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A Projection Approach to Monotonic Regression with Bernstein Polynomials

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Journal of Systems Science & Complexity 2022年第5期35卷 1910-1928页

作者： ZHU Guo fang xiangzhong School of Mathematical Sciences Peking UniversityBeijing 100871China

Monotonic regression problems have been widely seen in many fields like economics and *** the monotonic parameter space is used by the Bayesian methods using Bernstein *** this paper the authors extend the usual parameter space to a larger space in which all the proper parameters making the regression function to be monotonic are *** order to ensure that the problem could be solved in the new parameter space,the authors use a projection posterior method to make *** authors show the proposed method has good approximation properties and performs well compared with other competing methods both in simulations and in practical applications.

关键词： Bayesian nonparametics monotonic regression posterior projection

Estimation in Discrete Reliability Growth,a Growth Model with Coefficient Condition

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Journal of Systems Science & Complexity 2016年第4期29卷 1112-1122页

作者： SHAO Xiang fang xiangzhong School of Mathematics Science Peking UniversityBeijing 100871China

This paper considers the well known problem of estimating reliability in discrete reliability growth context with sequence of dichotomous success-failure outcomes. More precisely, the authors generalize the simple order relationship constraint with some coefficients. The authors prove that under some mild conditions, the generalized constraint MLE problem can be transformed to a traditional isotonic problem. The authors also study the lower confidence limit estimation of reliability with sample space ranking method. A simulation is conducted to illustrate the superiority of the proposed method.

关键词： Confidence limit discrete reliability growth isotonic regression point estimation

The computation of Buehler confidence limits

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Science China Mathematics 2005年第8期48卷 1065-1074页

作者： fang xiangzhong CHEN Jiading School of Mathematical Science LMAM Peking University Beijing 100871 China School of Mathematical Science LMAM Peking University Beijing 100871 China

In medicine and industry, small sample size often arises owing to the high test cost. Then exact confidence inference is important. Buehler confidence limit is a kind of exact confidence limit for the function of parameters in a model. It can be always defined if the order in sample space is given. But the computing problem is often difficult, especially for the cases with high dimension parameter or with incomplete data. This paper presents an algorithm to compute the Buehler confidence limits by EM algorithm. This is the firsttime usage of EM algorithm on Buehler confidence limits, but the algorithm is often used for maximum likelihood estimate in literatures. Three computation examples are given to illustrate the method.

关键词： Buehler confidence limits, EM algorithm, small sample.

Confidence limits for the mean of exponential distribution in any time-sequential samples

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Science China Mathematics 2005年第9期48卷 1182-1193页

作者： CHEN Jiading fang xiangzhong School of Mathematical Sciences LMAM Peking University Beijing 100871 China School of Mathematical Sciences LMAM Peking University Beijing 100871 China

We present the general results determining confidence limits for the mean of exponential distribution in any time-sequential samples, which are obtained in any sequential life tests with replacement or without replace... 详细信息

关键词： confidence limits, time-sequential samples, exponential distribution.

Ovarian Cancer Screening Based on Mixture Change-Point Model

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Journal of Systems Science & Complexity 2015年第2期28卷 471-488页

作者： ZOU Chenchen fang xiangzhong ZHAI Guanghe School of Mathematics Peking University

Ovarian cancer is one of the most deadly female genital malignant tumors in many regions while an effective early screening strategy can save numerous ***125 and HE4 are tumor markers validated efficacious as well as most commonly used in recent screening research of ovarian *** this paper,the authors construct a change-point and mixture model on the basis of longitudinal CA125 and HE4 levels and estimated parameters using maximum likelihood method with the preclinical duration assumed right-censored,which is more adaptive and yields comparable results in comparison to the Bayesian approach raised by *** of estimators is *** authors also run a 5-year simulation of sequential screening by calculating the risk of cancer and hypothesis testing the true incidence time *** show that diagnosis based on hypothesis test performs better in early detection.

关键词： Change-point mixture model longitudinal data analysis maximum likelihood estimation ovarian caner screening.

