Large Deviations and Moderate Deviations for the Chi-Square Test in Type Ⅱ Error

We study the asymptotics tot the statistic of chi-square in type Ⅱ error. By the contraction principle, the large deviations and moderate deviations are obtained, and the rate function of moderate deviations can be calculated explicitly which is a squared function.

大锻件统计学Chi-square test的研究和应用

根据大锻件生产的特点和统计学的基本理论方法,首次深入浅出地论述了大锻件的Chi-square test,即X2检验,并给出了具体应用示例。该方法可用于大锻件工艺参数的科学分析和生产验证,可用于大锻件质量分析和判断,可帮助逐步建立起大锻件的工序能力,帮助实现稳定并提升大锻件工艺和质量控制水平。

Efficient ECG classification based on Chi-square distance for arrhythmia

This study introduces a new classifier tailored to address the limitations inherent in conventional classifiers such as K-nearest neighbor(KNN),random forest(RF),decision tree(DT),and support vector machine(SVM)for arrhythmia detection.The proposed classifier leverages the Chi-square distance as a primary metric,providing a specialized and original approach for precise arrhythmia detection.To optimize feature selection and refine the classifier’s performance,particle swarm optimization(PSO)is integrated with the Chi-square distance as a fitness function.This synergistic integration enhances the classifier’s capabilities,resulting in a substantial improvement in accuracy for arrhythmia detection.Experimental results demonstrate the efficacy of the proposed method,achieving a noteworthy accuracy rate of 98% with PSO,higher than 89% achieved without any previous optimization.The classifier outperforms machine learning(ML)and deep learning(DL)techniques,underscoring its reliability and superiority in the realm of arrhythmia classification.The promising results render it an effective method to support both academic and medical communities,offering an advanced and precise solution for arrhythmia detection in electrocardiogram(ECG)data.

Usability perceptions and beliefs about smart thermostats by chi-square test, signal detection theory, and fuzzy detection theory in regions of Mexico

It is well known that smart thermostats (STs) have become key devices in the implementation of smart homes;thus, they are considered as primary elements for the control of electrical energy consumption in households. Moreover, energy consumption is drastically affected when the end users select unsuitable STs or when they do not use the STs correctly. Furthermore, in future, Mexico will face serious electrical energy challenges that can be considerably resolved if the end users operate the STs in a correct manner. Hence, it is important to carry out an in-depth study and analysis on thermostats, by focusing on social aspects that influence the technological use and performance of the thermostats. This paper proposes the use of a signal detection theory (SDT), fuzzy detection theory (FDT), and chi-square (CS) test in order to understand the perceptions and beliefs of end users about the use of STs in Mexico. This paper extensively shows the perceptions and beliefs about the selected thermostats in Mexico. Besides, it presents an in-depth discussion on the cognitive perceptions and beliefs of end users. Moreover, it shows why the expectations of the end users about STs are not met. It also promotes the technological and social development of STs such that they are relatively more accepted in complex electrical grids such as smart grids.

Chi-Square and PCA Based Feature Selection for Diabetes Detection with Ensemble Classifier

Diabetes mellitus is a metabolic disease that is ranked among the top 10 causes of death by the world health organization.During the last few years,an alarming increase is observed worldwide with a 70%rise in the disease since 2000 and an 80%rise in male deaths.If untreated,it results in complications of many vital organs of the human body which may lead to fatality.Early detection of diabetes is a task of significant importance to start timely treatment.This study introduces a methodology for the classification of diabetic and normal people using an ensemble machine learning model and feature fusion of Chi-square and principal component analysis.An ensemble model,logistic tree classifier(LTC),is proposed which incorporates logistic regression and extra tree classifier through a soft voting mechanism.Experiments are also performed using several well-known machine learning algorithms to analyze their performance including logistic regression,extra tree classifier,AdaBoost,Gaussian naive Bayes,decision tree,random forest,and k nearest neighbor.In addition,several experiments are carried out using principal component analysis(PCA)and Chi-square(Chi-2)fea-tures to analyze the influence of feature selection on the performance of machine learning classifiers.Results indicate that Chi-2 features show high performance than both PCA features and original features.However,the highest accuracy is obtained when the proposed ensemble model LTC is used with the proposed fea-ture fusion framework-work which achieves a 0.85 accuracy score which is the highest of the available approaches for diabetes prediction.In addition,the statis-tical T-test proves the statistical significance of the proposed approach over other approaches.

