We propose to determine the underlying causal structure of the elements of happiness from a set of empirically obtained data based on Bayesian. We consider the proposal to study happiness as a multidimensional constru...We propose to determine the underlying causal structure of the elements of happiness from a set of empirically obtained data based on Bayesian. We consider the proposal to study happiness as a multidimensional construct which converges four dimensions with two different Bayesian techniques, in the first we use the Bonferroni correction to estimate the mean multiple comparisons, on this basis it is that we use the function t and a z-test, in both cases the results do not vary, so it is decided to present only those shown by the t test. In the Bayesian Multiple Linear Regression, we prove that happiness can be explained through three dimensions. The technical numerical used is MCMC, of four samples. The results show that the sample has not atypical behavior too and that suitable modifications can be described through a test. Another interesting result obtained is that the predictive probability for the case of sense positive of life and personal fulfillment dimensions exhibit a non-uniform variation.展开更多
Network attack graphs are originally used to evaluate what the worst security state is when a concerned net-work is under attack. Combined with intrusion evidence such like IDS alerts, attack graphs can be further use...Network attack graphs are originally used to evaluate what the worst security state is when a concerned net-work is under attack. Combined with intrusion evidence such like IDS alerts, attack graphs can be further used to perform security state posterior inference (i.e. inference based on observation experience). In this area, Bayesian network is an ideal mathematic tool, however it can not be directly applied for the following three reasons: 1) in a network attack graph, there may exist directed cycles which are never permitted in a Bayesian network, 2) there may exist temporal partial ordering relations among intrusion evidence that can-not be easily modeled in a Bayesian network, and 3) just one Bayesian network cannot be used to infer both the current and the future security state of a network. In this work, we improve an approximate Bayesian posterior inference algorithm–the likelihood-weighting algorithm to resolve the above obstacles. We give out all the pseudocodes of the algorithm and use several examples to demonstrate its benefit. Based on this, we further propose a network security assessment and enhancement method along with a small network scenario to exemplify its usage.展开更多
The topic of this article is one-sided hypothesis testing for disparity, i.e., the mean of one group is larger than that of another when there is uncertainty as to which group a datum is drawn. For each datum, the unc...The topic of this article is one-sided hypothesis testing for disparity, i.e., the mean of one group is larger than that of another when there is uncertainty as to which group a datum is drawn. For each datum, the uncertainty is captured with a given discrete probability distribution over the groups. Such situations arise, for example, in the use of Bayesian imputation methods to assess race and ethnicity disparities with certain insurance, health, and financial data. A widely used method to implement this assessment is the Bayesian Improved Surname Geocoding (BISG) method which assigns a discrete probability over six race/ethnicity groups to an individual given the individual’s surname and address location. Using a Bayesian framework and Markov Chain Monte Carlo sampling from the joint posterior distribution of the group means, the probability of a disparity hypothesis is estimated. Four methods are developed and compared with an illustrative data set. Three of these methods are implemented in an R-code and one method in WinBUGS. These methods are programed for any number of groups between two and six inclusive. All the codes are provided in the appendices.展开更多
A complex mechatronics system Bayesian plan of demonstration test is studied based on the mixed beta distribution. During product design and improvement various information is appropriately considered by introducing i...A complex mechatronics system Bayesian plan of demonstration test is studied based on the mixed beta distribution. During product design and improvement various information is appropriately considered by introducing inheritance factor, moreover, the inheritance factor is thought as a random variable, and the Bayesian decision of the qualification test plan is obtained, and the correctness of a Bayesian model presented is verified. The results show that the quantity of the test is too conservative according to classical methods under small binomial samples. Although traditional Bayesian analysis can consider test information of related or similar products, it ignores differences between such products. The method has solved the above problem, furthermore, considering the requirement in many practical projects, the differences among this method, the classical method and Bayesian with beta distribution are compared according to the plan of reliability acceptance test.展开更多
