minority class is assigned with higher weights for misclassification costs, while each testing sample has a variable penalty factor to induce the ensemble to correct current error. In our experiments with UCI disease datasets, instead of classification accuracy, F-value and G-means are used as the evaluation rule. Compared with other ensemble methods, our method shows best performance, and needs less labeled samples.展开更多
Uncertainty characterization has become increasingly recognized as an integral component in thematic mapping based on remotely sensed imagery, and descriptors such as percent correctly classified pixels (PCC) and Kapp...Uncertainty characterization has become increasingly recognized as an integral component in thematic mapping based on remotely sensed imagery, and descriptors such as percent correctly classified pixels (PCC) and Kappa coefficients of agreement have been devised as thematic accuracy metrics. However, such spatially averaged measures about accuracy neither offer hints about spatial variation in misclassification, nor are useful for quantifying error margins in derivatives, such as the areal extents of different land cover types and the land cover change statistics. Such limitations originate from the deficiency that spatial dependency is not accommodated in the conventional methods for error analysis. Geostatistics provides a good framework for uncertainty characterization in land cover information. Methods for predicting and propagating misclassification will be described on the basis of indicator samples and covariates, such as spectrally derived posteriori probabilities. An experiment using simulated datasets was carried out to quantify the error in land cover change derived from postclassification comparison. It was found that significant biases result from applying joint probability rules assuming temporal independence between misclassifications across time, thus emphasizing the need for the stochastic simulation in error modeling. Further investigations, incorporating indicators and probabilistic data for mapping and propagating misclassification, are anticipated.展开更多
To deal with Byzantine attacks in 5 G cognitive radio networks,a bilateral threshold selection-based algorithm is proposed in the spectrum sensing process. In each round,secondary uses( SUs) first submit the energy va...To deal with Byzantine attacks in 5 G cognitive radio networks,a bilateral threshold selection-based algorithm is proposed in the spectrum sensing process. In each round,secondary uses( SUs) first submit the energy values and instantaneous detection signal-to-noise ratios( SNRs) to the fusion center( FC). According to detection SNRs,the FC conducts normalization calculations on the energy values. Then,the FC makes a sort operation for these normalized energy values and traverses all the possible mid-points between these sorted normalized energy values to maximize the classification accuracy of each SU. Finally,by introducing the recognition probability and misclassification probability,the distributions of the normalized energy values are analyzed and the bilateral threshold of classification accuracy is obtained via a target misclassification probability. Hence,the blacklist of malicious secondary users( MSUs) is obtained. Simulation results show that the proposed scheme outperforms the current mainstream schemes in correct sensing probability,false alarm probability and detection probability.展开更多
To study the trend of hepatocellular carcinoma incidence after correcting the misclassification in registering cancer incidence across Iranian provinces in cancer registry data. METHODSIncidence data of hepatocellular...To study the trend of hepatocellular carcinoma incidence after correcting the misclassification in registering cancer incidence across Iranian provinces in cancer registry data. METHODSIncidence data of hepatocellular carcinoma were extracted from Iranian annual of national cancer registration reports 2004 to 2008. A Bayesian method was implemented to estimate the rate of misclassification in registering cancer incidence in neighboring province. A beta prior is considered for misclassification parameter. Each time two neighboring provinces were selected to be entered in the Bayesian model based on their expected coverage of cancer cases which is reported by medical university of the province. It is assumed that some cancer cases from a province that has an expected coverage of cancer cases lower than 100% are registered in their neighboring facilitate province with more than 100% expected coverage. RESULTSThere is an increase in the rate of hepatocellular carcinoma in Iran. Among total of 30 provinces of Iran, 21 provinces were selected to be entered to the Bayesian model for correcting the existed misclassification. Provinces with more medical facilities of Iran are Tehran (capital of the country), Razavi Khorasan in north-east of Iran, East Azerbaijan in north-west of the country, Isfahan in central part and near to Tehran, Khozestan and Fars in south and Mazandaran in north of the Iran, had an expected coverage more than their expectation. Those provinces had significantly higher rates of hepatocellular carcinoma than their neighboring provinces. In years 2004 to 2008, it was estimated to be on average 34% misclassification between North Khorasan province and Razavi Khorasan, 43% between South Khorasan province and Razavi Khorasan, 47% between Sistan and balochestan province and Razavi Khorasan, 23% between West Azerbaijan province and East Azerbaijan province, 25% between Ardebil province and East Azerbaijan province, 41% between Hormozgan province and Fars province, 22% betweenChaharmahal and bakhtyari province and Isfahan province, 22% between Kogiloye and boyerahmad province and Isfahan, 22% between Golestan province and Mazandaran province, 43% between Bushehr province and Khozestan province, 41% between Ilam province and Khuzestan province, 42% between Qazvin province and Tehran province, 44% between Markazi province and Tehran, and 30% between Qom province and Tehran. CONCLUSIONAccounting and correcting the regional misclassification is necessary for identifying high risk areas and planning for reducing the cancer incidence.展开更多
