融合ARIMA模型和MCMC方法的非一致性设计洪水计算

常规非一致性频率分析方法在选择协变量、建立统计参数与协变量的函数关系方面均存在主观性,且仅获得设计洪水估计值,不能同时进行不确定性分析。为改进上述不足,建立了ARIMA-MCMC模型,在贝叶斯MCMC方法抽样过程中考虑统计参数拟合期内的时变性,进而对未来气候变化条件下的非一致性设计洪水频率分布模型参数进行抽样,基于参数后验分布进行设计洪水计算,并推求相应的置信区间。选取雅砻江流域小得石水文站作为分析对象,采用ARIMA-MCMC模型定量评估未来气候变化条件下小得石站设计洪水的变化情况。结果表明:基于ARIMA-MCMC方法的参数抽样收敛效果较好,3种情景下的模型统计量D均小于显著水平5%的临界值;除SSP2-4.5情景下P=0.1%和P=0.05%的设计值外,其他情况的设计最大日流量较历史期均明显增加,其中SSP1-2.6、SSP5-8.5情景下的增幅分别为7.1%~10.5%、13.9%~27.2%。本文建立的ARIMA-MCMC方法能够有效进行非一致性设计洪水频率分析。

Ensemble Bayesian method for parameter distribution inference:application to reactor physics

The estimation of model parameters is an important subject in engineering.In this area of work,the prevailing approach is to estimate or calculate these as deterministic parameters.In this study,we consider the model parameters from the perspective of random variables and describe the general form of the parameter distribution inference problem.Under this framework,we propose an ensemble Bayesian method by introducing Bayesian inference and the Markov chain Monte Carlo(MCMC)method.Experiments on a finite cylindrical reactor and a 2D IAEA benchmark problem show that the proposed method converges quickly and can estimate parameters effectively,even for several correlated parameters simultaneously.Our experiments include cases of engineering software calls,demonstrating that the method can be applied to engineering,such as nuclear reactor engineering.

基于Bayesian-MCMC算法的水利工程投标报价分布预测

投标是水利工程承包商获取项目的主要途径,投标报价的高低直接影响承包商能否获取项目的承建权,投标前对拟投水利工程投标报价分布进行预测可优化己方报价制定。为此,通过全局寻优的Bayesian-MCMC算法对投标报价分布模型进行反演,并通过数值分析模拟承包商投标行为。结果表明,Bayesian-MCMC算法无需考虑贝叶斯估计中先验分布与似然函数的共轭性,且模拟所需数据更少,得到的分布稳定性好且更加精确。

基于Bayesian MCMC方法的美式障碍期权模拟定价

在最小二乘蒙特卡洛(LSM)方法基础上,提出用加权最小二乘与蒙特卡洛(MC)方法相结合,得到加权最小二乘蒙特卡洛(WLSM)方法,研究了障碍期权模拟定价的问题.假设标的资产价格过程遵循几何布朗运动,分析了是否支付红利和生成期权价格路径的问题.使用随机化Faure序列替换LSM方法中伪随机数,给出了WLSM方法在美式障碍期权定价的算法步骤.使用R语言对美式障碍上升敲出看跌期权(up-and-out put)在支付红利的情形下进行数值模拟,结果表明此方法与其他定价模型方法相比,定价更准确,说明该方法具有可行性和有效性.

Comparative Study of Probabilistic and Least-Squares Methods for Developing Predictive Models

This article explores the comparison between the probability method and the least squares method in the design of linear predictive models. It points out that these two approaches have distinct theoretical foundations and can lead to varied or similar results in terms of precision and performance under certain assumptions. The article underlines the importance of comparing these two approaches to choose the one best suited to the context, available data and modeling objectives.