Aiming at that the successive test data set of the strapdown inertial measurement unit is always small,a Bayesian method is used to study its statistical characteristics.Its prior and posterior distributions are set u...Aiming at that the successive test data set of the strapdown inertial measurement unit is always small,a Bayesian method is used to study its statistical characteristics.Its prior and posterior distributions are set up by the method and the pretest,sample and population information.Some statistical inferences can be made based on the posterior distribution.It can reduce the statistical analysis error in the case of small sample set.展开更多
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 deve...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.展开更多
The risk decision of small multi-frequency investment mode of agricultural products is studied based on Bayesian method. This method can take advantage of new market information reasonably,analyze the posterior risk a...The risk decision of small multi-frequency investment mode of agricultural products is studied based on Bayesian method. This method can take advantage of new market information reasonably,analyze the posterior risk and quantify the decision risk. It provides a scientific way for the risk decision of agricultural enterprises and is advantageous to enhancing the benefit of project.展开更多
This paper considers the Bayes and hierarchical Bayes approaches for analyzing clinical data on response times with available values for one or more concomitant variables. Response times are assumed to follow simple e...This paper considers the Bayes and hierarchical Bayes approaches for analyzing clinical data on response times with available values for one or more concomitant variables. Response times are assumed to follow simple exponential distributions, with a different parameter for each patient. The analyses are carried out in case of progressive censoring assuming squared error loss function and gamma distribution as priors and hyperpriors. The possibilities of using the methodology in more general situations like dose- response modeling have also been explored. Bayesian estimators derived in this paper are applied to lung cancer data set with concomitant variables.展开更多
Testing the equality of means of two normally distributed random variables when their variances are unequal is known in the statistical literature as the “Behrens-Fisher problem”. It is well-known that the posterior...Testing the equality of means of two normally distributed random variables when their variances are unequal is known in the statistical literature as the “Behrens-Fisher problem”. It is well-known that the posterior distributions of the parameters of interest are the primitive of Bayesian statistical inference. For routine implementation of statistical procedures based on posterior distributions, simple and efficient approaches are required. Since the computation of the exact posterior distribution of the Behrens-Fisher problem is obtained using numerical integration, several approximations are discussed and compared. Tests and Bayesian Highest-Posterior Density (H.P.D) intervals based upon these approximations are discussed. We extend the proposed approximations to test of parallelism in simple linear regression models.展开更多
Decision-theoretic interval estimation requires the use of loss functions that, typically, take into account the size and the coverage of the sets. We here consider the class of monotone loss functions that, under qui...Decision-theoretic interval estimation requires the use of loss functions that, typically, take into account the size and the coverage of the sets. We here consider the class of monotone loss functions that, under quite general conditions, guarantee Bayesian optimality of highest posterior probability sets. We focus on three specific families of monotone losses, namely the linear, the exponential and the rational losses whose difference consists in the way the sizes of the sets are penalized. Within the standard yet important set-up of a normal model we propose: 1) an optimality analysis, to compare the solutions yielded by the alternative classes of losses;2) a regret analysis, to evaluate the additional loss of standard non-optimal intervals of fixed credibility. The article uses an application to a clinical trial as an illustrative example.展开更多
This paper deals with Bayesian inference and prediction problems of the Burr type XII distribution based on progressive first failure censored data. We consider the Bayesian inference under a squared error loss functi...This paper deals with Bayesian inference and prediction problems of the Burr type XII distribution based on progressive first failure censored data. We consider the Bayesian inference under a squared error loss function. We propose to apply Gibbs sampling procedure to draw Markov Chain Monte Carlo (MCMC) samples, and they have in turn, been used to compute the Bayes estimates with the help of importance sampling technique. We have performed a simulation study in order to compare the proposed Bayes estimators with the maximum likelihood estimators. We further consider two sample Bayes prediction to predicting future order statistics and upper record values from Burr type XII distribution based on progressive first failure censored data. The predictive densities are obtained and used to determine prediction intervals for unobserved order statistics and upper record values. A real life data set is used to illustrate the results derived.展开更多