The author, who has published numerous meta-analyses of epidemiological studies, particularly on tobacco, comments on various aspects of their content. While such meta-analyses, even when well conducted, are more diff...The author, who has published numerous meta-analyses of epidemiological studies, particularly on tobacco, comments on various aspects of their content. While such meta-analyses, even when well conducted, are more difficult to draw inferences from than are meta-analyses of clinical trials, they allow greater insight into an association than do simple qualitative reviews. This editorial starts with a discussion of some problems relating to hypothesis definition. These include the definition of the outcome, the exposure and the population to be considered, as well as the study inclusion and exclusion criteria. Under literature searching, the author argues against restriction to studies published in peer-reviewed journals, emphasising the fact that relevant data may be available from other sources. Problems of identifying studies and double counting are discussed, as are various issues in regard to data entry. The need to check published effect estimates is emphasised, and techniques to calculate estimates from material provided in the source publication are described. Once the data have been collected and an overall effect estimate obtained, tests for heterogeneity should be conducted in relation to different study characteristics. Though some meta-analysts recommend classifying studies by an overall index of study quality, the author prefers to separately investigate heterogeneity by those factors which contribute to the assessment of quality. Reasons why an association may not actually reflect a true causal relationship are also discussed, with the editorial describing techniques for investigating the relevance of confounding, and referring to problems resulting from misclassification of key variables. Misclassification of disease, exposure and confounding variables can all produce a spurious association, as can misclassification of the variable used to determine whether an individual can enter the study, and the author points to techniques to adjust for this. Issues relating to publication bias and the interpretation of "statistically significant" results are also discussed. The editorial should give the reader insight into the difficulties of producing a good meta-analysis.展开更多
For the case where all multivariate normal parameters are known, we derive a new linear dimension reduction (LDR) method to determine a low-dimensional subspace that preserves or nearly preserves the original feature-...For the case where all multivariate normal parameters are known, we derive a new linear dimension reduction (LDR) method to determine a low-dimensional subspace that preserves or nearly preserves the original feature-space separation of the individual populations and the Bayes probability of misclassification. We also give necessary and sufficient conditions which provide the smallest reduced dimension that essentially retains the Bayes probability of misclassification from the original full-dimensional space in the reduced space. Moreover, our new LDR procedure requires no computationally expensive optimization procedure. Finally, for the case where parameters are unknown, we devise a LDR method based on our new theorem and compare our LDR method with three competing LDR methods using Monte Carlo simulations and a parametric bootstrap based on real data.展开更多
Tests for a proportion that may be zero are described. The setting is an environment in which there can be misclassifications or misdiagnoses, giving the possibility of nonzero counts from false positives even though ...Tests for a proportion that may be zero are described. The setting is an environment in which there can be misclassifications or misdiagnoses, giving the possibility of nonzero counts from false positives even though no real examples may exist. Both frequentist and Bayesian tests and analyses are presented, and examples are given.展开更多
Binary measurement systems that classify parts as either pass or fail are widely used. Inspectors or inspection systems are often subject to error. The error rates are unlikely to be identical across inspectors. We pr...Binary measurement systems that classify parts as either pass or fail are widely used. Inspectors or inspection systems are often subject to error. The error rates are unlikely to be identical across inspectors. We propose a random effects Bayesian approach to model the error probabilities and overall conforming rate. We also introduce a feature-subset selection procedure to determine the best inspector in terms of overall classification accuracy. We provide simulation studies that demonstrate the viability of our proposed estimation ranking and subset-selection methods and apply the methods to a real data set.展开更多
