Exploring the Abnormal Brain Regions and Abnormal Functional Connections in SZ by Multiple Hypothesis Testing Technique

Schizophrenia(SZ)is one of the most common mental diseases.Its main characteristics are abnormal social behavior and inability to correctly understand real things.In recent years,the magnetic resonance imaging(MRI)technique has been popularly utilized to study SZ.However,it is still a great challenge to reveal the essential information contained in the MRI data.In this paper,we proposed a biomarker selection approach based on the multiple hypothesis testing techniques to explore the difference between SZ and healthy controls by using both functional and structural MRI data,in which biomarkers represent both abnormal brain functional connectivity and abnormal brain regions.By implementing the biomarker selection approach,six abnormal brain regions and twenty-three abnormal functional connectivity in the brains of SZ are explored.It is discovered that compared with healthy controls,the significantly reduced gray matter volumes are mainly distributed in the limbic lobe and the basal ganglia,and the significantly increased gray matter volumes are distributed in the frontal gyrus.Meanwhile,it is revealed that the significantly strengthened connections are those between the middle frontal gyrus and the superior occipital gyrus,the superior occipital gyrus and the middle occipital gyrus as well as the middle occipital gyrus and the fusiform gyrus,and the rest connections are significantly weakened.

A New Deghosting Algorithm with Hypothesis Testing Data Fusion

Eliminating the false intersection (deghosting) is a difficult problem in a passive cross location system. Using a decentralized decision fusion topology, a new deghosting algorithm derived from hypothesis testing theory is developed. It uses the difference between ghosts and true targets in the statistical error, which occurs between their projection angles on a deghosting sensor and is measured from a deghosting sensor, and constructs a corresponding test statistic. Under the Gaussian assumption, ghosts and true targets are decided and discriminated by Chi-square distribution. Simulation results show the feasibility of the algorithm.

Hypothesis Testing of Population Percentiles via the Wald Test with Bootstrap Variance Estimates

Testing the equality of percentiles (quantiles) between populations is an effective method for robust, nonparametric comparison, especially when the distributions are asymmetric or irregularly shaped. Unlike global nonparametric tests for homogeneity such as the Kolmogorv-Smirnov test, testing the equality of a set of percentiles (i.e., a percentile profile) yields an estimate of the location and extent of the differences between the populations along the entire domain. The Wald test using bootstrap estimates of variance of the order statistics provides a unified method for hypothesis testing of functions of the population percentiles. Simulation studies are conducted to show performance of the method under various scenarios and to give suggestions on its use. Several examples are given to illustrate some useful applications to real data.

Sensitivity and Specificity Analysis Relation to Statistical Hypothesis Testing and Its Errors: Application to Cryptosporidium Detection Techniques

The use of Statistical Hypothesis Testing procedure to determine type I and type II errors was linked to the measurement of sensitivity and specificity in clinical trial test and experimental pathogen detection techniques. A theoretical analysis of establishing these types of errors was made and compared to determination of False Positive, False Negative, True Positive and True Negative. Experimental laboratory detection methods used to detect Cryptosporidium spp. were used to highlight the relationship between hypothesis testing, sensitivity, specificity and predicted values. The study finds that, sensitivity and specificity for the two laboratory methods used for Cryptosporidium detection were low hence lowering the probability of detecting a “false null hypothesis” for the presence of cryptosporidium in the water samples using either Microscopic or PCR. Nevertheless, both procedures for cryptosporidium detection had higher “true negatives” increasing its probability of failing to reject a “true null hypothesis” with specificity of 1.00 for both Microscopic and PCR laboratory detection methods.

Comparison of Vs and SPT Soil Liquefaction Assessments of NCEER: Including Hypothesis Testing

Soil liquefaction is one of the complex research topics in geotechnical engineering and engineering geology. Especially after the 1964 Niigata earthquake (Japan) induced many soil liquefaction incidents, a variety of soil liquefaction studies were conducted and reported, including the liquefaction potential assessment methods utilizing the shear wave velocity (Vs) or SPT-N profiles (SPT: standard penetration test). This study used the Vs and SPT methods recommended by the National Center for Earthquake Engineering Research (NCEER) to examine which is more conservative according to the assessment results on 41 liquefiable soil layers at sites in two major cities in Taiwan. Statistical hypothesis testing was used to make the analysis more quantitative and objective. Based on three sets of hypothesis tests, it shows that the hypothesis—the SPT method is more conservative than the Vs method—was not rejected on a 5% level of significance.

