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贝叶斯统计是当今世界的两大主要统计学派之一,本文系统地论述了贝叶斯统计理论的起源、基本观点及其与频率统计学派的差异,并阐述了贝叶斯统计推断的理论研究与实践应用现状。 相似文献
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贝叶斯统计是当今世界的两大主要统计学派之一,本文系统地论述了贝叶斯统计理论的起源,基本观点及其与频率统计学派的差异,并阐述了贝叶斯统计推断的理论研究与实践应用现状。 相似文献
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因子分析模型的贝叶斯推断是贝叶斯多元统计推断理论的重要组成部分。本文通过分析因子分析模型的统计结构,构造了模型参数的混合先验分布;利用贝叶斯定理,结合模型样本似然函数和参数的先验分布推导了参数的后验分布;证明了因子载荷阵的条件后验分布为矩阵t分布,协方差阵的条件后验分布为逆Wishart分布。实证研究结果表明:由于参数先验分布的作用,贝叶斯因子分析的结论与传统的因子分析之间存在显著性的差异。 相似文献
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文章利用贝叶斯方法研究分位数回归的组间和组内双变量选择问题。基于偏态拉普拉斯分布和贝叶斯统计推断方法,结合组间和组内系数的Spike-and-Slab先验分布,提出了分位数回归的贝叶斯双层变量选择方法,并给出易于实施的Gibbs后验抽样算法。通过大量数值模拟和实证分析验证了所提变量选择方法的有效性。 相似文献
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一、“九五”期间统计学发展回顾“九五”期间 ,国内外统计学研究主要围绕统计理论的完善与发展、统计方法的应用、统计学与信息技术的结合等领域来进行。随着统计理论的不断发展 ,统计学与概率论及数学其他分支的交叉联系不断加强 ,统计学的内容体系越来越丰富。在一些前沿性领域 ,如探索性数据分析、计算机模拟、贝叶斯推断及应用、生存分析等方面的研究正在不断深入。国际统计标准分类、SNA的完善等诸多方面的研究也已取得重大成果。具体表现为 :1 在统计理论的完善与发展方面 ,有关统计推断、随机过程、多元分析、生存分析、时间序列… 相似文献
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为了尝试使用贝叶斯方法研究比例数据的分位数回归统计推断问题,首先基于Tobit模型给出了分位数回归建模方法,然后通过选取合适的先验分布得到了贝叶斯层次模型,进而给出了各参数的后验分布并用于Gibbs抽样。数值模拟分析验证了所提出的贝叶斯推断方法对于比例数据分析的有效性。最后,将贝叶斯方法应用于美国加州海洛因吸毒数据,在不同的分位数水平下揭示了吸毒频率的影响因素。 相似文献
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收入分配不公平测度的统计推断一直是收入分配研究的一个重点。文章首先回顾和评述了国内外学者在收入分配测度统计推断方面的成果,选用泰尔指数作为收入分配不公平的测量指标,介绍了泰尔指数统计推断的渐近分布方法,提出了适用于小样本数据的自助方法和置换检验方法。在此基础上,对我国主要年份的真实收入泰尔指数进行了统计推断。 相似文献
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Efthymios G. Tsionas 《统计学通讯:理论与方法》2013,42(3):388-407
This study takes up inference in linear models with generalized error and generalized t distributions. For the generalized error distribution, two computational algorithms are proposed. The first is based on indirect Bayesian inference using an approximating finite scale mixture of normal distributions. The second is based on Gibbs sampling. The Gibbs sampler involves only drawing random numbers from standard distributions. This is important because previously the impression has been that an exact analysis of the generalized error regression model using Gibbs sampling is not possible. Next, we describe computational Bayesian inference for linear models with generalized t disturbances based on Gibbs sampling, and exploiting the fact that the model is a mixture of generalized error distributions with inverse generalized gamma distributions for the scale parameter. The linear model with this specification has also been thought not to be amenable to exact Bayesian analysis. All computational methods are applied to actual data involving the exchange rates of the British pound, the French franc, and the German mark relative to the U.S. dollar. 相似文献
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Muhammad Faisal Andreas Futschik Ijaz Hussain Mitwali Abd-el.Moemen 《Journal of applied statistics》2016,43(12):2191-2202
Bayesian statistical inference relies on the posterior distribution. Depending on the model, the posterior can be more or less difficult to derive. In recent years, there has been a lot of interest in complex settings where the likelihood is analytically intractable. In such situations, approximate Bayesian computation (ABC) provides an attractive way of carrying out Bayesian inference. For obtaining reliable posterior estimates however, it is important to keep the approximation errors small in ABC. The choice of an appropriate set of summary statistics plays a crucial role in this effort. Here, we report the development of a new algorithm that is based on least angle regression for choosing summary statistics. In two population genetic examples, the performance of the new algorithm is better than a previously proposed approach that uses partial least squares. 相似文献
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James H. Matis 《The American statistician》2013,67(2):84-85
Even to the initiated, statistical calculations based on Bayes's Theorem can be daunting because of the numerical integrations required in all but the simplest applications. Moreover, from a teaching perspective, introductions to Bayesian statistics—if they are given at all—are circumscribed by these apparent calculational difficulties. Here we offer a straightforward sampling-resampling perspective on Bayesian inference, which has both pedagogic appeal and suggests easily implemented calculation strategies. 相似文献
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《Journal of Statistical Computation and Simulation》2012,82(1-2):25-36
The sensitivity of-a Bayesian inference to prior assumptions is examined by Monte Carlo simulation for the beta-binomial conjugate family of distributions. Results for the effect on a Bayesian probability interval of the binomial parameter indicate that the Bayesian inference is for the most part quite sensitive to misspecification of the prior distribution. The magnitude of the sensitivity depends primarily on the difference of assigned means and variances from the respective means and variances of the actually-sampled prior distributions. The effect of a disparity in form between the assigned prior and actually-sampled distributions was less important for the cases tested. 相似文献