There are four serious problems in the discriminant analysis. We developed an optimal linear discriminant function （optimal LDF） based on the minimum number of misclassification （minimum NM） using integer programm...There are four serious problems in the discriminant analysis. We developed an optimal linear discriminant function （optimal LDF） based on the minimum number of misclassification （minimum NM） using integer programming （IP）. We call this LDF as Revised IP-OLDF. Only this LDF can discriminate the cases on the discriminant hyperplane （Probleml）. This LDF and a hard-margin SVM （H-SVM） can discriminate the lineary separable data （LSD） exactly. Another LDFs may not discriminate the LSD theoretically （Problem2）. When Revised IP-OLDF discriminate the Swiss banknote data with six variables, we find MNM of two-variables model such as （X4, X6） is zero. Because MNMk decreases monotounusly （MNMk 〉= MNM（k＋1））, sixteen MNMs including （X4, X6） are zero. Until now, because there is no research of the LSD, we surveyed another three linear separable data sets such as： 18 exam scores data sets, the Japanese 44 cars data and six microarray datasets. When we discriminate the exam scores with MNM=0, we find the generalized inverse matrix technique causes the serious Problem3 and confirmed this fact by the cars data. At last, we claim the discriminant analysis is not the inferential statistics because there is no standard errors （SEs） of error rates and discriminant coefficients （Problem4）. Therefore, we poroposed the ＂100-fold cross validation for the small sample＂ method （the method）. By this break-through, we can choose the best model having minimum mean of error rate （M2） in the validation sample and obtaine two 95% confidence intervals （CIs） of error rate and discriminant coefficients. When we discriminate the exam scores by this new method, we obtaine the surprising results seven LDFs except for Fisher＇s LDF are almost the same as the trivial LDFs. In this research, we discriminate the Japanese 44 cars data because we can discuss four problems. There are six independent variables to discriminate 29 regular cars and 15 small cars. This data is linear separable by the emission rate （X1） and the number of seats （X3）. We examine the validity of the new model selection procedure of the discriminant analysis. We proposed the model with minimum mean of error rates （M2） in the validation samples is the best model. We had examined this procedure by the exam scores, and we obtain good results. Moreover, the 95% CI of eight LDFs offers us real perception of the discriminant theory. However, the exam scores are different from the ordinal data. Therefore, we apply our theory and procedure to the Japanese 44 cars data and confirmed the same conclution.展开更多
基金supported by the National Natural Science Foundation of China(Grant No.72091212).
文摘Group testing is a method that can be used to estimate the prevalence of rare infectious diseases,which can effectively save time and reduce costs compared to the method of random sampling.However,previous literature only demonstrated the optimality of group testing strategy while estimating prevalence under some strong assumptions.This article weakens the assumption of misclassification rate in the previous literature,considers the misclassification rate of the infected samples as a differentiable function of the pool size,and explores some optimal properties of group testing for estimating prevalence in the presence of differential misclassification conforming to this assumption.This article theoretically demonstrates that the group testing strategy performs better than the sample by sample procedure in estimating disease prevalence when the total number of sample pools is given or the size of the test population is determined.Numerical simulation experiments were conducted to evaluate the performance of group tests in estimating prevalence in the presence of dilution effect.
文摘To correct for misclassification error in registering causes of death in Iran death registry using Bayesian method. METHODSNational death statistic from 2006 to 2010 for gastric cancer which reported annually by the Ministry of Health and Medical Education included in this study. To correct the rate of gastric cancer mortality with reassigning the deaths due to gastric cancer that registered as cancer without detail, a Bayesian method was implemented with Poisson count regression and beta prior for misclassified parameter, assuming 20% misclassification in registering causes of death in Iran. RESULTSRegistered mortality due to gastric cancer from 2006 to 2010 was considered in this study. According to the Bayesian re-estimate, about 3%-7% of deaths due to gastric cancer have registered as cancer without mentioning details. It makes an undercount of gastric cancer mortality in Iranian population. The number and age standardized rate of gastric cancer death is estimated to be 5805 (10.17 per 100000 populations), 5862 (10.51 per 100000 populations), 5731 (10.23 per 100000 populations), 5946 (10.44 per 100000 populations), and 6002 (10.35 per 100000 populations), respectively for years 2006 to 2010. CONCLUSIONThere is an undercount in gastric cancer mortality in Iranian registered data that researchers and authorities should notice that in sequential estimations and policy making.