基于Bayesian-MCMC方法的深受弯构件受剪概率模型研究

考虑主观、客观不确定性因素的影响,以深受弯构件受剪分析模型为研究对象,基于引入马尔科夫链-蒙特卡洛(MCMC)高效采样方法,通过R语言对深受弯构件概率模型参数进行MCMC随机模拟,给出参数的最优估计值及其对应的可信度,在先验模型基础上建立钢筋混凝土深受弯构件受剪承载力概率模型,完成模型前后的对比分析,并根据不同置信水平确定了深受弯构件受剪承载力的特征值。结果表明:基于MCMC方法得到的受剪承载力概率模型是在50000次迭代分析后产生的结果,能合理地解释影响参数的不确定性,可信度较高;后验概率模型计算结果与试验结果吻合良好,较先验模型更接近试验值,且离散性小。

Hierarchical Bayesian Calibration and On-line Updating Method for Influence Coefficient of Automatic Dynamic Balancing Machine

Measurement error of unbalance＇s vibration response plays a crucial role in calibration and on-line updating of influence coefficient（IC）. Focusing on the two problems that the moment estimator of data used in calibration process cannot fulfill the accuracy requirement under small sample and the disturbance of measurement error cannot be effectively suppressed in updating process, an IC calibration and on-line updating method based on hierarchical Bayesian method for automatic dynamic balancing machine was proposed. During calibration process, for the repeatedly-measured data obtained from experiments with different trial weights, according to the fact that measurement error of each sensor had the same statistical characteristics, the joint posterior distribution model for the true values of the vibration response under all trial weights and measurement error was established. During the updating process, information obtained from calibration was regarded as prior information, which was utilized to update the posterior distribution of IC combined with the real-time reference information to implement online updating. Moreover, Gibbs sampling method of Markov Chain Monte Carlo（MCMC） was adopted to obtain the maximum posterior estimation of parameters to be estimated. On the independent developed dynamic balancing testbed, prediction was carried out for multiple groups of data through the proposed method and the traditional method respectively, the result indicated that estimator of influence coefficient obtained through the proposed method had higher accuracy; the proposed updating method more effectively guaranteed the measurement accuracy during the whole producing process, and meantime more reasonably compromised between the sensitivity of IC change and suppression of randomness of vibration response.

不同建议分布MCMC算法在地下水污染源反演识别中的对比研究

为了探究正态分布、均匀分布和随机游走三种不同建议分布的MCMC算法对地下水污染源反演识别结果的影响,并遴选出最优的建议分布.本文根据假想案例建立了污染质运移模拟模型及基于Kriging方法的替代模型,并建立了基于正态分布、均匀分布和随机游走三种建议分布的MCMC算法以反演识别地下水污染源的释放历史.结果表明,针对本文算例,以均匀分布为建议分布的MCMC算法具有反演精度高、稳定性好、收敛速度快等优点,最为适合作为本研究案例的建议分布进行地下水污染源反演识别研究.

Improvement of X-Band Polarization Radar Melting Layer Recognition by the Bayesian Method and ITS Impact on Hydrometeor Classification