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This paper describes the Bayesian inference and prediction of the two-parameter Weibull distribution when the data are Type-II censored data. The aim of this paper is twofold. First we consider the Bayesian inference of the unknown parameters under different loss functions. The Bayes estimates cannot be obtained in closed form. We use Gibbs sampling procedure to draw Markov Chain Monte Carlo (MCMC) samples and it has been used to compute the Bayes estimates and also to construct symmetric credible intervals. Further we consider the Bayes prediction of the future order statistics based on the observed sample. We consider the posterior predictive density of the future observations and also construct a predictive interval with a given coverage probability. Monte Carlo simulations are performed to compare different methods and one data analysis is performed for illustration purposes. 相似文献
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Approximate Bayesian inference on the basis of summary statistics is well-suited to complex problems for which the likelihood
is either mathematically or computationally intractable. However the methods that use rejection suffer from the curse of dimensionality
when the number of summary statistics is increased. Here we propose a machine-learning approach to the estimation of the posterior
density by introducing two innovations. The new method fits a nonlinear conditional heteroscedastic regression of the parameter
on the summary statistics, and then adaptively improves estimation using importance sampling. The new algorithm is compared
to the state-of-the-art approximate Bayesian methods, and achieves considerable reduction of the computational burden in two
examples of inference in statistical genetics and in a queueing model. 相似文献
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Mathias Raschke 《统计学通讯:理论与方法》2017,46(15):7621-7629
The predictive distribution is a mixture of the original distribution model and is used for predicting a future observation. Therein, the mixing distribution is the posterior distribution of the distribution parameters in the Bayesian inference. The mixture can also be computed for the frequentist inference because the Bayesian posterior distribution has the same meaning as a frequentist confidence interval. I present arguments against the concept of predictive distribution. Examples illustrate these. The most important argument is that the predictive distribution can depend on the parameterization. An improvement of the theory of the predictive distribution is recommended. 相似文献
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《统计学通讯:理论与方法》2013,42(4):747-756
The paper considers Bayesian analysis of the generalized four-parameter gamma distribution. Estimation of parameters using classical techniques is associated with important technical problems while Bayesian methods are not currently available for such distributions. Posterior inference is performed using numerical methods organized around Gibbs sampling. Predictive distributions and reliability can be estimated routinely using the proposed methods. 相似文献
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Per Gösta Andersson 《统计学通讯:理论与方法》2020,49(22):5493-5503
AbstractThe Poisson distribution is here used to illustrate Bayesian inference concepts with the ultimate goal to construct credible intervals for a mean. The evaluation of the resulting intervals is in terms of “mismatched” priors and posteriors. The discussion is in the form of an imaginary dialog between a teacher and a student, who have met earlier, discussing and evaluating the Wald and score confidence intervals, as well as confidence intervals based on transformation and bootstrap techniques. From the perspective of the student the learning process is akin to a real research situation. The student is supposed to have studied mathematical statistics for at least two semesters. 相似文献
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Christina Schneider 《统计学通讯:理论与方法》2013,42(10):3841-3850
In his articles (1966-1968) concerning statistical inference based on lower and upper probabilities, Dempster refers to the connection between Fisher's fiducial argument and his own ideas of statistical inference. Dempster's main concern however focuses on the “Bayesian” aspects of his theory and not on an elaboration of the relation between Fisher's and his ideas. This article attempts to work out the connection between those two approaches and focuses primarily on the question, whether Dempster's combination rule, his upper and lower probabilty based on sufficient statistics and inference based on sufficient statistics in Fisher's sense are consistent. To be adequate to Fisher's reasoning, we deal with absolutely continuous, one parametric families of distributions.This is certainly not the usual assumption in context with Dempster's theory and implies a normative but straightforward definition concerning the underlying conditional distribution; this definition however is done in Dempster's spirit as can be seen from his articles, (1966, 1968,a,b). Under those assumptions it can be shown that - similar to Lindley's results concerning consistency in fiducial reasoning (1958) - the combination rule, Dempster's procedure based on sufficient statistics and fiducial inference by sufficient statistics agree iff the parametric family under consideration can be transformed to location parameter form. 相似文献