文章提出基于贝叶斯推理的结构非线性概率模型参数估计方法,结合非线性参数的后验概率分布估计结果,实现结构在动力荷载作用下的失效概率预测。利用结构实测加速度响应作为输入,构建贝叶斯推理的似然函数,采用过渡马尔可夫蒙特卡洛(tran...文章提出基于贝叶斯推理的结构非线性概率模型参数估计方法,结合非线性参数的后验概率分布估计结果,实现结构在动力荷载作用下的失效概率预测。利用结构实测加速度响应作为输入,构建贝叶斯推理的似然函数,采用过渡马尔可夫蒙特卡洛(transitional Markov chain Monte Carlo,TMCMC)算法估计非线性概率模型参数的后验概率分布。当模型参数的后验概率分布被计算之后,利用更新后的参数后验概率分布作为输入,通过随机抽样算法预测结构在动力荷载作用下的失效概率。为验证方法的可行性,对地震荷载作用下的5层钢框架结构进行数值模拟,通过钢框架结构的缩尺振动台试验进一步验证该方法的有效性。研究结果表明:该方法能够准确实现非线性模型参数的后验概率密度计算,能够对结构在地震荷载下的失效概率进行有效预测。展开更多
文摘We propose to determine the underlying causal structure of the elements of happiness from a set of empirically obtained data based on Bayesian. We consider the proposal to study happiness as a multidimensional construct which converges four dimensions with two different Bayesian techniques, in the first we use the Bonferroni correction to estimate the mean multiple comparisons, on this basis it is that we use the function t and a z-test, in both cases the results do not vary, so it is decided to present only those shown by the t test. In the Bayesian Multiple Linear Regression, we prove that happiness can be explained through three dimensions. The technical numerical used is MCMC, of four samples. The results show that the sample has not atypical behavior too and that suitable modifications can be described through a test. Another interesting result obtained is that the predictive probability for the case of sense positive of life and personal fulfillment dimensions exhibit a non-uniform variation.
文摘Network attack graphs are originally used to evaluate what the worst security state is when a concerned net-work is under attack. Combined with intrusion evidence such like IDS alerts, attack graphs can be further used to perform security state posterior inference (i.e. inference based on observation experience). In this area, Bayesian network is an ideal mathematic tool, however it can not be directly applied for the following three reasons: 1) in a network attack graph, there may exist directed cycles which are never permitted in a Bayesian network, 2) there may exist temporal partial ordering relations among intrusion evidence that can-not be easily modeled in a Bayesian network, and 3) just one Bayesian network cannot be used to infer both the current and the future security state of a network. In this work, we improve an approximate Bayesian posterior inference algorithm–the likelihood-weighting algorithm to resolve the above obstacles. We give out all the pseudocodes of the algorithm and use several examples to demonstrate its benefit. Based on this, we further propose a network security assessment and enhancement method along with a small network scenario to exemplify its usage.
文摘The topic of this article is one-sided hypothesis testing for disparity, i.e., the mean of one group is larger than that of another when there is uncertainty as to which group a datum is drawn. For each datum, the uncertainty is captured with a given discrete probability distribution over the groups. Such situations arise, for example, in the use of Bayesian imputation methods to assess race and ethnicity disparities with certain insurance, health, and financial data. A widely used method to implement this assessment is the Bayesian Improved Surname Geocoding (BISG) method which assigns a discrete probability over six race/ethnicity groups to an individual given the individual’s surname and address location. Using a Bayesian framework and Markov Chain Monte Carlo sampling from the joint posterior distribution of the group means, the probability of a disparity hypothesis is estimated. Four methods are developed and compared with an illustrative data set. Three of these methods are implemented in an R-code and one method in WinBUGS. These methods are programed for any number of groups between two and six inclusive. All the codes are provided in the appendices.
基金National Advanced Research Project of China(No.51319030302)National Advanced Research Foundation of China(No.9140A 19030506KG0166)
文摘A complex mechatronics system Bayesian plan of demonstration test is studied based on the mixed beta distribution. During product design and improvement various information is appropriately considered by introducing inheritance factor, moreover, the inheritance factor is thought as a random variable, and the Bayesian decision of the qualification test plan is obtained, and the correctness of a Bayesian model presented is verified. The results show that the quantity of the test is too conservative according to classical methods under small binomial samples. Although traditional Bayesian analysis can consider test information of related or similar products, it ignores differences between such products. The method has solved the above problem, furthermore, considering the requirement in many practical projects, the differences among this method, the classical method and Bayesian with beta distribution are compared according to the plan of reliability acceptance test.