Aquifer Test求群孔抽水试验水文地质参数

在水文地质条件复杂的地区,往往采用大型的群孔抽水试验充分揭露含水层特征,获取水文地质参数。用Aquifer Test软件求解水文地质参数,则方便实用、简捷高效,可快速输出拟合图形和求参结果。Aquifer Test提供了丰富的求参方案,求参必须结合当地当时的水文地质条件实际情况考虑,选择适合的方案和时空数据求取水文地质参数。

Failure characterization of fully grouted rock bolts under triaxial testing

Confining stresses serve as a pivotal determinant in shaping the behavior of grouted rock bolts.Nonetheless,prior investigations have oversimplified the three-dimensional stress state,primarily assuming hydrostatic stress conditions.Under these conditions,it is assumed that the intermediate principal stress(σ_(2))equals the minimum principal stress(σ_(3)).This assumption overlooks the potential variations in magnitudes of in situ stress conditions along all three directions near an underground opening where a rock bolt is installed.In this study,a series of push tests was meticulously conducted under triaxial conditions.These tests involved applying non-uniform confining stresses(σ_(2)≠σ_(3))to cubic specimens,aiming to unveil the previously overlooked influence of intermediate principal stresses on the strength properties of rock bolts.The results show that as the confining stresses increase from zero to higher levels,the pre-failure behavior changes from linear to nonlinear forms,resulting in an increase in initial stiffness from 2.08 kN/mm to 32.51 kN/mm.The load-displacement curves further illuminate distinct post-failure behavior at elevated levels of confining stresses,characterized by enhanced stiffness.Notably,the peak load capacity ranged from 27.9 kN to 46.5 kN as confining stresses advanced from σ_(2)=σ_(3)=0 to σ_(2)=20 MPa and σ_(3)=10 MPa.Additionally,the outcomes highlight an influence of confining stress on the lateral deformation of samples.Lower levels of confinement prompt overall dilation in lateral deformation,while higher confinements maintain a state of shrinkage.Furthermore,diverse failure modes have been identified,intricately tied to the arrangement of confining stresses.Lower confinements tend to induce a splitting mode of failure,whereas higher loads bring about a shift towards a pure interfacial shear-off and shear-crushed failure mechanism.

Development of multi-functional anchorage support dynamic-static coupling performance test system and its application

In underground engineering with complex conditions,the bolt(cable)anchorage support system is in an environment where static and dynamic stresses coexist,under the action of geological conditions such as high stresses and strong disturbances and construction conditions such as the application of high prestress.It is essential to study the support components performance under dynamic-static coupling conditions.Based on this,a multi-functional anchorage support dynamic-static coupling performance test system(MAC system)is developed,which can achieve 7 types of testing functions,including single component performance,anchored net performance,anchored rock performance and so on.The bolt and cable mechanical tests are conducted by MAC system under different prestress levels.The results showed that compared to the non-prestress condition,the impact resistance performance of prestressed bolts(cables)is significantly reduced.In the prestress range of 50–160 k N,the maximum reduction rate of impact energy resisted by different types of bolts is 53.9%–61.5%compared to non-prestress condition.In the prestress range of 150–300 k N,the impact energy resisted by high-strength cable is reduced by76.8%–84.6%compared to non-prestress condition.The MAC system achieves dynamic-static coupling performance test,which provide an effective means for the design of anchorage support system.

Use of Pearson’s Chi-Square for Testing Equality of Percentile Profiles across Multiple Populations

In large sample studies where distributions may be skewed and not readily transformed to symmetry, it may be of greater interest to compare different distributions in terms of percentiles rather than means. For example, it may be more informative to compare two or more populations with respect to their within population distributions by testing the hypothesis that their corresponding respective 10th, 50th, and 90th percentiles are equal. As a generalization of the median test, the proposed test statistic is asymptotically distributed as Chi-square with degrees of freedom dependent upon the number of percentiles tested and constraints of the null hypothesis. Results from simulation studies are used to validate the nominal 0.05 significance level under the null hypothesis, and asymptotic power properties that are suitable for testing equality of percentile profiles against selected profile discrepancies for a variety of underlying distributions. A pragmatic example is provided to illustrate the comparison of the percentile profiles for four body mass index distributions.