基金Japan Tobacco International for financial support and assistance in obtaining some of the references
文摘BACKGROUND Misclassification of smoking habits leads to underestimation of true relationships between diseases and active smoking, and overestimation of true relationships with passive smoking. Information on misclassification rates can be obtained from studies using cotinine as a marker.AIM To estimate overall misclassification rates based on a review and meta-analysis of the available evidence, and to investigate how misclassification rates depend on other factors.METHODS We searched for studies using cotinine as a marker which involved at least 200 participants and which provided information on high cotinine levels in selfreported non-, never, or ex-smokers or on low levels in self-reported smokers. We estimated overall misclassification rates weighted on sample size and investigated heterogeneity by various study characteristics. Misclassification rates were calculated for two cotinine cut points to distinguish smokers and nonsmokers, the higher cut point intended to distinguish regular smoking.RESULTS After avoiding double counting, 226 reports provided 294 results from 205 studies. A total of 115 results were from North America, 128 from Europe, 25 from Asia and 26 from other countries. A study on 6.2 million life insurance applicants was considered separately. Based on the lower cut point, true current smokers represented 4.96%(95% CI 4.32-5.60%) of reported non-smokers, 3.00%(2.45-3.54%) of reported never smokers, and 10.92%(9.23-12.61%) of reported exsmokers. As percentages of true current smokers, non-, never and ex-smokers formed, respectively, 14.50%(12.36-16.65%), 5.70%(3.20-8.20%), and 8.93%(6.57-11.29%). Reported current smokers represented 3.65%(2.84-4.45%) of true non-smokers. There was considerable heterogeneity between misclassification rates.Rates of claiming never smoking were very high in Asian women smokers, the individual studies reporting rates of 12.5%, 22.4%, 33.3%, 54.2% and 66.3%. False claims of quitting were relatively high in pregnant women, in diseased individuals who may recently have been advised to quit, and in studies considering cigarette smoking rather than any smoking. False claims of smoking were higher in younger populations. Misclassification rates were higher in more recently published studies. There was no clear evidence that rates varied by the body fluid used for the cotinine analysis, the assay method used, or whether the respondent was aware their statements would be validated by cotinine-though here many studies did not provide relevant information. There was only limited evidence that rates were lower in studies classified as being of good quality,based on the extent to which other sources of nicotine were accounted for.CONCLUSION It is important for epidemiologists to consider the possibility of bias due to misclassification of smoking habits, especially in circumstances where rates are likely to be high. The evidence of higher rates in more recent studies suggests that the extent of misclassification bias in studies relating passive smoking to smoking-related disease may have been underestimated.
文摘Enterprises have vast amounts of customer behavior data in the era of big data. How to take advantage of these data to evaluate custom forfeit risks effectively is a common issue faced by enterprises. Most of traditional customer churn predicting models ignore customer segmentation and misclassification cost, which reduces the rationality of model. Dealing with these deficiencies, we established a research model of customer churn based on customer segmentation and misclassification cost. We utilized this model to analyze customer behavior data of a telecom company. The results show that this model is better than those models without customer segmentation and misclassification cost in terms of the performance, accuracy and coverage of model.
文摘Discrimination and classification rules are based on different types of assumptions. Also, all most statistical methods are based on some necessary assumptions. Parametric methods are the best choice if it follows all the underlying assumptions. When assumptions are violated, parametric approaches do not provide a better solution and nonparametric techniques are preferred. After Box-Cox transformation, when assumptions are satisfied, parametric methods provide fewer misclassification rates. With this problem in mind, our concern is to compare the classification accuracy of parametric and non-parametric approaches with the aid of Box-Cox transformation and Bootstrapping. We carried Support Vector Machines (SVMs) and different discrimination and classification rules to classify objects. The attention is to critically compare the SVMs with Linear discrimination Analysis (LDA), and Quadratic discrimination Analysis (QDA) for measuring the performance of these techniques before and after Box-Cox transformation using misclassification rates. From the apparent error rates, we observe that before Box-Cox transformation, SVMs perform better than existing classification techniques, on the other hand, after Box-Cox transformation, parametric techniques provide fewer misclassification rates compared to nonparametric method. We also investigated the performances of classification techniques using the Bootstrap approach and observed that Bootstrap-based classification techniques significantly reduce the classification error rate than the usual techniques of small samples. Thus, this paper proposes to apply classification techniques under the Bootstrap approach for classifying objects in case of small sample. A real and simulated datasets application is carried out to see the performance.
文摘In this work, we developed a theoretical framework leading to misclassification of the final size epidemic data for the stochastic SIR (Susceptible-In</span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">fective</span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">-Removed), household epidemic model, with false negative and false positive misclassification probabilities. Maximum likelihood based algorithm is then employed for its inference. We then analyzed and compared the estimates of the two dimensional model with those of the three and four dimensional models associated with misclassified final size data over arrange of theoretical parameters, local and global infection rates and corresponding proportion infected in the permissible region, away from its boundaries and misclassification probabilities.</span></span></span><span><span><span style="font-family:""> </span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">The adequacies of the three models to the final size data are examined. The four and three-dimensional models are found to outperform the two dimensional model on misclassified final size data.