Using melting layer(ML)and non-melting layer(NML)data observed with the X-band dual linear polarization Doppler weather radar(X-POL)in Shunyi,Beijing,the reflectivity(ZH),differential reflectivity(ZDR),and correlation coefficient(CC)in the ML and NML are obtained in several stable precipitation processes.The prior probability density distributions(PDDs)of the ZH,ZDR and CC are calculated first,and then the probabilities of ZH,ZDR and CC at each radar gate are determined(PBB in the ML and PNB in the NML)by the Bayesian method.When PBB>PNB the gate belongs to the ML,and when PBB<PNB the gate belongs to the NML.The ML identification results with the Bayesian method are contrasUsing melting layer(ML)and non-melting layer(NML)data observed with the X-band dual linear polarization Doppler weather radar(X-POL)in Shunyi,Beijing,the reflectivity(ZH),differential reflectivity(ZDR),and correlation coefficient(CC)in the ML and NML are obtained in several stable precipitation processes.The prior probability density distributions(PDDs)of the ZH,ZDR and CC are calculated first,and then the probabilities of ZH,ZDR and CC at each radar gate are determined(PBB in the ML and PNB in the NML)by the Bayesian method.When PBB>PNB the gate belongs to the ML,and when PBB<PNB the gate belongs to the NML.The ML identification results with the Bayesian method are contrasted under the conditions of the independent PDDs and joint PDDs of the ZH,ZDR and CC.The results suggest that MLs can be identified effectively,although there are slight differences between the two methods.Because the values of the polarization parameters are similar in light rain and dry snow,it is difficult for the polarization radar to distinguish them.After using the Bayesian method to identify the ML,light rain and dry snow can be effectively separated with the X-POL observed data.ted under the conditions of the independent PDDs and joint PDDs of the ZH,ZDR and CC.The results suggest that MLs can be identified effectively,although there are slight differences between the two methods.Because the values of the polarization parameters are similar in light rain and dry snow,it is difficult for the polarization radar to distinguish them.After using the Bayesian method to identify the ML,light rain and dry snow can be effectively separated with the X-POL observed data.

Uncertainty analysis of strain modal parameters by Bayesian method using frequency response function

Structural strain modes are able to detect changes in local structural performance, but errors are inevitably intermixed in the measured data. In this paper, strain modal parameters are considered as random variables, and their uncertainty is analyzed by a Bayesian method based on the structural frequency response function （FRF）. The estimates of strain modal parameters with maximal posterior probability are determined. Several independent measurements of the FRF of a four-story reinforced concrete flame structural model were performed in the laboratory. The ability to identify the stiffness change in a concrete column using the strain mode was verified. It is shown that the uncertainty of the natural frequency is very small. Compared with the displacement mode shape, the variations of strain mode shapes at each point are quite different. The damping ratios are more affected by the types of test systems. Except for the case where a high order strain mode does not identify local damage, the first order strain mode can provide an exact indication of the damage location.

Application of a Bayesian method to data-poor stock assessment by using Indian Ocean albacore (Thunnus alalunga) stock assessment as an example

It is widely recognized that assessments of the status of data-poor fish stocks are challenging and that Bayesian analysis is one of the methods which can be used to improve the reliability of stock assessments in data-poor situations through borrowing strength from prior information deduced from species with good-quality data or other known information. Because there is considerable uncertainty remaining in the stock assessment of albacore tuna（Thunnus alalunga） in the Indian Ocean due to the limited and low-quality data, we investigate the advantages of a Bayesian method in data-poor stock assessment by using Indian Ocean albacore stock assessment as an example. Eight Bayesian biomass dynamics models with different prior assumptions and catch data series were developed to assess the stock. The results show（1） the rationality of choice of catch data series and assumption of parameters could be enhanced by analyzing the posterior distribution of the parameters;（2） the reliability of the stock assessment could be improved by using demographic methods to construct a prior for the intrinsic rate of increase（r）. Because we can make use of more information to improve the rationality of parameter estimation and the reliability of the stock assessment compared with traditional statistical methods by incorporating any available knowledge into the informative priors and analyzing the posterior distribution based on Bayesian framework in data-poor situations, we suggest that the Bayesian method should be an alternative method to be applied in data-poor species stock assessment, such as Indian Ocean albacore.

A Bayesian Updating Method for Non-Probabilistic Reliability Assessment of Structures with Performance Test Data

For structures that only the predicted bounds of uncertainties are available,this study proposes a Bayesianmethod to logically evaluate the nonprobabilistic reliability of structures based on multi-ellipsoid convex model and performance test data.According to the given interval ranges of uncertainties,we determine the initial characteristic parameters of a multi-ellipsoid convex set.Moreover,to update the plausibility of characteristic parameters,a Bayesian network for the information fusion of prior uncertainty knowledge and subsequent performance test data is constructed.Then,an updated multi-ellipsoid set with the maximum likelihood of the performance test data can be achieved.The credible non-probabilistic reliability index is calculated based on the Kriging-based surrogate model of the performance function.Several numerical examples are presented to validate the proposed Bayesian updating method.

