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The p-value and model specification in statistics

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General psychiatry 2019年第3期32卷 163-166页

作者： Bokai Wang Zhirou Zhou Hongyue Wang Xin M Tu Changyong Feng Departments of Biostatistics and Computational Biology and Anesthesiology University of Rochester Rochester New York USA Family Medicine and public Health University of California San Diego San Diego. California USA Naval Health Research Center San Diego California USA

SUMMARY The p value has been widely used as a way to summarise the significance in data analysis. However, misuse and misinterpretation of the p value is common in practice. Our result shows that if the model specification is wrong, the distribution of the p value may be inappropriate, which makes the decision based on the p value invalid.

关键词： p-value model specification statistics

Hypothesis testing of poisson rates in COVID-19 offspring distributions

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Infectious Disease Modelling 2023年第4期8卷 980-1001页

作者： Rui Luo Department of Systems Engineering City University of Hong KongKowloon TownHong Kong Special Administrative Region

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.

关键词： poisson distribution Hypothesis testing Bayes factor posterior predictive p-value COVID-19

Transient postseismic slip and aftershock triggering:A case study of the 2008 M_W7.9 Wenchuan Earthquake,China

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Earthquake Science 2023年第6期36卷 445-457页

作者： Mengyu Xie Baoping Shi Lingyuan Meng China Earthquake Networks Center Beijing 100045China College of Earth Sciences University of Chinese Academy of SciencesBeijing 100049China

In this study,we investigate how a stress variation generated by a fault that experiences transient postseismic slip(TpS)affects the rate of aftershocks.First,we show that the postseismic slip from Rubin-Ampuero model is a TpS that can occur on the main fault with a velocity-weakening frictional motion,that the resultant slip function is similar to the generalized Jeffreys-Lomnitz creep law,and that the TpS can be explained by a continuous creep process undergoing reloading.Second,we obtain an approximate solution based on the Helmstetter-Shaw seismicity model relating the rate of aftershocks to such TpS.For the Wenchuan sequence,we perform a numerical fitting of the cumulative number of aftershocks using the Modified Omori Law(MOL),the Dieterich model,and the specific TpS model.The fitting curves indicate that the data can be better explained by the TpS model with a B/A ratio of approximately 1.12,where A and B are the parameters in the rate-and state-dependent friction law respectively.Moreover,the p and c that appear in the MOL can be interpreted by the B/A and the critical slip distance,respectively.Because the B/A ratio in the current model is always larger than 1,the model could become a possible candidate to explain aftershock rate commonly decay as a power law with a p-value larger than 1.Finally,the influence of the background seismicity rate r on parameters is studied;the results show that except for the apparent aftershock duration,other parameters are insensitive to r.

关键词： transient postseismic slip(TpS) Modified Omori Law(MOL) p-value rate-and state-dependent friction law Wenchuan earthquake

Bridging the semantic gap with human perception based features for scene categorization

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International Journal of Intelligent Computing and Cybernetics 2017年第3期10卷 387-406页

作者： padmavati Shrivastava K.K.Bhoyar A.S.Zadgaonkar Dr.C.V.Raman University BilaspurIndia Department of Information Technology Yeshwantrao Chavan College of EngineeringNagpurIndia

purpose–The purpose of this paper is to build a classification system which mimics the perceptual ability of human vision,in gathering knowledge about the structure,content and the surrounding environment of a real-world natural scene,at a quick glance accurately.This paper proposes a set of novel features to determine the gist of a given scene based on dominant color,dominant direction,openness and roughness features.Design/methodology/approach–The classification system is designed at two different levels.At the first level,a set of low level features are extracted for each semantic feature.At the second level the extracted features are subjected to the process of feature evaluation,based on inter-class and intra-class distances.The most discriminating features are retained and used for training the support vector machine(SVM)classifier for two different data sets.Findings–Accuracy of the proposed system has been evaluated on two data sets:the well-known Oliva-Torralba data set and the customized image data set comprising of high-resolution images of natural landscapes.The experimentation on these two data sets with the proposed novel feature set and SVM classifier has provided 92.68 percent average classification accuracy,using ten-fold cross validation approach.The set of proposed features efficiently represent visual information and are therefore capable of narrowing the semantic gap between low-level image representation and high-level human perception.Originality/value–The method presented in this paper represents a new approach for extracting low-level features of reduced dimensionality that is able to model human perception for the task of scene classification.The methods of mapping primitive features to high-level features are intuitive to the user and are capable of reducing the semantic gap.The proposed feature evaluation technique is general and can be applied across any domain.

关键词： Openness Roughness Human perception JND p-value Scene classification Semantic gap Feature elevation Dominant direction

An Exact Generalized Test for Homogeneity of Inverse Gaussian Scale parameters

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Acta Mathematicae Applicatae Sinica 2019年第4期35卷 761-769页

作者： Xu-hua LIU Xing-zhong XU Wei-yan MU Department of Mathematics China Agricultural University Beijing 100083 China College of Mathematics Beijing Institute of Technology Beijing 100081 China School of Science Beijing University of Civil Engineering and Architecture Beijing 100044 China

In this paper, we propose a new generalized p-value for testing homogeneity of scale parameters λi from k independent inverse Gaussian populations. The proposed generalized p-value is proved to have exact frequentist property, and it is also invariant under the group of scale transformation. Simulation results indicate that the proposed test is better than existing approximate χ^2 test.

