SLTBL模型的Bayes分析

利用M arkov cha in M on te C arlo技术对可分离的下三角双线性模型进行B ayes分析.由于参数联合后验密度的复杂性,我们导出了所有的条件后验分布,以便利用G ibbs抽样器方法抽取后验密度的样本.特别地,由于从模型的方向向量的后验分布中直接抽样是困难的,我们特别设计了一个M etropolis-H astings算法以解决该难题.我们用仿真的方法验证了所建议方法的有效性,并成功应用于分析实际数据.     

识别Rayleigh-Stokes方程源项的分数阶Landweber迭代正则化方法

该文研究具有Riemann-Liouville时间分数阶导数的Rayleigh-Stokes方程未知源识别问题.首先证明这个问题是不适定的,并应用分数阶Landweber正则化方法求解此反问题.基于条件稳定性结果,在先验和后验正则化参数选取规则下,分别给出精确解与正则解之间的误差估计.最后通过数值例子说明此方法求解此类...     

非协调有限元逼近的梯度恢复型后验误差估计（英文）

本文给出二阶椭圆型方程的非协调有限元的梯度恢复型后验误差估计.后验误差估计是在Crouzeix-Raviart非协调有限单元上得到的,并且给出误差的上下界,更进一步可以证明所得的后验误差估计在拟一致网格上是渐近精确的,所以误差估计是可行的、有效的.上界证明过程依赖于"Helmholtz分解",下界证明主要依赖"bubble函数".数值结果验证了理论的正确性.     

中子输运方程误差估计及自适应计算

 本文研究了全离散方法求解二维中子输运方程的有限元自适应算法, 角度变量用离散纵坐标方法展开, 空间变量用间断元方法求解. 基于间断元方法给出了空间离散的残量型后验误差估计. 在后验误差估计的基础上, 我们设计了自适应有限元算法.由残量型后验估计可以给出局部加密网格的自适应算法. 最后, 我们给出了数值算例来验证我们的理论结果.     

MCMC样本确定的后验密度的收敛性

本文讨论用MCMC样本确定的缺失数据的后验分布收敛到精确分布的问题，给出了几种度量形式下的收敛性。并严格证明了经验分布的后验形式的几个极限定理。     

基于GM(1,1)残差模型的科技园区财政收入预测

根据科技园区财政收入预测的需要,在对历史数据分析的基础上,利用灰色预测理论建立了丰台科技园区财政收入预测的GM(1,1)模型,为了提高预测精度,用GM(1,1)残差模型对其修正,得出预测公式.通过预测结果的对比分析和模型的后验差检验,证明预测模型精度较高.模型的应用为科技园区财政收入预测提供了一种科学方法,同时也为园区管理决策提供了依据.     

产品失效率的验前分布稳健性分析

研究Bayes统计分析中利用验前信息的稳健性.首先,用一般方法研究了指数寿命型分布中失效率的验前分布的稳健性.然后利用Gamma分布函数的典型性质,并以平方损失下的后验期望损失为判别准则,讨论了失效率的最优Bayes稳健区间.给出了失效率的最优Bayes稳健点估计.     

没有验前知识时的验前分布

本文指出了 Bayes 假设存在的问题,并建议用下述两种方法处理验前分布问题:一、对满足信息分解条件的未知参数,可用 Bayes 定理分解信息,推导出该参数在没有验前知识时的共轭型验前分布.文中将这种方法用于最常见的过程参数,并用典型事实与数学推导验证其合理性.二、对一般的未知参数,在扬弃 Bayes-Jeffreys 假设的基础上,将随机变量的函数的分布密度的变换法则贯彻到底,并辅以共轭性,来改进 Bayes-Jeffreys 假设.应用新假设的结果与上述方法完全一样,但这个假设的正确性尚待作进一步的理论探讨与实践检验.     

一类抛物方程的降基连续时空有限元方法

本文将连续时空有限元方法和降基方法相结合研究一类抛物方程.该类降基连续时空有限元方法既具有时空高精度的优势,又具有降基法减少自由度的优点.并给出一类抛物方程的降基离散形式,证明数值解的存在唯一性.通过给出输出函数,研究对偶问题,证明降基连续时空有限元解的后验误差估计.     

带有测量误差的Wiener退化模型的客观Bayes分析

本文研究了带有测量误差的Wiener退化模型的客观Bayes分析.对于该退化模型,利用重参数化导出了Jeffreys先验和reference先验,从理论上证明了其中两个reference先验所诱导的后验是正常的,而其它先验的后验均不正常.随机模拟研究了所提Bayes方法相对于最大似然估计的频率表现.最后,将所提方法应用到一个实际退化数据的分析中.     