基金appreciation to Prince Sattam bin Abdulaziz University for funding for funding this research work through the project number(PSAU/2024/01/30782).
文摘The human gastrointestinal(GI)tract is influenced by numerous disorders.If not detected in the early stages,they may result in severe consequences such as organ failure or the development of cancer,and in extreme cases,become life-threatening.Endoscopy is a specialised imaging technique used to examine the GI tract.However,physicians might neglect certain irregular morphologies during the examination due to continuous monitoring of the video recording.Recent advancements in artificial intelligence have led to the development of high-performance AI-based systems,which are optimal for computer-assisted diagnosis.Due to numerous limitations in endoscopic image analysis,including visual similarities between infected and healthy areas,retrieval of irrelevant features,and imbalanced testing and training datasets,performance accuracy is reduced.To address these challenges,we proposed a framework for analysing gastrointestinal tract images that provides a more robust and secure model,thereby reducing the chances of misclassification.Compared to single model solutions,the proposed methodology improves performance by integrating diverse models and optimizing feature fusion using a dual-branch CNN transformer architecture.The proposed approach employs a dual-branch feature extraction mechanism,where in the first branch,features are extracted using Extended BEiT,and EfficientNet-B5 is utilized in the second branch.Additionally,crossentropy loss is used to measure the error of prediction at both branches,followed by model stacking.This multimodal framework outperforms existing approaches acrossmultiple metrics,achieving 94.12%accuracy,recall and F1-score,as well as 94.15%precision on the Kvasir dataset.Furthermore,the model successfully reduced the false negative rate to 5.88%,enhancing its ability to minimize misdiagnosis.These results highlight the adaptability of the proposed work in clinical practice,where it can provide fast and accurate diagnostic assistance crucial for improving the early diagnosis of diseases in the gastrointestinal tract.
基金Five Oaks Ag Research&Education Center(DS18849)the University of Arkansas Division of Agriculture(PR02276)funding was provided by the U.S.Department of Agriculture,the National Institute of Food and Agriculture,and the McIntire-Stennis Capacity Grant(2729 YR21-25 and ARK02594).
文摘Individual tree health plays a vital role in maintaining a forest's ecological functions,including resources for waterfowl and other wildlife.Seasonal flooding due to altered hydrology is a major stressor on individual tree health in Greentree reservoirs(GTR),impounded bottomland hardwood forests especially less water tolerant species like red oaks(Quercus spp.).We evaluated the health of individual red oak species(n=6,432)in 662 plots across elevation gradients in 12 GTRs within the lower Mississippi Alluvial Valley using two tree health assessment approaches.The first approach assigns tree conditions(i.e.,stressed,moderate,low)based on overall qualitative tree attributes,while the second approach ranks stress,assigning numerical value based on the severity of four distinct qualitative tree attributes(i.e.,tip dieback,epicormics branch,bark condition,basal swell).The result indicated that the highest mean stress rank and the highest proportion of stressed tree conditions were red oak species,nuttall oak(Q.texana;18.59,0.44),willow oak(Q.phellos;18.66,0.38)and cherrybark oak(Q.pagoda;18.90,0.37).Red oak stress is positively correlated to elevation across the landscape(τ=0.10,p<0.001),but is negatively correlated to relative elevation,topographical changes,within each GTR(τ=-0.11,p<0.001).Additionally,the two health assessments are significantly associated(χ^(2)=313.78,df=2,p<0.001)and had a 13.1%misclassification rate.By utilizing the stress rank method for better classification of tree conditions to understand the adverse effect of prolonged flooding on the health of desirable red oak and other native tree species,management practices can be adjusted to improve tree health in GTRs,benefiting both wildlife and economic value.
文摘The purpose of this paper is to provide an error analysis for the multicategory support vector machine （MSVM） classificaton problems. We establish the uniform convergency approach for MSVMs and estimate the misclassification error. The main difficulty we overcome here is to bound the offset vector. As a result, we confirm that the MSVM classification algorithm with polynomial kernels is always efficient when the degree of the kernel polynomial is large enough. Finally the rate of convergence and examples are given to demonstrate the main results.