关键词： Inverse Gaussian distribution Generalized p-value Exact frequentist property

Epidemiological Analysis of the Coronavirus Disease Outbreak with Random Effects

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Computers, Materials & Continua 2021年第6期67卷 3215-3227页

作者： Muhammad Farman Aqeel Ahmad Ali Akgül Muhammad Umer Saleem Muhammad Naeem Dumitru Baleanu Department of Mathematics and Statistics University of LahorePakistan Department of Mathematics Faculty of Art and ScienceSiirt UniversitySiirt56100Turkey Department of Mathematics University of EducationLahorePakistan Department of Economics and Business Administration University of EducationLahorePakistan Department of Mathematics Cankaya UniversityBalgat06530Turkey Institute of Space Sciences Magurele-BucharestR76900Romania Department of Medical Research China Medical UniversityTaichung40402Taiwan

Today,coronavirus appears as a serious challenge to the whole world.Epidemiological data of coronavirus is collected through media and web sources for the purpose of analysis.New data on COVID-19 are available daily,yet information about the biological aspects of SARS-CoV-2 and epidemiological characteristics of COVID-19 remains limited,and uncertainty remains around nearly all its parameters’values.This research provides the scientic and public health communities better resources,knowledge,and tools to improve their ability to control the infectious diseases.Using the publicly available data on the ongoing pandemic,the present study investigates the incubation period and other time intervals that govern the epidemiological dynamics of the COVID-19 infections.Formulation of the testing hypotheses for different countries with a 95%level of condence,and descriptive statistics have been calculated to analyze in which region will COVID-19 fall according to the tested hypothesized mean of different countries.The results will be helpful in decision making as well as in further mathematical analysis and control strategy.Statistical tools are used to investigate this pandemic,which will be useful for further research.The testing of the hypothesis is done for the differences in various effects including standard errors.Changes in states’variables are observed over time.The rapid outbreak of coronavirus can be stopped by reducing its transmission.Susceptible should maintain safe distance and follow precautionary measures regarding COVID-19 transmission.

关键词： Covid-19 infectious disease statistical analysis p-value epidemiology hypothesis

FDR Control for pairwise Comparisons of Normal Means Based on Goodness of Fit Test

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Acta Mathematicae Applicatae Sinica 2016年第3期32卷 701-712页

作者： pei JIN Xing-zhong XU Na LI School of Mathematics and Statistics Beijing Institute of Technology School of Economics and Management University of the Chinese Academy of Sciences

This study is undertaken to apply a bootstrap method of controlling the false discovery rate （FDR） when performing pairwise comparisons of normal means. Due to the dependency of test statistics in pairwise comparisons, many conventional multiple testing procedures can＇t be employed directly. Some modified pro- cedures that control FDR with dependent test statistics are too conservative. In the paper, by bootstrap and goodness-of-fit methods, we produce independent p-values for pairwise comparisons. Based on these indepen- dent p-values, plenty of procedures can be used, and two typical FDR controlling procedures are applied here. An example is provided to illustrate the proposed approach. Extensive simulations show the satisfactory FDR control and power performance of our approach. In addition, the proposed approach can be easily extended to more than two normal, or non-normal, balance or unbalance cases.

关键词： multiple testing false discovery rate goodness-of-fit test pairwise comparisons p-value resampling

A sea change in statistics:A reconsideration of what is important in the age of big data

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Journal of Management Analytics 2014年第4期1卷 241-248页

作者： Wenbo Guo Detmar Straub pengzhu Zhang Antai College of Economics and Management Shanghai Jiao Tong UniversityShanghai 200052China J.Mack Robinson College of Business Georgia State UniversityAtlantaGA 30303USA

The development of information technology(IT)in the last decade has ushered us into the‘big data’era.Whereas sampling error has been of high interest in such studies over the last century,extremely large datasets will virtually rule out the possibility that statistics generated from samples are not also true of the population.The critical discussion must move on to how much the exogenous and endogenous variables explain ultimate outcomes.The stress will have to move from generalizability to explanatory power.By examining the three common statistical tests–the T-value,the F-value and the beta coefficient(or‘b’in the sample)–this paper aims to show how important effect size analysis is with the trend toward larger and larger samples and big data.In the end,the paper points out the gap of what the acceptable ranges of effects that appears in our sundry scientific literatures are.We call for studies in this regard so that social sciences can move forward and strengthen weak theory bases,and recognize strong theories when they do appear.

关键词： p-value effect size sample size big data

A Note on the Nonparametric Least-squares Test for Checking a polynomial Relationship

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Acta Mathematicae Applicatae Sinica 2003年第3期19卷 511-520页

作者： Chang-lin Mei, Shu-yuan He, Yan-hua WangLMAM, Institute of Mathematics, peking University, Beijing 100871, China School of Sciences, Xi’an Jiaotong University, Xi’an 710049, China LMAM Institute of Mathematics Peking University Beijing China School of Sciences Xi’an Jiaotong University Xi’an China

Recently, Gijbels and Rousson[6] suggested a new approach, called nonparametric least-squares test, to check polynomial regression relationships. Although this test procedure is not only simple but also powerful in mo... 详细信息

Recently, Gijbels and Roussonp>[6]p> suggested a new approach, called nonparametric least-squares test, to check polynomial regression relationships. Although this test procedure is not only simple but also powerful in most cases, there are several other parameters to be chosen in addition to the kernel and bandwidth. As shown in their paper, choice of these parameters is crucial but sometimes intractable. We propose in this paper a new statistic which is based on sample variance of the locally estimated pth derivative of the regression function at each design point. The resulting test is still simple but includes no extra parameters to be determined besides the kernel and bandwidth that are necessary for nonparametric smoothing techniques. Comparison by simulations demonstrates that our test performs as well as or even better than Gijbels and Rousson’s approach. Furthermore, a real-life data set is analyzed by our method and the results obtained are satisfactory.

关键词： Local polynomial fitting polynomial regression derivative estimation p-value