GROUP CONTINGENCY TEST FOR TWO OR SEVERAL INDEPENDENT SAMPLES

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Journal of Systems Science & Complexity 2011年第6期24卷 1183-1192页

作者： Hexin ZHANG xiangzhong fang Xiaojing MA Department of Probability and Statistics School of Mathematical Sciences Peking University Beijing 100871 China

This paper proposes a new and distribution-free test called ＂Group Contingency＂ test （GC, for short） for testing two or several independent samples. Compared with traditional nonparametric tests, GC test tends to explore more information based on samples, and it＇s location-, scale-, and shapesensitive. The authors conduct some simulation studies comparing GC test with Wilcoxon rank sum test （W）, Kolmogorov-Smirnov test （KS） and Wald-Wolfowitz runs test （WW） for two sample case, and with Kruskal-Wallis （KW） for testing several samples. Simulation results reveal that GC test usually outperforms other methods.

关键词： Clustering group contingency test nonparametric test

A novel dynamic frame rate control algorithm for H.264 low-bit-rate video coding

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High Technology Letters 2007年第1期13卷 53-57页

作者：杨静 fang xiangzhong Institute of Image Communication ＆ Information Processing Shanghai Jiaotong University Shanghai 200030 P.R. China

The goal of this paper is to improve human visual perceptual quality as well as coding efficiency of H. 264 video at low bit rate conditions by adaptively adjusting the number of skipped frames. The encoding frames are selected according to the motion activity of each frame and the motion accumulation of successive frames. The motion activity analysis is based on the statistics of motion vectors and with consider- ation of the characteristics of H. 264 coding standard. A prediction model of motion accumulation is pro- posed to reduce complex computation of motion estimation. The dynamic encoding frame rate control algorithm is applied to both the frame level and the GOB （Group of Macroblocks ） level. Simulation is done to compare the performance of JM76 with the proposed frame level scheme and GOB level scheme.

关键词： H.264 motion analysis frame rate control low-bit-rate

Semiparametric Bayesian Inference for Accelerated Failure Time Models with Errors-in-Covariates and Doubly Censored Data

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Journal of Systems Science & Complexity 2017年第5期30卷 1189-1205页

作者： SHEN Junshan LI Zhaonan YU Hanjun fang xiangzhong School of Mathematical Sciences Peking UniversityBeijing 100871China

This paper proposes a Bayesian semiparametric accelerated failure time model for doubly censored data with errors-in-covariates. The authors model the distributions of the unobserved covariates and the regression errors via the Dirichlet processes. Moreover, the authors extend the Bayesian Lasso approach to our semiparametric model for variable selection. The authors develop the Markov chain Monte Carlo strategies for posterior calculation. Simulation studies are conducted to show the performance of the proposed method. The authors also demonstrate the implementation of the method using analysis of PBC data and ACTG 175 data.

关键词： Accelerated failure time model Dirichlet process errors-in-covariates Gibbs sampling,variable selection

On Solving a System of Volterra Integral Equations with Relaxed Monte Carlo Method

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Journal of Applied Mathematics and Physics 2016年第7期4卷 1315-1320页

作者： Zhimin Hong xiangzhong fang Zaizai Yan Hui Hao Department of Mathematics Science College of Inner Mongolia University of Technology Hohhot China Department of Statistics School of Mathematical Sciences Peking University Beijing China

A random simulation method was used for treatment of systems of Volterra integral equations of the second kind. Firstly, a linear algebra system was obtained by discretization using quadrature formula. Secondly, this algebra system was solved by using relaxed Monte Carlo method with importance sampling and numerical approximation solutions of the integral equations system were achieved. It is theoretically proved that the validity of relaxed Monte Carlo method is based on importance sampling to solve the integral equations system. Finally, some numerical examples from literatures are given to show the efficiency of the method.

关键词： Systems of Volterra Integral Equations Quadrature Formula Relaxed Monte Carlo Method Importance Sampling