文摘AIM To correct the misclassification in registered gastric cancer incidence across Iranian provinces in cancer registry data. METHODS Gastric cancer data is extracted from Iranian annual of national cancer registration report 2008. A Bayesian method with beta prior is implemented to estimate the rate of misclassification in registering patient'spermanent residence in neighboring province. Each time two neighboring provinces with lower and higher than 100% expected coverage of cancer cases are selected to be entered in the model. The expected coverage of cancerous patient is reported by medical university of each province. It is assumed that some cancer cases from a province with a lower than 100% expected coverage are registered in their neighboring province with more than 100% expected coverage. RESULTS The condition was true for 21 provinces from a total of 30 provinces of Iran. It was estimated that 43% of gastric cancer cases of North and South Khorasan provinces in north-east of Iran was registered in Razavi Khorasan as the neighboring facilitate province; also 72% misclassification was estimated between Sistan and balochestan province and Razavi Khorasan. The misclassification rate was estimated to be 36% between West Azerbaijan province and East Azerbaijan province, 21% between Ardebil province and East Azerbaijan, 63% between Hormozgan province and Fars province, 8% between Chaharmahal and bakhtyari province and Isfahan province, 8% between Kogiloye and boyerahmad province and Isfahan, 43% Golestan province and Mazandaran province, 54% between Bushehr province and Khozestan province, 26% between Ilam province and Khuzestan province, 32% between Qazvin province and Tehran province(capital of Iran), 43% between Markazi province and Tehran, and 37% between Qom province and Tehran. CONCLUSION Policy makers should consider the regional misclassification in the time of programming for cancer control, prevention and resource allocation.
基金This project was funded by the Movember Foundation as part of their Australian and New Zealand prostate cancer outcomes registry initiative(PCOR-ANZ)which aims to develop a binational clinical registry for outcomes monitoring and research to inform practice and improve outcomes for men with prostate cancer.Dr.Beckmann is supported by an NHMRC Early Career Researcher Fellowship.
文摘Object:To determine the extent and impact of upgrading and downgrading among men who underwent radical prostatectomy(RP)according to new grade groupings and to identify predictors of upgrading from biopsy grade Group Ⅰ and Ⅱ,and downgrading to grade Group I,in a community setting.Methods:Study participants included 2279 men with non-metastatic prostate cancer diagnosed 2006-2015 who underwent prostatectomy,from the multi-institutional South Australia Prostate Cancer Clinical Outcomes Collaborative registry.Extent of up-or down-grading was assessed by comparing biopsy and prostatectomy grade groupings.Risk of biochemical recurrence(BCR)with upgrading was assessed using multivariable competing risk regression.Binomial logistic regression was used to identify pre-treatment predictors of upgrading from grade Groups Ⅰ and Ⅱ,and risk group reclassification among men with low risk disease.Results:Upgrading occurred in 35%of cases,while downgrading occurred in 13%of cases.Sixty percent with grade Group I disease were upgraded following prostatectomy.Upgrading from grade Group I was associated with greater risk of BCR compared with concordant grading(Hazard ratio:3.1,95%confidence interval:1.7-6.0).Older age,higher prostate-specific antigen levels(PSA),fewer biopsy cores,higher number of positive cores and more recent diagnosis predicted upgrading from grade Group Ⅰ,while higher PSA and clinical stage predicted upgrading from grade Group Ⅱ.No clinical risk factors for reclassification were identified.Conclusion:Biopsy sampling errors may play an important role in upgrading from grade Group I.Improved clinical assessment of grade is needed to encourage greater uptake of active surveillance.
文摘In medical diagnosis, the problem of class imbalance is popular. Though there are abundant unlabeled data, it is very difficult and expensive to get labeled ones. In this paper, an ensemble-based active learning algorithm is proposed to address the class imbalance problem. The artificial data are created according to the distribution of the training dataset to make the ensemble diverse, and the random subspace re-sampling method is used to reduce the data dimension. In selecting member classifiers based on misclassification cost estimation, the minority class is assigned with higher weights for misclassification costs, while each testing sample has a variable penalty factor to induce the ensemble to correct current error. In our experiments with UCI disease datasets, instead of classification accuracy, F-value and G-means are used as the evaluation rule. Compared with other ensemble methods, our method shows best performance, and needs less labeled samples.