C-CORE:Clustering by Code Representation to Prioritize Test Cases in Compiler Testing

Edge devices,due to their limited computational and storage resources,often require the use of compilers for program optimization.Therefore,ensuring the security and reliability of these compilers is of paramount importance in the emerging field of edge AI.One widely used testing method for this purpose is fuzz testing,which detects bugs by inputting random test cases into the target program.However,this process consumes significant time and resources.To improve the efficiency of compiler fuzz testing,it is common practice to utilize test case prioritization techniques.Some researchers use machine learning to predict the code coverage of test cases,aiming to maximize the test capability for the target compiler by increasing the overall predicted coverage of the test cases.Nevertheless,these methods can only forecast the code coverage of the compiler at a specific optimization level,potentially missing many optimization-related bugs.In this paper,we introduce C-CORE(short for Clustering by Code Representation),the first framework to prioritize test cases according to their code representations,which are derived directly from the source codes.This approach avoids being limited to specific compiler states and extends to a broader range of compiler bugs.Specifically,we first train a scaled pre-trained programming language model to capture as many common features as possible from the test cases generated by a fuzzer.Using this pre-trained model,we then train two downstream models:one for predicting the likelihood of triggering a bug and another for identifying code representations associated with bugs.Subsequently,we cluster the test cases according to their code representations and select the highest-scoring test case from each cluster as the high-quality test case.This reduction in redundant testing cases leads to time savings.Comprehensive evaluation results reveal that code representations are better at distinguishing test capabilities,and C-CORE significantly enhances testing efficiency.Across four datasets,C-CORE increases the average of the percentage of faults detected(APFD)value by 0.16 to 0.31 and reduces test time by over 50% in 46% of cases.When compared to the best results from approaches using predicted code coverage,C-CORE improves the APFD value by 1.1% to 12.3% and achieves an overall time-saving of 159.1%.

A Simple Chi-Square Statistic for Testing Homogeneity of Zero-Inflated Distributions

Zero-inflated distributions are common in statistical problems where there is interest in testing homogeneity of two or more independent groups. Often, the underlying distribution that has an inflated number of zero-valued observations is asymmetric, and its functional form may not be known or easily characterized. In this case, comparisons of the groups in terms of their respective percentiles may be appropriate as these estimates are nonparametric and more robust to outliers and other irregularities. The median test is often used to compare distributions with similar but asymmetric shapes but may be uninformative when there are excess zeros or dissimilar shapes. For zero-inflated distributions, it is useful to compare the distributions with respect to their proportion of zeros, coupled with the comparison of percentile profiles for the observed non-zero values. A simple chi-square test for simultaneous testing of these two components is proposed, applicable to both continuous and discrete data. Results of simulation studies are reported to summarize empirical power under several scenarios. We give recommendations for the minimum sample size which is necessary to achieve suitable test performance in specific examples.

Unbound^(28)O,the heaviest oxygen isotope observed:a cutting-edge probe for testing nuclear models

The beyond-dripline oxygen isotopes^(27,28)O were recently observed at RIKEN,and were found to be unbound decaying into^(24)O by emitting neutrons.The unbound feature of the heaviest oxygen isotope,^(28)O,provides an excellent test for stateof-the-art nuclear models.The atomic nucleus is a self-organized quantum manybody system comprising specific numbers of protons Z and neutrons N.

Urea breath test for Helicobacter pylori infection in adult dyspeptic patients: A meta-analysis of diagnostic test accuracy

BACKGROUND Helicobacter pylori(H.pylori)infection has been well-established as a significant risk factor for several gastrointestinal disorders.The urea breath test(UBT)has emerged as a leading non-invasive method for detecting H.pylori.Despite numerous studies confirming its substantial accuracy,the reliability of UBT results is often compromised by inherent limitations.These findings underscore the need for a rigorous statistical synthesis to clarify and reconcile the diagnostic accuracy of the UBT for the diagnosis of H.pylori infection.AIM To determine and compare the diagnostic accuracy of 13C-UBT and 14C-UBT for H.pylori infection in adult patients with dyspepsia.METHODS We conducted an independent search of the PubMed/MEDLINE,EMBASE,and Cochrane Central databases until April 2022.Our search included diagnostic accuracy studies that evaluated at least one of the index tests(^(13)C-UBT or ^(14)C-UBT)against a reference standard.We used the QUADAS-2 tool to assess the methodo-logical quality of the studies.We utilized the bivariate random-effects model to calculate sensitivity,specificity,positive and negative test likelihood ratios(LR+and LR-),as well as the diagnostic odds ratio(DOR),and their 95%confidence intervals.We conducted subgroup analyses based on urea dosing,time after urea administration,and assessment technique.To investigate a possible threshold effect,we conducted Spearman correlation analysis,and we generated summary receiver operating characteristic(SROC)curves to assess heterogeneity.Finally,we visually inspected a funnel plot and used Egger’s test to evaluate publication bias.endorsing both as reliable diagnostic tools in clinical practice.CONCLUSION In summary,our study has demonstrated that ^(13)C-UBT has been found to outperform the ^(14)C-UBT,making it the preferred diagnostic approach.Additionally,our results emphasize the significance of carefully considering urea dosage,assessment timing,and measurement techniques for both tests to enhance diagnostic precision.Nevertheless,it is crucial for researchers and clinicians to evaluate the strengths and limitations of our findings before implementing them in practice.