Exclusive Hypothesis Testing for Cox's Proportional Hazards Model

Exclusive hypothesis testing is a new and special class of hypothesis testing.This kind of testing can be applied in survival analysis to understand the association between genomics information and clinical information about the survival time.Besides,it is well known that Cox's proportional hazards model is the most commonly used model for regression analysis of failure time.In this paper,the authors consider doing the exclusive hypothesis testing for Cox's proportional hazards model with right-censored data.The authors propose the comprehensive test statistics to make decision,and show that the corresponding decision rule can control the asymptotic TypeⅠerrors and have good powers in theory.The numerical studies indicate that the proposed approach works well for practical situations and it is applied to a set of real data arising from Rotterdam Breast Cancer Data study that motivated this study.

Moderate deviations and hypothesis testing for signal detection problem

Abstract We use moderate deviations to study the signal detection problem for a diffusion model. We establish a moderate deviation principle for the log-likelihood function of the diffusion model. Then applying the moderate deviation estimates to hypothesis testing for signal detection problem we give a decision region such that its error probability of the second kind tends to zero with faster speed than the error probability of the first kind when the error probability of the first kind is approximated by e-ατ（T）, where α〉 0, τ（T） = o（T） and τ（T）→∞ as the observation time T goes to infinity.

Hypothesis testing for reliability with a three-parameter Weibull distribution using minimum weighted relative entropy norm and bootstrap

With the help of relative entropy theory,norm theory,and bootstrap methodology,a new hypothesis testing method is proposed to verify reliability with a three-parameter Weibull distribution.Based on the relative difference information of the experimental value vector to the theoretical value vector of reliability,six criteria of the minimum weighted relative entropy norm are established to extract the optimal information vector of the Weibull parameters in the reliability experiment of product lifetime.The rejection region used in the hypothesis testing is deduced via the area of intersection set of the estimated truth-value function and its confidence interval function of the three-parameter Weibull distribution.The case studies of simulation lifetime,helicopter component failure,and ceramic material failure indicate that the proposed method is able to reflect the practical situation of the reliability experiment.

Hypothesis testing and statistical analysis of microbiome

After the initiation of Human Microbiome Project in 2008,various biostatistic and bioinformatic tools for data analysis and computational methods have been developed and applied to microbiome studies.In this review and perspective,we discuss the research and statistical hypotheses in gut microbiome studies,focusing on mechanistic concepts that underlie the complex relationships among host,microbiome,and environment.We review the current available statistic tools and highlight recent progress of newly developed statistical methods and models.Given the current challenges and limitations in biostatistic approaches and tools,we discuss the future direction in developing statistical methods and models for the microbiome studies.

Empirical likelihood hypothesis test on mean with inequality constraints

Hypothesis test on the population mean with various inequality constraints is studied in this paper.The empirical likelihood method is applied to construct test statistics.Limiting distributions of the empirical likelihood ratio test statistics are proven to be a weighted mixture of chi-square distributions.Numerical results are presented to show the validity of the proposed method.

Hypothesis testing of Poisson rates in COVID-19 offspring distributions

In the present study,we undertake the task of hypothesis testing in the context of Poissondistributed data.The primary objective of our investigation is to ascertain whether two distinct sets of discrete data share the same Poisson rate.We delve into a comprehensive review and comparative analysis of various frequentist and Bayesian methodologies specifically designed to address this problem.Among these are the conditional test,the likelihood ratio test,and the Bayes factor.Additionally,we employ the posterior predictive p-value in our analysis,coupled with its corresponding calibration procedures.As the culmination of our investigation,we apply these diverse methodologies to test both simulated datasets and real-world data.The latter consists of the offspring distributions linked to COVID-19 cases in two disparate geographies-Hong Kong and Rwanda.This allows us to provide a practical demonstration of the methodologies’applications and their potential implications in the field of epidemiology.

Hypothesis Test for the Parameters of Linear Part in the Partial Linear EV Model

Hypothesis testing for the parametric component in the partial linear errors-in-variables （EV） regression models is discussed in this paper. Based on the corrected profile least square estimator, five test statistics are proposed and the asymptotic null distributions of them are deduced. Simulations have been done to show the performance of these test statistics under null and alternative hypothesis.