基于Bayesian-MCMC方法的少量数据初因事件频率的不确定性分析

在计算初因事件频率的过程中,当初因事件获取的数据较少时,便要考虑不确定性。在概率安全评估(PSA)中,通常以概率分布的形式表示事件的不确定性。本文针对"贮罐内压过大"这个初因事件数据量获取少的问题,采用贝叶斯-马尔科夫链蒙特卡洛方法(Bayesian-MCMC方法)对其频率进行了不确定性分析,得到了初因事件频率的不确定分布图形,并分析了不确定分布图形的特点,同时与直接计算频率方法进行了结果比较,从而验证了该方法的正确性和有效性。

Bayesian-MCMC算法在计算机图像处理中的实践

本文从计算机图像处理技术及过程出发,分析了计算机图像处理的重要作用,并就如何在计算机图像处理中应用Bayesian-MCMC算法进行了分析和讨论,旨在推动计算机图像处理技术的发展。

Bayesian machine learning-based method for prediction of slope failure time

The data-driven phenomenological models based on deformation measurements have been widely utilized to predict the slope failure time(SFT).The observational and model uncertainties could lead the predicted SFT calculated from the phenomenological models to deviate from the actual SFT.Currently,very limited study has been conducted on how to evaluate the effect of such uncertainties on SFT prediction.In this paper,a comprehensive slope failure database was compiled.A Bayesian machine learning(BML)-based method was developed to learn the model and observational uncertainties involved in SFT prediction,through which the probabilistic distribution of the SFT can be obtained.This method was illustrated in detail with an example.Verification studies show that the BML-based method is superior to the traditional inverse velocity method(INVM)and the maximum likelihood method for predicting SFT.The proposed method in this study provides an effective tool for SFT prediction.

Bayesian Study Using MCMC of Three-Parameter Frechet Distribution Based on Type-I Censored Data

Type-I censoring mechanism arises when the number of units experiencing the event is random but the total duration of the study is fixed. There are a number of mathematical approaches developed to handle this type of data. The purpose of the research was to estimate the three parameters of the Frechet distribution via the frequentist Maximum Likelihood and the Bayesian Estimators. In this paper, the maximum likelihood method (MLE) is not available of the three parameters in the closed forms;therefore, it was solved by the numerical methods. Similarly, the Bayesian estimators are implemented using Jeffreys and gamma priors with two loss functions, which are: squared error loss function and Linear Exponential Loss Function (LINEX). The parameters of the Frechet distribution via Bayesian cannot be obtained analytically and therefore Markov Chain Monte Carlo is used, where the full conditional distribution for the three parameters is obtained via Metropolis-Hastings algorithm. Comparisons of the estimators are obtained using Mean Square Errors (MSE) to determine the best estimator of the three parameters of the Frechet distribution. The results show that the Bayesian estimation under Linear Exponential Loss Function based on Type-I censored data is a better estimator for all the parameter estimates when the value of the loss parameter is positive.

Comparison of the Bayesian Methods on Interval-Censored Data for Weibull Distribution

This study considers the estimation of Maximum Likelihood Estimator and the Bayesian Estimator of the Weibull distribution with interval-censored data. The Bayesian estimation can’t be used to solve the parameters analytically and therefore Markov Chain Monte Carlo is used, where the full conditional distribution for the scale and shape parameters are obtained via Metropolis-Hastings algorithm. Also Lindley’s approximation is used. The two methods are compared to maximum likelihood counterparts and the comparisons are made with respect to the mean square error (MSE) to determine the best for estimating of the scale and shape parameters.