Evaluation of urea breath test as a diagnostic tool for Helicobacter pylori infection in adult dyspeptic patients

In this editorial,we discuss the article in the World Journal of Gastroenterology.The article conducts a meta-analysis of the diagnostic accuracy of the urea breath test(UBT),a non-invasive method for detecting Helicobacter pylori(H.pylori)infection in humans.It is based on radionuclide-labeled urea.Various methods,both invasive and non-invasive,are available for diagnosing H.pylori infection,inclu-ding endoscopy with biopsy,serology for immunoglobulin titers,stool antigen analysis,and UBT.Several guidelines recommend UBTs as the primary choice for diagnosing H.pylori infection and for reexamining after eradication therapy.It is used to be the first choice non-invasive test due to their high accuracy,specificity,rapid results,and simplicity.Moreover,its performance remains unaffected by the distribution of H.pylori in the stomach,allowing a high flow of patients to be tested.Despite its widespread use,the performance characteristics of UBT have been inconsistently described and remain incompletely defined.There are two UBTs available with Food and Drug Administration approval:The 13C and 14C tests.Both tests are affordable and can provide real-time results.Physicians may prefer the 13C test because it is non-radioactive,compared to 14C which uses a radioactive isotope,especially in young children and pregnant women.Although there was heterogeneity among the studies regarding the diagnostic accuracy of both UBTs,13C-UBT consistently outperforms the 14C-UBT.This makes the 13C-UBT the preferred diagnostic approach.Furthermore,the provided findings of the meta-analysis emphasize the significance of precise considerations when choosing urea dosage,assessment timing,and measurement techniques for both the 13C-UBT and 14C-UBT,to enhance diagnostic precision.

Infectious Disease Update in Obstetrics: A Modern Approach to the Patient with a Positive Screening Test for Syphyilis in Pregnancy

Screening for maternal syphilis has been an essential component of routine antenatal screening tests in most countries for many years. This is not only because of the virulence of the spirochete which causes the infection but also because of its vertical transmission rate and the potential severe adverse complications/morbidity that can result from its transmission to the fetus. Although the incidence of maternal syphilis and its fetal sequalae in low-income countries has been considerable for several years, the disease has been almost non-existent in high income countries with wide antenatal screening coverage and effective treatment programmes for Syphilis. The recent alarming increase in the incidence of maternal syphilis in high income countries has spawned a renewed public health interest in the infection, with several countries updating and strengthening public health guidance in an attempt to stem this dramatic trend. This is a short clinical update for the practising obstetrician on how to manage the antenatal patient with a positive syphilis screening test.

Research on aiming methods for small sample size shooting tests of two-dimensional trajectory correction fuse

The longitudinal dispersion of the projectile in shooting tests of two-dimensional trajectory corrections fused with fixed canards is extremely large that it sometimes exceeds the correction ability of the correction fuse actuator.The impact point easily deviates from the target,and thus the correction result cannot be readily evaluated.However,the cost of shooting tests is considerably high to conduct many tests for data collection.To address this issue,this study proposes an aiming method for shooting tests based on small sample size.The proposed method uses the Bootstrap method to expand the test data;repeatedly iterates and corrects the position of the simulated theoretical impact points through an improved compatibility test method;and dynamically adjusts the weight of the prior distribution of simulation results based on Kullback-Leibler divergence,which to some extent avoids the real data being"submerged"by the simulation data and achieves the fusion Bayesian estimation of the dispersion center.The experimental results show that when the simulation accuracy is sufficiently high,the proposed method yields a smaller mean-square deviation in estimating the dispersion center and higher shooting accuracy than those of the three comparison methods,which is more conducive to reflecting the effect of the control algorithm and facilitating test personnel to iterate their proposed structures and algorithms.;in addition,this study provides a knowledge base for further comprehensive studies in the future.

