<p> <span><span style="font-family:""><span style="font-family:Verdana;">Simulation (stochastic) methods are based on obtaining random samples </span><spa...<p> <span><span style="font-family:""><span style="font-family:Verdana;">Simulation (stochastic) methods are based on obtaining random samples </span><span style="color:#4F4F4F;font-family:Simsun;white-space:normal;background-color:#FFFFFF;"><span style="font-family:Verdana;">θ</span><sup><span style="font-family:Verdana;">5</span></sup></span><span style="font-family:Verdana;"></span><span style="font-family:Verdana;"> </span><span><span style="font-family:Verdana;"> </span><span><span style="font-family:Verdana;">from the desired distribution </span><em><span style="font-family:Verdana;">p</span></em><span style="font-family:Verdana;">(</span><span style="color:#4F4F4F;font-family:Verdana;white-space:normal;background-color:#FFFFFF;">θ</span><span style="font-family:Verdana;"></span><span style="font-family:Verdana;">)</span><span style="font-family:Verdana;"> </span><span style="font-family:Verdana;">and estimating the expectation of any </span></span><span><span style="font-family:Verdana;">function </span><em><span style="font-family:Verdana;">h</span></em><span style="font-family:Verdana;">(</span><span style="color:#4F4F4F;font-family:Verdana;white-space:normal;background-color:#FFFFFF;">θ</span><span style="font-family:Verdana;"></span><span style="font-family:Verdana;">)</span><span style="font-family:Verdana;">. Simulation methods can be used for high-dimensional dis</span></span><span style="font-family:Verdana;">tributions, and there are general algorithms which work for a wide variety of models. Markov chain Monte Carlo (MCMC) methods have been important </span><span style="font-family:Verdana;">in making Bayesian inference practical for generic hierarchical models in</span><span style="font-family:Verdana;"> small area estimation. Small area estimation is a method for producing reliable estimates for small areas. Model based Bayesian small area estimation methods are becoming popular for their ability to combine information from several sources as well as taking account of spatial prediction of spatial data. In this study, detailed simulation algorithm is given and the performance of a non-trivial extension of hierarchical Bayesian model for binary data under spatial misalignment is assessed. Both areal level and unit level latent processes were considered in modeling. The process models generated from the predictors were used to construct the basis so as to alleviate the problem of collinearity </span><span style="font-family:Verdana;">between the true predictor variables and the spatial random process. The</span><span style="font-family:Verdana;"> performance of the proposed model was assessed using MCMC simulation studies. The performance was evaluated with respect to root mean square error </span><span style="font-family:Verdana;">(RMSE), Mean absolute error (MAE) and coverage probability of corres</span><span style="font-family:Verdana;">ponding 95% CI of the estimate. The estimates from the proposed model perform better than the direct estimate.</span></span></span></span> </p> <p> <span></span> </p>展开更多
A modified Bayesian reliability assessment method of binomial components was proposed by fusing prior information of similar products.The traditional Bayesian method usually directly used all the prior data,ignoring t...A modified Bayesian reliability assessment method of binomial components was proposed by fusing prior information of similar products.The traditional Bayesian method usually directly used all the prior data,ignoring the differences between them,which might decrease the credibility level of reliability evaluation and result in data submergence.To solve the problem,a revised approach was derived to calculate groups of prior data's quantitative credibility,used for weighted data fusion.Then inheritance factor was introduced to build a mixed beta distribution to illustrate the innovation of new products.However,in many cases,inheritance factor was determined by Chi-square test that could not give out exact result with respect to rare failures.To make the model more precise,Barnard's exact test was suggested being used to calculate the inheritance factor.A numerical example is given to demonstrate that the modified method is successful and rational,while the classical method is too conservative and the traditional Bayesian method is too risky.展开更多
The longitudinal dispersion of the projectile in shooting tests of two-dimensional trajectory corrections fused with fixed canards is extremely large that it sometimes exceeds the correction ability of the correction ...The longitudinal dispersion of the projectile in shooting tests of two-dimensional trajectory corrections fused with fixed canards is extremely large that it sometimes exceeds the correction ability of the correction fuse actuator.The impact point easily deviates from the target,and thus the correction result cannot be readily evaluated.However,the cost of shooting tests is considerably high to conduct many tests for data collection.To address this issue,this study proposes an aiming method for shooting tests based on small sample size.The proposed method uses the Bootstrap method to expand the test data;repeatedly iterates and corrects the position of the simulated theoretical impact points through an improved compatibility test method;and dynamically adjusts the weight of the prior distribution of simulation results based on Kullback-Leibler divergence,which to some extent avoids the real data being"submerged"by the simulation data and achieves the fusion Bayesian estimation of the dispersion center.The experimental results show that when the simulation accuracy is sufficiently high,the proposed method yields a smaller mean-square deviation in estimating the dispersion center and higher shooting accuracy than those of the three comparison methods,which is more conducive to reflecting the effect of the control algorithm and facilitating test personnel to iterate their proposed structures and algorithms.;in addition,this study provides a knowledge base for further comprehensive studies in the future.展开更多
