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
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
Extreme-mass-ratio inspiral(EMRI)signals pose significant challenges to gravitational wave(GW)data analysis,mainly owing to their highly complex waveforms and high-dimensional parameter space.Given their extended time...Extreme-mass-ratio inspiral(EMRI)signals pose significant challenges to gravitational wave(GW)data analysis,mainly owing to their highly complex waveforms and high-dimensional parameter space.Given their extended timescales of months to years and low signal-to-noise ratios,detecting and analyzing EMRIs with confidence generally relies on long-term observations.Besides the length of data,parameter estimation is particularly challenging due to non-local parameter degeneracies,arising from multiple local maxima,as well as flat regions and ridges inherent in the likelihood function.These factors lead to exceptionally high time complexity for parameter analysis based on traditional matched filtering and random sampling methods.To address these challenges,the present study explores a machine learning approach to Bayesian posterior estimation of EMRI signals,leveraging the recently developed flow matching technique based on ordinary differential equation neural networks.To our knowledge,this is also the first instance of applying continuous normalizing flows to EMRI analysis.Our approach demonstrates an increase in computational efficiency by several orders of magnitude compared to the traditional Markov chain Monte Carlo(MCMC)methods,while preserving the unbiasedness of results.However,we note that the posterior distributions generated by FMPE may exhibit broader uncertainty ranges than those obtained through full Bayesian sampling,requiring subsequent refinement via methods such as MCMC.Notably,when searching from large priors,our model rapidly approaches the true values while MCMC struggles to converge to the global maximum.Our findings highlight that machine learning has the potential to efficiently handle the vast EMRI parameter space of up to seventeen dimensions,offering new perspectives for advancing space-based GW detection and GW astronomy.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
在遥感图像多变化检测领域中,后验概率空间变化向量分析(change vector analysis in posterior probability space,CVAPS)是一种得到广泛使用的变化检测方法。然而,CVAPS利用支持向量机来估计遥感图像像素的后验概率向量,易受到遥感图...在遥感图像多变化检测领域中,后验概率空间变化向量分析(change vector analysis in posterior probability space,CVAPS)是一种得到广泛使用的变化检测方法。然而,CVAPS利用支持向量机来估计遥感图像像素的后验概率向量,易受到遥感图像中同物异谱、异物同谱、混合像元等因素的影响,从而难以准确估计复杂像元的后验概率向量的强度和方向,并影响了其后多元变化检测的精度。因此,文章在CVAPS的框架下,提出了一种采用模糊C均值聚类分解混合像元,并耦合上下文敏感的贝叶斯网络,使用角度阈值进行多变化类型检测的方法。当夹角小于一定阈值时,则判定该像素为该标准变化向量所代表的变化类型。实验结果证明该算法具有较高变化检测性能,取得了高于对比算法的精度。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.
基金supported by the National Key Research and Development Program of China(Grant Nos.2021YFC2201901,2021YFC2203004,2020YFC2200100 and 2021YFC2201903)International Partnership Program of the Chinese Academy of Sciences(Grant No.025GJHZ2023106GC)+4 种基金the financial support from Brazilian agencies Funda??o de AmparoàPesquisa do Estado de S?o Paulo(FAPESP)Funda??o de Amparoà Pesquisa do Estado do Rio Grande do Sul(FAPERGS)Fundacao de Amparoà Pesquisa do Estado do Rio de Janeiro(FAPERJ)Conselho Nacional de Desenvolvimento Científico e Tecnológico(CNPq)Coordenacao de Aperfeicoamento de Pessoal de Nível Superior(CAPES)。
文摘Extreme-mass-ratio inspiral(EMRI)signals pose significant challenges to gravitational wave(GW)data analysis,mainly owing to their highly complex waveforms and high-dimensional parameter space.Given their extended timescales of months to years and low signal-to-noise ratios,detecting and analyzing EMRIs with confidence generally relies on long-term observations.Besides the length of data,parameter estimation is particularly challenging due to non-local parameter degeneracies,arising from multiple local maxima,as well as flat regions and ridges inherent in the likelihood function.These factors lead to exceptionally high time complexity for parameter analysis based on traditional matched filtering and random sampling methods.To address these challenges,the present study explores a machine learning approach to Bayesian posterior estimation of EMRI signals,leveraging the recently developed flow matching technique based on ordinary differential equation neural networks.To our knowledge,this is also the first instance of applying continuous normalizing flows to EMRI analysis.Our approach demonstrates an increase in computational efficiency by several orders of magnitude compared to the traditional Markov chain Monte Carlo(MCMC)methods,while preserving the unbiasedness of results.However,we note that the posterior distributions generated by FMPE may exhibit broader uncertainty ranges than those obtained through full Bayesian sampling,requiring subsequent refinement via methods such as MCMC.Notably,when searching from large priors,our model rapidly approaches the true values while MCMC struggles to converge to the global maximum.Our findings highlight that machine learning has the potential to efficiently handle the vast EMRI parameter space of up to seventeen dimensions,offering new perspectives for advancing space-based GW detection and GW astronomy.
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.
文摘在遥感图像多变化检测领域中,后验概率空间变化向量分析(change vector analysis in posterior probability space,CVAPS)是一种得到广泛使用的变化检测方法。然而,CVAPS利用支持向量机来估计遥感图像像素的后验概率向量,易受到遥感图像中同物异谱、异物同谱、混合像元等因素的影响,从而难以准确估计复杂像元的后验概率向量的强度和方向,并影响了其后多元变化检测的精度。因此,文章在CVAPS的框架下,提出了一种采用模糊C均值聚类分解混合像元,并耦合上下文敏感的贝叶斯网络,使用角度阈值进行多变化类型检测的方法。当夹角小于一定阈值时,则判定该像素为该标准变化向量所代表的变化类型。实验结果证明该算法具有较高变化检测性能,取得了高于对比算法的精度。