SARS-CoV-2 Pooled Testing Methodology for PCR Testing Applied in Private Laboratory in Armenia

Since the beginning of COVID-19 pandemics many countries were facing challenges with testing capacity recourse limitations. Throughout the waves of the pandemic countries were trying to address the existing constrains exploring solutions to increase the testing capacity with more cost-effective approaches. Pooled methodology was one of the methods which many have validated and used. It is evident that in case of pooled sample testing the sensitivity becomes lower, however the variation highly depends on the pool size as well as the incidence rate at the certain point. Armenia as well as many other countries has adopted regulations for mandatory COVID-19 PCR testing for all the travelers. Current study aimed to explore the efficiency of COVID-19 pooled PCR testing for nasopharyngeal swabs of individuals with no symptoms in a time period with good epidemiological state of the infection. Nasopharingeal swab samples from individuals were collected. The manual extraction of RNAs of samples was performed after pooling up to 5 samples. The pools with Cycle Threshold (CT) of < 37 were considered positive and were retested individually. In total 28,015 samples were grouped in 667 pools of which 57 were positive. The total number of positive samples was 65. The median difference (CT-pool–CT samples) was 2.4 (ranging from–3.0 to 8.9). The correlation of CT of pools and positive samples was positive. The correlation coefficient r = 0.84, P < 0.000, 95% CI range 0.7423 to 0.9243). The total economic saving when using pools compared to the individual testing was 72%. The minor difference between CT values of pools and samples can be explained by the dilution effect in the pool. However, the positive correlation between the values as well as the amount of cost saving demonstrate that pooling on nasopharyngeal samples for COVID-19 PCR testing can be a good method for efficient screening with significant resource saving. One of the most important advantages of the proposed method is the fact that samples are pooled prior extraction, which avoids the possibilities with misinterpretation of IC due to low yield of RNA in the extraction process.

Adjustments for Kurtosis and Continuity on the Prentice Test

The test of Prentice [1] is a non-parametric statistical test for the two-way analysis of variance using ranks. The null distribution of this test typically is approximated using the Chi-square distribution. However, the exact null distribution deviates from the Chi-square approximation in certain cases commonly found in applications of the test, motivating adjustments to the distribution. This manuscript presents adjustments to this null distribution correcting for continuity, multivariate skewness, and multivariate kurtosis. The effects of alternative scoring methods as non-polynomial functions of rank sums are also presented as a broader application of the approximation.

Contribution of Stress Testing to the Management of Ischemic Heart Disease in Mali

Introduction: Exercise stress testing (on a treadmill or ergometer bicycle) is an important test in cardiology for diagnosing myocardial ischemia. This test in Mali is still in its beginning compared to other countries in the sub-region. The lack of data in Mali prompted this study, which aimed to evaluate the indications of this activity and its diagnostic contribution to cardiology in Mali. Materials and Methods: This was a retrospective, descriptive study. The study was conducted at the “TOUCAM” medical clinic in Kati based on the analysis of stress test reports between January 2016 and August 2022. Result: During the study period, we documented 73 patients who underwent exercise testing on a bicycle ergometer for suspected coronary heart disease. The mean age of our patients was 47.5 ± 13.8 years (14 and 79 years). Males accounted for the majority (78.1%). The sex ratio is 3.5. More than half of our patients were overweight or obese (77.1%). Hypertension and diabetes affected 52.1% and 25.8% of patients, respectively. 20.8% of patients had coronary artery disease. renin-angiotensin-aldosterone system blockers (56.8%) and beta-blockers (51.3%). The main indications were chest pain (63.0%) and ischemia detection (15.1%). A modified STEEP protocol was used. The majority of our patients (71.2%) achieved at least 85% of their maximum theoretical heart rate. The main reason for the termination of the study was fatigue (57.3%). The average duration was 11.3 ± 4.2 minutes. 24.7% thought the stress tests were positive and 17.8% thought they were controversial. Conclusion: This study demonstrates the importance of stress testing in the diagnosis and treatment of ischemic heart disease, especially in settings where we have very limited access to coronary angiography.