文摘Aiming at that the successive test data set of the strapdown inertial measurement unit is always small,a Bayesian method is used to study its statistical characteristics.Its prior and posterior distributions are set up by the method and the pretest,sample and population information.Some statistical inferences can be made based on the posterior distribution.It can reduce the statistical analysis error in the case of small sample set.
基金The National Natural Science Foundation of China (Nos.50778180 and 50808179)
文摘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.
基金Supported by Intelligent Logistics System of Beijing Key Laboratory(BZ0211)039 Specialty Construction-Professional Group Construction at Municipal Level(PXM2015-014214-000039)
文摘The risk decision of small multi-frequency investment mode of agricultural products is studied based on Bayesian method. This method can take advantage of new market information reasonably,analyze the posterior risk and quantify the decision risk. It provides a scientific way for the risk decision of agricultural enterprises and is advantageous to enhancing the benefit of project.
文摘This paper considers the Bayes and hierarchical Bayes approaches for analyzing clinical data on response times with available values for one or more concomitant variables. Response times are assumed to follow simple exponential distributions, with a different parameter for each patient. The analyses are carried out in case of progressive censoring assuming squared error loss function and gamma distribution as priors and hyperpriors. The possibilities of using the methodology in more general situations like dose- response modeling have also been explored. Bayesian estimators derived in this paper are applied to lung cancer data set with concomitant variables.
文摘Testing the equality of means of two normally distributed random variables when their variances are unequal is known in the statistical literature as the “Behrens-Fisher problem”. It is well-known that the posterior distributions of the parameters of interest are the primitive of Bayesian statistical inference. For routine implementation of statistical procedures based on posterior distributions, simple and efficient approaches are required. Since the computation of the exact posterior distribution of the Behrens-Fisher problem is obtained using numerical integration, several approximations are discussed and compared. Tests and Bayesian Highest-Posterior Density (H.P.D) intervals based upon these approximations are discussed. We extend the proposed approximations to test of parallelism in simple linear regression models.
文摘Decision-theoretic interval estimation requires the use of loss functions that, typically, take into account the size and the coverage of the sets. We here consider the class of monotone loss functions that, under quite general conditions, guarantee Bayesian optimality of highest posterior probability sets. We focus on three specific families of monotone losses, namely the linear, the exponential and the rational losses whose difference consists in the way the sizes of the sets are penalized. Within the standard yet important set-up of a normal model we propose: 1) an optimality analysis, to compare the solutions yielded by the alternative classes of losses;2) a regret analysis, to evaluate the additional loss of standard non-optimal intervals of fixed credibility. The article uses an application to a clinical trial as an illustrative example.
文摘This paper deals with Bayesian inference and prediction problems of the Burr type XII distribution based on progressive first failure censored data. We consider the Bayesian inference under a squared error loss function. We propose to apply Gibbs sampling procedure to draw Markov Chain Monte Carlo (MCMC) samples, and they have in turn, been used to compute the Bayes estimates with the help of importance sampling technique. We have performed a simulation study in order to compare the proposed Bayes estimators with the maximum likelihood estimators. We further consider two sample Bayes prediction to predicting future order statistics and upper record values from Burr type XII distribution based on progressive first failure censored data. The predictive densities are obtained and used to determine prediction intervals for unobserved order statistics and upper record values. A real life data set is used to illustrate the results derived.
文摘文章提出基于贝叶斯推理的结构非线性概率模型参数估计方法,结合非线性参数的后验概率分布估计结果,实现结构在动力荷载作用下的失效概率预测。利用结构实测加速度响应作为输入,构建贝叶斯推理的似然函数,采用过渡马尔可夫蒙特卡洛(transitional Markov chain Monte Carlo,TMCMC)算法估计非线性概率模型参数的后验概率分布。当模型参数的后验概率分布被计算之后,利用更新后的参数后验概率分布作为输入,通过随机抽样算法预测结构在动力荷载作用下的失效概率。为验证方法的可行性,对地震荷载作用下的5层钢框架结构进行数值模拟,通过钢框架结构的缩尺振动台试验进一步验证该方法的有效性。研究结果表明:该方法能够准确实现非线性模型参数的后验概率密度计算,能够对结构在地震荷载下的失效概率进行有效预测。