基金Supported by the National 973 Program of China (No. 2006CB701302)the Hubei Department of Science and Technology (No. 2007ABA276)
文摘Uncertainty characterization has become increasingly recognized as an integral component in thematic mapping based on remotely sensed imagery, and descriptors such as percent correctly classified pixels (PCC) and Kappa coefficients of agreement have been devised as thematic accuracy metrics. However, such spatially averaged measures about accuracy neither offer hints about spatial variation in misclassification, nor are useful for quantifying error margins in derivatives, such as the areal extents of different land cover types and the land cover change statistics. Such limitations originate from the deficiency that spatial dependency is not accommodated in the conventional methods for error analysis. Geostatistics provides a good framework for uncertainty characterization in land cover information. Methods for predicting and propagating misclassification will be described on the basis of indicator samples and covariates, such as spectrally derived posteriori probabilities. An experiment using simulated datasets was carried out to quantify the error in land cover change derived from postclassification comparison. It was found that significant biases result from applying joint probability rules assuming temporal independence between misclassifications across time, thus emphasizing the need for the stochastic simulation in error modeling. Further investigations, incorporating indicators and probabilistic data for mapping and propagating misclassification, are anticipated.
基金The National Natural Science Foundation of China(No.61771126,61372104)the Science and Technology Project of State Grid Corporation of China(No.SGRIXTKJ[2015]349)
文摘To deal with Byzantine attacks in 5 G cognitive radio networks,a bilateral threshold selection-based algorithm is proposed in the spectrum sensing process. In each round,secondary uses( SUs) first submit the energy values and instantaneous detection signal-to-noise ratios( SNRs) to the fusion center( FC). According to detection SNRs,the FC conducts normalization calculations on the energy values. Then,the FC makes a sort operation for these normalized energy values and traverses all the possible mid-points between these sorted normalized energy values to maximize the classification accuracy of each SU. Finally,by introducing the recognition probability and misclassification probability,the distributions of the normalized energy values are analyzed and the bilateral threshold of classification accuracy is obtained via a target misclassification probability. Hence,the blacklist of malicious secondary users( MSUs) is obtained. Simulation results show that the proposed scheme outperforms the current mainstream schemes in correct sensing probability,false alarm probability and detection probability.
文摘To study the trend of hepatocellular carcinoma incidence after correcting the misclassification in registering cancer incidence across Iranian provinces in cancer registry data. METHODSIncidence data of hepatocellular carcinoma were extracted from Iranian annual of national cancer registration reports 2004 to 2008. A Bayesian method was implemented to estimate the rate of misclassification in registering cancer incidence in neighboring province. A beta prior is considered for misclassification parameter. Each time two neighboring provinces were selected to be entered in the Bayesian model based on their expected coverage of cancer cases which is reported by medical university of the province. It is assumed that some cancer cases from a province that has an expected coverage of cancer cases lower than 100% are registered in their neighboring facilitate province with more than 100% expected coverage. RESULTSThere is an increase in the rate of hepatocellular carcinoma in Iran. Among total of 30 provinces of Iran, 21 provinces were selected to be entered to the Bayesian model for correcting the existed misclassification. Provinces with more medical facilities of Iran are Tehran (capital of the country), Razavi Khorasan in north-east of Iran, East Azerbaijan in north-west of the country, Isfahan in central part and near to Tehran, Khozestan and Fars in south and Mazandaran in north of the Iran, had an expected coverage more than their expectation. Those provinces had significantly higher rates of hepatocellular carcinoma than their neighboring provinces. In years 2004 to 2008, it was estimated to be on average 34% misclassification between North Khorasan province and Razavi Khorasan, 43% between South Khorasan province and Razavi Khorasan, 47% between Sistan and balochestan province and Razavi Khorasan, 23% between West Azerbaijan province and East Azerbaijan province, 25% between Ardebil province and East Azerbaijan province, 41% between Hormozgan province and Fars province, 22% betweenChaharmahal and bakhtyari province and Isfahan province, 22% between Kogiloye and boyerahmad province and Isfahan, 22% between Golestan province and Mazandaran province, 43% between Bushehr province and Khozestan province, 41% between Ilam province and Khuzestan province, 42% between Qazvin province and Tehran province, 44% between Markazi province and Tehran, and 30% between Qom province and Tehran. CONCLUSIONAccounting and correcting the regional misclassification is necessary for identifying high risk areas and planning for reducing the cancer incidence.