文摘<p> <span><span style="font-family:""><span style="font-family:Verdana;">Simulation (stochastic) methods are based on obtaining random samples </span><span style="color:#4F4F4F;font-family:Simsun;white-space:normal;background-color:#FFFFFF;"><span style="font-family:Verdana;">θ</span><sup><span style="font-family:Verdana;">5</span></sup></span><span style="font-family:Verdana;"></span><span style="font-family:Verdana;"> </span><span><span style="font-family:Verdana;"> </span><span><span style="font-family:Verdana;">from the desired distribution </span><em><span style="font-family:Verdana;">p</span></em><span style="font-family:Verdana;">(</span><span style="color:#4F4F4F;font-family:Verdana;white-space:normal;background-color:#FFFFFF;">θ</span><span style="font-family:Verdana;"></span><span style="font-family:Verdana;">)</span><span style="font-family:Verdana;"> </span><span style="font-family:Verdana;">and estimating the expectation of any </span></span><span><span style="font-family:Verdana;">function </span><em><span style="font-family:Verdana;">h</span></em><span style="font-family:Verdana;">(</span><span style="color:#4F4F4F;font-family:Verdana;white-space:normal;background-color:#FFFFFF;">θ</span><span style="font-family:Verdana;"></span><span style="font-family:Verdana;">)</span><span style="font-family:Verdana;">. Simulation methods can be used for high-dimensional dis</span></span><span style="font-family:Verdana;">tributions, and there are general algorithms which work for a wide variety of models. Markov chain Monte Carlo (MCMC) methods have been important </span><span style="font-family:Verdana;">in making Bayesian inference practical for generic hierarchical models in</span><span style="font-family:Verdana;"> small area estimation. Small area estimation is a method for producing reliable estimates for small areas. Model based Bayesian small area estimation methods are becoming popular for their ability to combine information from several sources as well as taking account of spatial prediction of spatial data. In this study, detailed simulation algorithm is given and the performance of a non-trivial extension of hierarchical Bayesian model for binary data under spatial misalignment is assessed. Both areal level and unit level latent processes were considered in modeling. The process models generated from the predictors were used to construct the basis so as to alleviate the problem of collinearity </span><span style="font-family:Verdana;">between the true predictor variables and the spatial random process. The</span><span style="font-family:Verdana;"> performance of the proposed model was assessed using MCMC simulation studies. The performance was evaluated with respect to root mean square error </span><span style="font-family:Verdana;">(RMSE), Mean absolute error (MAE) and coverage probability of corres</span><span style="font-family:Verdana;">ponding 95% CI of the estimate. The estimates from the proposed model perform better than the direct estimate.</span></span></span></span> </p> <p> <span></span> </p>
基金National Natural Science Foundation of China(No.71371182)
文摘A modified Bayesian reliability assessment method of binomial components was proposed by fusing prior information of similar products.The traditional Bayesian method usually directly used all the prior data,ignoring the differences between them,which might decrease the credibility level of reliability evaluation and result in data submergence.To solve the problem,a revised approach was derived to calculate groups of prior data's quantitative credibility,used for weighted data fusion.Then inheritance factor was introduced to build a mixed beta distribution to illustrate the innovation of new products.However,in many cases,inheritance factor was determined by Chi-square test that could not give out exact result with respect to rare failures.To make the model more precise,Barnard's exact test was suggested being used to calculate the inheritance factor.A numerical example is given to demonstrate that the modified method is successful and rational,while the classical method is too conservative and the traditional Bayesian method is too risky.
基金the National Natural Science Foundation of China(Grant No.61973033)Preliminary Research of Equipment(Grant No.9090102010305)for funding the experiments。
文摘The longitudinal dispersion of the projectile in shooting tests of two-dimensional trajectory corrections fused with fixed canards is extremely large that it sometimes exceeds the correction ability of the correction fuse actuator.The impact point easily deviates from the target,and thus the correction result cannot be readily evaluated.However,the cost of shooting tests is considerably high to conduct many tests for data collection.To address this issue,this study proposes an aiming method for shooting tests based on small sample size.The proposed method uses the Bootstrap method to expand the test data;repeatedly iterates and corrects the position of the simulated theoretical impact points through an improved compatibility test method;and dynamically adjusts the weight of the prior distribution of simulation results based on Kullback-Leibler divergence,which to some extent avoids the real data being"submerged"by the simulation data and achieves the fusion Bayesian estimation of the dispersion center.The experimental results show that when the simulation accuracy is sufficiently high,the proposed method yields a smaller mean-square deviation in estimating the dispersion center and higher shooting accuracy than those of the three comparison methods,which is more conducive to reflecting the effect of the control algorithm and facilitating test personnel to iterate their proposed structures and algorithms.;in addition,this study provides a knowledge base for further comprehensive studies in the future.