Partition Weighted Approach For Estimating the Marginal Posterior Density With Applications

The computation of marginal posterior density in Bayesian analysis is essential in that it can provide complete information about parameters of interest. Furthermore, the marginal posterior density can be used for computing Bayes factors, posterior model probabilities, and diagnostic measures. The conditional marginal density estimator (CMDE) is theoretically the best for marginal density estimation but requires the closed-form expression of the conditional posterior density, which is often not available in many applications. We develop the partition weighted marginal density estimator (PWMDE) to realize the CMDE. This unbiased estimator requires only a single Markov chain Monte Carlo output from the joint posterior distribution and the known unnormalized posterior density. The theoretical properties and various applications of the PWMDE are examined in detail. The PWMDE method is also extended to the estimation of conditional posterior densities. We carry out simulation studies to investigate the empirical performance of the PWMDE and further demonstrate the desirable features of the proposed method with two real data sets from a study of dissociative identity disorder patients and a prostate cancer study, respectively. Supplementary materials for this article are available online.     

Bayesian Conditional Density Filtering

We propose a conditional density filtering (C-DF) algorithm for efficient online Bayesian inference. C-DF adapts MCMC sampling to the online setting, sampling from approximations to conditional posterior distributions obtained by propagating surrogate conditional sufficient statistics (a function of data and parameter estimates) as new data arrive. These quantities eliminate the need to store or process the entire dataset simultaneously and offer a number of desirable features. Often, these include a reduction in memory requirements and runtime and improved mixing, along with state-of-the-art parameter inference and prediction. These improvements are demonstrated through several illustrative examples including an application to high dimensional compressed regression. In the cases where dimension of the model parameter does not grow with time, we also establish sufficient conditions under which C-DF samples converge to the target posterior distribution asymptotically as sampling proceeds and more data arrive. Supplementary materials of C-DF are available online.     

基于MCMC的贝叶斯变结构金融时序GARCH模型研究

针对变结构GARCH模型没有解析形式的条件后验分布的问题。借助辅助变量把没有具体解析形式的后验分布转化为一系列完全条件分布,实现了变结构GARCH模型参数的贝叶斯估计。中国外汇市场波动性的实证研究,表明了辅助变量-Gibbs抽样有效的解决了贝叶斯变结构GARCH模型中的高维数值计算问题,并发现其波动持续性是由时间序列的状态转移引起的。     

工序能力Bayes推断

本文从Ｂａｙｅｓ观点研究工序能力，对无信息先验和共轭先验，给出了Ｃｐ的后验分布、条件期望估计和最大后验估计、Ｂａｙｅｓ置信下限和判断工序是否有能力的临界值，适于对相似工序作统计推断。     

三段直线回归模型的贝叶斯分析

对于三段直线回归模型，本文利用贝叶斯观点，给出了转换点和参数的边沿后验分布，参数的条件后验分布和它的点估计     

用于指数可靠性增长模型的一类新的先验分布

该文提出了可用于指数分布产品四种可靠性增长试验方案的一类新的先验分布. 这类先验分布以条件分布形式给出, 它适合可靠性增长试验中的各种情况. 各阶段的条件均值和条件方差的表达式被获得, 先验分布的形式与它们的参数间的关系被讨论. 这些结果有助于与专家意见相结合.本文还给出试验末尾产品可靠性的后验密度, Bayesian估计和Bayesian下限.     

Bayesian analysis of quantile regression for censored dynamic panel data

This paper develops a Bayesian approach to analyzing quantile regression models for censored dynamic panel data. We employ a likelihood-based approach using the asymmetric Laplace error distribution and introduce lagged observed responses into the conditional quantile function. We also deal with the initial conditions problem in dynamic panel data models by introducing correlated random effects into the model. For posterior inference, we propose a Gibbs sampling algorithm based on a location-scale mixture representation of the asymmetric Laplace distribution. It is shown that the mixture representation provides fully tractable conditional posterior densities and considerably simplifies existing estimation procedures for quantile regression models. In addition, we explain how the proposed Gibbs sampler can be utilized for the calculation of marginal likelihood and the modal estimation. Our approach is illustrated with real data on medical expenditures.     

Reversals of signal-posterior monotonicity for any bounded prior

Paul Milgrom [Milgrom, P.R., 1981. Goods news and bad news: representation theorems and applications. The Bell Journal of Economics 12, 380-391] showed that if the strict monotone likelihood ratio property (MLRP) does not hold for a conditional distribution then there exists some non-degenerate prior and pair of signals where the higher-signal posterior does not stochastically dominate the lower-signal posterior. We show that for any non-degenerate prior with bounded support there exists a conditional distribution (satisfying several natural properties) and pair of signals such that the lower signal’s posterior stochastically dominates that of the higher signal. Thus, for every bounded prior, higher signals may represent strictly “worse” news.