文摘The author, who has published numerous meta-analyses of epidemiological studies, particularly on tobacco, comments on various aspects of their content. While such meta-analyses, even when well conducted, are more difficult to draw inferences from than are meta-analyses of clinical trials, they allow greater insight into an association than do simple qualitative reviews. This editorial starts with a discussion of some problems relating to hypothesis definition. These include the definition of the outcome, the exposure and the population to be considered, as well as the study inclusion and exclusion criteria. Under literature searching, the author argues against restriction to studies published in peer-reviewed journals, emphasising the fact that relevant data may be available from other sources. Problems of identifying studies and double counting are discussed, as are various issues in regard to data entry. The need to check published effect estimates is emphasised, and techniques to calculate estimates from material provided in the source publication are described. Once the data have been collected and an overall effect estimate obtained, tests for heterogeneity should be conducted in relation to different study characteristics. Though some meta-analysts recommend classifying studies by an overall index of study quality, the author prefers to separately investigate heterogeneity by those factors which contribute to the assessment of quality. Reasons why an association may not actually reflect a true causal relationship are also discussed, with the editorial describing techniques for investigating the relevance of confounding, and referring to problems resulting from misclassification of key variables. Misclassification of disease, exposure and confounding variables can all produce a spurious association, as can misclassification of the variable used to determine whether an individual can enter the study, and the author points to techniques to adjust for this. Issues relating to publication bias and the interpretation of "statistically significant" results are also discussed. The editorial should give the reader insight into the difficulties of producing a good meta-analysis.
文摘For the case where all multivariate normal parameters are known, we derive a new linear dimension reduction (LDR) method to determine a low-dimensional subspace that preserves or nearly preserves the original feature-space separation of the individual populations and the Bayes probability of misclassification. We also give necessary and sufficient conditions which provide the smallest reduced dimension that essentially retains the Bayes probability of misclassification from the original full-dimensional space in the reduced space. Moreover, our new LDR procedure requires no computationally expensive optimization procedure. Finally, for the case where parameters are unknown, we devise a LDR method based on our new theorem and compare our LDR method with three competing LDR methods using Monte Carlo simulations and a parametric bootstrap based on real data.
文摘Tests for a proportion that may be zero are described. The setting is an environment in which there can be misclassifications or misdiagnoses, giving the possibility of nonzero counts from false positives even though no real examples may exist. Both frequentist and Bayesian tests and analyses are presented, and examples are given.
文摘Binary measurement systems that classify parts as either pass or fail are widely used. Inspectors or inspection systems are often subject to error. The error rates are unlikely to be identical across inspectors. We propose a random effects Bayesian approach to model the error probabilities and overall conforming rate. We also introduce a feature-subset selection procedure to determine the best inspector in terms of overall classification accuracy. We provide simulation studies that demonstrate the viability of our proposed estimation ranking and subset-selection methods and apply the methods to a real data set.
文摘There are four serious problems in the discriminant analysis. We developed an optimal linear discriminant function （optimal LDF） based on the minimum number of misclassification （minimum NM） using integer programming （IP）. We call this LDF as Revised IP-OLDF. Only this LDF can discriminate the cases on the discriminant hyperplane （Probleml）. This LDF and a hard-margin SVM （H-SVM） can discriminate the lineary separable data （LSD） exactly. Another LDFs may not discriminate the LSD theoretically （Problem2）. When Revised IP-OLDF discriminate the Swiss banknote data with six variables, we find MNM of two-variables model such as （X4, X6） is zero. Because MNMk decreases monotounusly （MNMk 〉= MNM（k＋1））, sixteen MNMs including （X4, X6） are zero. Until now, because there is no research of the LSD, we surveyed another three linear separable data sets such as： 18 exam scores data sets, the Japanese 44 cars data and six microarray datasets. When we discriminate the exam scores with MNM=0, we find the generalized inverse matrix technique causes the serious Problem3 and confirmed this fact by the cars data. At last, we claim the discriminant analysis is not the inferential statistics because there is no standard errors （SEs） of error rates and discriminant coefficients （Problem4）. Therefore, we poroposed the ＂100-fold cross validation for the small sample＂ method （the method）. By this break-through, we can choose the best model having minimum mean of error rate （M2） in the validation sample and obtaine two 95% confidence intervals （CIs） of error rate and discriminant coefficients. When we discriminate the exam scores by this new method, we obtaine the surprising results seven LDFs except for Fisher＇s LDF are almost the same as the trivial LDFs. In this research, we discriminate the Japanese 44 cars data because we can discuss four problems. There are six independent variables to discriminate 29 regular cars and 15 small cars. This data is linear separable by the emission rate （X1） and the number of seats （X3）. We examine the validity of the new model selection procedure of the discriminant analysis. We proposed the model with minimum mean of error rates （M2） in the validation samples is the best model. We had examined this procedure by the exam scores, and we obtain good results. Moreover, the 95% CI of eight LDFs offers us real perception of the discriminant theory. However, the exam scores are different from the ordinal data. Therefore, we apply our theory and procedure to the Japanese 44 cars data and confirmed the same conclution.