Performance analysis of empirical models for predicting rock mass deformation modulus using regression and Bayesian methods

Deformation modulus of rock mass is one of the input parameters to most rock engineering designs and constructions.The field tests for determination of deformation modulus are cumbersome,expensive and time-consuming.This has prompted the development of various regression equations to estimate deformation modulus from results of rock mass classifications,with rock mass rating(RMR)being one of the frequently used classifications.The regression equations are of different types ranging from linear to nonlinear functions like power and exponential.Bayesian method has recently been developed to incorporate regression equations into a Bayesian framework to provide better estimates of geotechnical properties.The question of whether Bayesian method improves the estimation of geotechnical properties in all circumstances remains open.Therefore,a comparative study was conducted to assess the performances of regression and Bayesian methods when they are used to characterize deformation modulus from the same set of RMR data obtained from two project sites.The study also investigated the performance of different types of regression equations in estimation of the deformation modulus.Statistics,probability distributions and prediction indicators were used to assess the performances of regression and Bayesian methods and different types of regression equations.It was found that power and exponential types of regression equations provide a better estimate than linear regression equations.In addition,it was discovered that the ability of the Bayesian method to provide better estimates of deformation modulus than regression method depends on the quality and quantity of input data as well as the type of the regression equation.

Packet Cache-Forward Method Based on Improved Bayesian Outlier Detection for Mobile Handover in Satellite Networks

In this paper, we propose a Packet Cache-Forward(PCF) method based on improved Bayesian outlier detection to eliminate out-of-order packets caused by transmission path drastically degradation during handover events in the moving satellite networks, for improving the performance of TCP. The proposed method uses an access node satellite to cache all received packets in a short time when handover occurs and forward them out in order. To calculate the cache time accurately, this paper establishes the Bayesian based mixture model for detecting delay outliers of the entire handover scheme. In view of the outliers' misjudgment, an updated classification threshold and the sliding window has been suggested to correct category collections and model parameters for the purpose of quickly identifying exact compensation delay in the varied network load statuses. Simulation shows that, comparing to average processing delay detection method, the average accuracy rate was scaled up by about 4.0%, and there is about 5.5% cut in error rate in the meantime. It also behaves well even though testing with big dataset. Benefiting from the advantage of the proposed scheme in terms of performance, comparing to conventional independent handover and network controlled synchronizedhandover in simulated LEO satellite networks, the proposed independent handover with PCF eliminates packet out-of-order issue to get better improvement on congestion window. Eventually the average delay decreases more than 70% and TCP performance has improved more than 300%.

Comparison of two Bayesian-point-estimation methods in multiple-source localization

Environmental uncertainty represents the limiting factor in matched-field localization. Within a Bayesian framework, both the environmental parameters, and the source parameters are considered to be unknown variables. However, including environmental parameters in multiple-source localization greatly increases the complexity and computational demands of the inverse problem. In the paper, the closed-form maximumlikelihood expressions for source strengths and noise variance at each frequency allow these parameters to be sampled implicitly, substantially reducing the dimensionality and difficulty of the inversion. This paper compares two Bayesian-point-estimation methods： the maximum a posteriori（MAP） approach and the marginal posterior probability density（PPD） approach to source localization. The MAP approach determines the sources locations by maximizing the PPD over all source and environmental parameters. The marginal PPD approach integrates the PPD over the unknowns to obtain a sequence of marginal probability distribution over source range or depth.Monte Carlo analysis of the two approaches for a test case involving both geoacoustic and water-column uncertainties indicates that：（1） For sensitive parameters such as source range, water depth and water sound speed, the MAP solution is better than the marginal PPD solution.（2） For the less sensitive parameters, such as,bottom sound speed, bottom density, bottom attenuation and water sound speed, when the SNR is low, the marginal PPD solution can better smooth the noise, which leads to better performance than the MAP solution.Since the source range and depth are sensitive parameters, the research shows that the MAP approach provides a slightly more reliable method to locate multiple sources in an unknown environment.