Hypothesis Testing for Arbitrarily Varying Source

Hypothesis testing for arbitrarily varying source (AVS), which is to decide between the two hypotheses for the varying behavior of the distribution of AVS, is considered in this paper. We determine the best asymptotic exponent of the second kind of error probability when the first kind of error probability is fixed. This result generalizes the well-known lemma of Stein in statistics. As a corollary, Strassen’s coding theorem for AVS is obtained.

Robust hypothesis testing for asymmetric nominal densities under a relative entropy tolerance

In this paper, we address an open problem raised by Levy(2009) regarding the design of a binary minimax test without the symmetry assumption on the nominal conditional probability densities of observations. In the binary minimax test, the nominal likelihood ratio is a monotonically increasing function and the probability densities of the observations are located in neighborhoods characterized by placing a bound on the relative entropy between the actual and nominal densities. The general minimax testing problem at hand is an infinite-dimensional optimization problem, which is quite difficult to solve. In this paper, we prove that the complicated minimax testing problem can be substantially reduced to solve a nonlinear system of two equations having only two unknown variables, which provides an efficient numerical solution.

Objective Bayesian hypothesis testing and estimation for the intraclass model

The intraclass correlation coefficient (ICC) plays an important role in various fields of study asa coefficient of reliability. In this paper, we consider objective Bayesian analysis for the ICCin the context of normal linear regression model. We first derive two objective priors for theunknown parameters and show that both result in proper posterior distributions. Within aBayesian decision-theoretic framework, we then propose an objective Bayesian solution to theproblems of hypothesis testing and point estimation of the ICC based on a combined use of theintrinsic discrepancy loss function and objective priors. The proposed solution has an appealinginvariance property under one-to-one reparametrisation of the quantity of interest. Simulationstudies are conducted to investigate the performance the proposed solution. Finally, a real dataapplication is provided for illustrative purposes.

Hypothesis Testing for Independence Under Blocked Compound Symmetric Covariance Structure

One type of covariance structure is known as blocked compound symmetry.Recently,Roy et al.(J Multivar Anal 144:81–90,2016)showed that,assuming this covariance structure,unbiased estimators are optimal under normality and described hypothesis testing for independence as an open problem.In this paper,we derive the distributions of unbiased estimators and consider hypothesis testing for independence.Representative test statistics such as the likelihood ratio criterion,Waldstatistic,Rao’s score statistic,and gradient statistic are derived,and we evaluate the accuracy of the test using these statistics through numerical simulations.The power of the Wald test is the largest when the dimension is high,and the power of the likelihood ratio test is the largest when the dimension is low.

IDENTIFICATION AND HYPOTHESIS TESTING ON ARIMA (p, d, q) MODELS

This paper eonsiders an ARIMA (p, d, q) medel. A method for estimating the order d and testingthe hypothesis: d=d_0 is given. The asymptotic properties of the estimator have been discussed.

Independence Test of Wheat Head Blight Infection

The relationship between wheat varieties and occurrence of head blight was discussed, the independence test was carried out by using contingency table.

A Test Method for the Static/Moving State of Targets Applied to Airport Surface Surveillance MLAT System

Due to the particularity of its location algorithm,there are some unique difficulties and features regarding the test of target motion states of multilateration(MLAT)system for airport surface surveillance.This paper proposed a test method applicable for the airport surface surveillance MLAT system,which can effectively determine whether the target is static or moving at a certain speed.Via a normalized test statistic designed in the sliding data window,the proposed method not only eliminates the impact of geometry Dilution of precision(GDOP)effectively,but also transforms the test of different motion states into the test of different probability density functions.Meanwhile,by adjusting the size of the sliding window,it can fulfill different test performance requirements.The method was developed through strict theoretical extrapolation and performance analysis,and simulations results verified its correctness and effectiveness.

Incorporating Uncertain Costs within a Series of Sequential Probability Ratio Tests

We consider an extension to Sequential Probability Ratio Tests for when we have uncertain costs, but also opportunity to learn about these in an adaptive manner. In doing so we demonstrate the effects that allowing uncertainty has on observation cost, and the costs associated with Type I and Type II error. The value of information relating to modelled uncertainties is derived and the case of statistical dependence between the parameter affecting decision outcome and the parameter affecting unknown cost is also examined. Numerical examples of the derived theory are provided, along with a simulation comparing this adaptive learning framework to the classical one.