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Application of Bayesian approach to hydrological frequency analysis

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Science China(Technological Sciences) 2011年第5期54卷 1183-1192页

作者： LIANG ZhongMin LI BinQuan YU ZhongBo CHANG Wen Juan College of Hydrology and Water Resources Hohai University Nanjing 210098 China Department of Geosciences University of Nevada Las Vegas NV 89154 USA

An existing Bayesian flood frequency analysis method is applied to quantile estimation for Pearson type three (P-III) probability distribution. The method couples prior and sample information under the framework of Bayesian formula, and the Markov Chain Monte Carlo (MCMC) sampling approach is used to estimate posterior distributions of parameters. Different from the original sampling algorithm (i.e. the important sampling) used in the existing approach, we use the adaptive metropolis (AM) sampling technique to generate a large number of parameter sets from Bayesian parameter posterior distributions in this paper. Consequently, the sampling distributions for quantiles or the hydrological design values are constructed. The sampling distributions of quantiles are estimated as the Bayesian method can provide not only various kinds of point estimators for quantiles, e.g. the expectation estimator, but also quantitative evaluation on uncertainties of these point estimators. Therefore, the Bayesian method brings more useful information to hydrological frequency analysis. As an example, the flood extreme sample series at a gauge are used to demonstrate the procedure of application.

关键词： Bayesian theory hydrological frequency analysis Markov Chain Monte Carlo prior distribution posterior distribution

PARAMETER IDENTIFICATION OF DYNAMIC MODELS USING A BAYES APPROACH

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Applied Mathematics and Mechanics(English Edition) 2000年第4期21卷 447-454页

作者：李书卓家寿任青文 Institute of Aircraft Design Beijing University of Aeronautics & Astronautics Beijing P R China Institute of Civil Engineering Hehai University Nanjing P R China

The Bayesian method of statistical analysis has been applied to the parameter identification problem. A method is presented to identify parameters of dynamic models with the Bayes estimators of measurement frequencies. This is based on the solution of an inverse generalized evaluate problem. The stochastic nature of test data is considered and a normal distribution is used for the measurement frequencies. An additional feature is that the engineer's confidence in the measurement frequencies is quantified and incorporated into the identification procedure. A numerical example demonstrates the efficiency of the method.

关键词： parameter identification dynamic models Bayes estimators inverse eigenvalue problem prior distribution posterior distribution

Reliability Estimation of Aviation Pyrotechnics System Based on Mixed Beta distribution

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Journal of Donghua University(English Edition) 2014年第6期31卷 766-769页

作者：赖岳华董海平程涛杨树彬 School of Mechatronical Engineering Beijing Institute of Technology The 213th Research Institute of China Ordnance Industry

For evaluating reliability of an aviation pyrotechnics system,a Bayesian reliability estimation method utilizing reliability information of a system and its units was put forward. Firstly,an inheritance factor was determined by chi-square goodness of fit *** the mixed prior distribution was obtained based on the inheritance factor. Finally, the density function of posterior distribution was obtained and used to assess the reliability of *** to the new method, the reliability of an aviation pyrotechnics system was evaluated to reach 0. 989 6 at the confidence level of 0. 90. To reach the reliability index,the required numbers of trials of system and its units were given. It is instructional to apply the new method on the reliability estimation of aviation pyrotechnics systems.

关键词： aviation pyrotechnics system reliability mixed Beta distribution inheritance factor posterior distribution

Three-Component Mixture of RayleighModel Under Doubly Censored Samples:A Bayesian Look

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Communications in Mathematics and Statistics 2019年第4期7卷 417-443页

作者： Navid Feroze Muhammad Aslam Department of Mathematics and Statistics Riphah International UniversityIslamabadPakistan

Feroze and Aslam(J Natl Sci Found Sri Lanka 42:325-334,2014)and Sindhu et al.(J Mod Appl Stat Methods 13:259-286,2014)have considered the Bayesian analysis of the two-component mixture of lifetime distributions under doubly censored *** this paper,the concept has been extended for the three-component mixture of lifetime(Rayleigh)distribution under doubly censored *** likelihood function for the mixture of lifetime models under doubly type-II censored samples has been *** priors and loss functions have been assumed for the derivation of Bayes estimators and posterior *** comparisons among various estimators have been made by analyzing the simulated and real data sets.

关键词： Mixture distributions Prior elicitation posterior distribution Loss functions

Bayesian Inference of Empirical Coefficient for Foundation Settlement

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Journal of Southwest Jiaotong University(English Edition) 2009年第4期17卷 314-318页

作者：李珍玉王永和杨果林 School of Civil Engineering and Mechanics Central South University of Technology School of Civil Architectural Engineering Central South University

A new approach based on Bayesian theory is proposed to determine the empirical coefficient in soil settlement calculation. Prior distribution is assumed to he uniform in [ 0.2,1.4 ]. posterior density function is developed in the condition of prior distribution combined with the information of observed samples at four locations on a passenger dedicated fine. The results show that the posterior distribution of the empirical coefficient obeys Gaussian distribution. The mean value of the empirical coefficient decreases gradually with the increasing of the load on ground, and variance variation shows no regularity.

关键词： Bayesian theory Empirical coefficient Prior knowledge posterior distribution