Various random models with balanced data that are relevant for analyzing practical test data are described, along with several hypothesis testing and interval estimation problems concerning variance components. In thi...Various random models with balanced data that are relevant for analyzing practical test data are described, along with several hypothesis testing and interval estimation problems concerning variance components. In this paper, we mainly consider these problems in general random effect model with balanced data. Exact tests and confidence intervals for a single variance component corresponding to random effect are developed by using generalized p-values and generalized confidence intervals. The resulting procedures are easy to compute and are applicable to small samples. Exact tests and confidence intervals are also established for comparing the random-effects variance components and the sum of random-effects variance components in two independent general random effect models with balanced data. Furthermore, we investigate the statistical properties of the resulting tests. Finally, some simulation results on the type Ⅰ error probability and power of the proposed test are reported. The simulation results indicate that exact test is extremely satisfactory for controlling type Ⅰ error probability.展开更多
Some fundamental issues on statistical inferences relating to varying-coefficient regression models are addressed and studied. An exact testing procedure is proposed for checking the goodness of fit of a varying-coeff...Some fundamental issues on statistical inferences relating to varying-coefficient regression models are addressed and studied. An exact testing procedure is proposed for checking the goodness of fit of a varying-coefficient model fited by the locally weighted regression technique versus an ordinary linear regression model. Also, an appropriate statistic for testing variation of model parameters over the locations where the observations are collected is constructed and a formal testing approach which is essential to exploring spatial non-stationarity in geography science is suggested.展开更多
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 th...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.展开更多
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...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.展开更多
文摘Various random models with balanced data that are relevant for analyzing practical test data are described, along with several hypothesis testing and interval estimation problems concerning variance components. In this paper, we mainly consider these problems in general random effect model with balanced data. Exact tests and confidence intervals for a single variance component corresponding to random effect are developed by using generalized p-values and generalized confidence intervals. The resulting procedures are easy to compute and are applicable to small samples. Exact tests and confidence intervals are also established for comparing the random-effects variance components and the sum of random-effects variance components in two independent general random effect models with balanced data. Furthermore, we investigate the statistical properties of the resulting tests. Finally, some simulation results on the type Ⅰ error probability and power of the proposed test are reported. The simulation results indicate that exact test is extremely satisfactory for controlling type Ⅰ error probability.
基金the National Natural Science Foundation of China (No.60075001) and Xi'anJiaotong University Natural Science Foundation.
文摘Some fundamental issues on statistical inferences relating to varying-coefficient regression models are addressed and studied. An exact testing procedure is proposed for checking the goodness of fit of a varying-coefficient model fited by the locally weighted regression technique versus an ordinary linear regression model. Also, an appropriate statistic for testing variation of model parameters over the locations where the observations are collected is constructed and a formal testing approach which is essential to exploring spatial non-stationarity in geography science is suggested.
基金supported by a grant from City University of Hong Kong (Project No.9610639).
文摘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.
基金supported by the National Natural Science Foundation of China (Nos.41974068 and 41574040)Key International S&T Cooperation Project of P.R.China (No.2015DFA21260)。
文摘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.
