基于贝叶斯理论的钢筋混凝土柱受剪承载力计算

现行混凝土结构设计规范中钢筋混凝土柱的受剪承载力公式为半经验半理论计算公式,由于试验数据的有限性和钢筋混凝土材料离散性较大的本质特性,规范建议公式缺乏明确的理论模型。该文以贝叶斯动态信息更新思路,根据主观经验信息选定现行规范中钢筋混凝土柱受剪承载力计算公式作为贝叶斯先验模型,通过已完成试验研究的柱受剪承载力数据,应用贝叶斯方法综合这两类信息进行推断,建立钢筋混凝土柱在反复荷载作用下受剪承载力的概率模型,对未知参数进行估计,修正先验模型并建立后验模型,以达到对先验模型的更新。通过先验模型计算值、后验模型计算值及试验值相互间的对比分析可知:贝叶斯方法继承了先验信息的完备性和大量试验数据的准确性,能够更准确地预测钢筋混凝土柱的受剪承载力。     

Discrete uniform mixtures via posterior means

In this paper, we are concerned with identification of a discrete uniform mixture by the posterior mean. An exact formula for a prior distribution is given. Also some examples featuring negative binomial, negative hypergeometric and beta-Pascal distributions are provided.     

基于贝叶斯信息融合的测量不确定度评定与实时更新

基于贝叶斯信息融合与统计推断原理,建立不确定度动态评定模型,对测量不确定度进行实时更新。引入最大熵原理和爬山搜索优化算法,确定先验分布概率密度函数及样本信息似然函数,结合贝叶斯公式求出后验分布概率密度函数,实现不确定度的优化估计。仿真及实例分析表明,基于贝叶斯和最大熵方法评定及更新的测量不确定度更加接近理论值。     

多元先验信息的融合问题

在多元先验信息条件下，运用Bayes理论讨论问题时，必然会遇到先验信息融合问题，文中提出了几种简化形式，并针对产品失效率的多个先验信息情形，结合实例与熵度量的拟合优度说明了该方法的合理性。     

Information tradeoff

Summary A prior may be noninformative for one parameter at the cost of being informative for another parameter. This leads to the idea of tradeoff priors: priors that give up noninformativity for some parameters to achieve noninformativity for others. We propose a general framework where priors are selected by optimizing a functional with two components. The first component formalizes the requirement that the optimal prior be noninformative for the parameter of interest. The second component is a penalty term that forces the optimizing prior to be close to some target prior. Optimizing such a functional results in a parameterized family of priors from which a specific prior may be selected as the tradeoff prior. An important particular example of such functionals is provided by choosing the first term to be the marginal missing information for the parameter of interest (generalizing Bernardo’s notion of missing information) and the second term to be the relative entropy between the unknown prior and the Jeffreys prior. In this case we find a closed form expression for the tradeoff prior and we make explicit connections with the Berger-Bernardo prior. In particular, we show that under certain conditions, the Berger-Bernardo prior and the Jeffreys prior are special cases of the tradeoff prior. We consider several examples.     

MI-Pack: Increased confidence of metabolite identification in mass spectra by integrating accurate masses and metabolic pathways

Metabolite identification is of central importance to metabolomics as it provides the route to new knowledge. Automated identification of the thousands of peaks detected by high resolution mass spectrometry is currently not possible, largely due to the finite mass accuracy of the spectrometer and the complexity that one peak can be assigned to one or more empirical formula(e) and each formula maps to one or more metabolites. Biological samples are not, however, composed of random metabolite mixtures, but instead comprise of thousands of compounds related through specific chemical transformations. Here we evaluate if prior biological knowledge of these transformations can improve metabolite identification accuracy.Our identification algorithm - which uses metabolite interconnectivity from the KEGG database to putatively identify metabolites by name - is based on mapping an experimentally-derived empirical formula difference for a pair of peaks to a known empirical formula difference between substrate-product pairs derived from KEGG, termed transformation mapping (TM). To maximize identification accuracy, we also developed a novel semi-automated method to calculate a mass error surface associated with experimental peak-pair differences. The TM algorithm with mass error surface has been extensively validated using simulated and experimental datasets by calculating false positive and false negative rates of metabolite identification. Compared to the traditional identification method of database searching accurate masses on a single-peak-by-peak basis, the TM algorithm reduces the false positive rate of identification by > 4-fold, while maintaining a minimal false negative rate. The mass error surface, putative identification of metabolite names, and calculation of false positive and false negative rates collectively advance and improve upon related previous research on this topic [1, 2]. We conclude that inclusion of prior biological knowledge in the form of metabolic pathways provides one route to more accurate metabolite identification.     

评估ATAM计算效率提高程度的新算法

在《与荷载同步变化的时间步自动调整方法》中提出的时间步自动调整方法(apriori time adaptive method,ATAM)是先验式误差评估研究领域的一次有益尝试。在ATAM使用过程中,由于一般情况下难以获得解析解,所以对数值计算程序应用ATAM自动调整时间步长后,相比时间步调整前,无法评估计算效率具体提高了多少。为了解决这个问题,提出了解决方法并对其进行了验证。在此基础上,进一步提出了一种简易评估算法,并推导出评估计算效率提高程度的计算公式。根据此计算公式,不需要采用最小时间步长代入到原数值程序中进行计算,可直接获得计算效率的提高程度,节省了大量计算成本。同时,对简易评估算法进行了验证,结果证实所提算法实用有效。     

改进的模糊阈值图像分割方法

提出了一种自适应的模糊阈值图像分割方法,通过预分割和直方图信息相结合的方法,解决了传统的模糊闽值图像分割法难以自动获取窗宽的困难;并针对模糊闽值图像分割方法不能适用于直方图呈单峰分布的图像的缺陷,提出了一个新的平滑迭代公式。该平滑迭代公式利用像素点的邻域信息使图像增强,再使用自适应的模糊阈值图像分割方法进行分割,可以拓宽模糊阈值图像分割方法的适用范围。实验结果表明,使用该方法的目标分割正确率达97.3％,显示了较高的分割精度和较强的鲁棒性。     

Implicit and explicit prior information in near-infrared spectral imaging: accuracy, quantification and diagnostic value

Near-infrared spectroscopy (NIRS) of tissue provides quantification of absorbers, scattering and luminescent agents in bulk tissue through the use of measurement data and assumptions. Prior knowledge can be critical about things such as (i) the tissue shape and/or structure, (ii) spectral constituents, (iii) limits on parameters, (iv) demographic or biomarker data, and (v) biophysical models of the temporal signal shapes. A general framework of NIRS imaging with prior information is presented, showing that prior information datasets could be incorporated at any step in the NIRS process, with the general workflow being: (i) data acquisition, (ii) pre-processing, (iii) forward model, (iv)?inversion/reconstruction, (v) post-processing, and (vi) interpretation/diagnosis. Most of the development in NIRS has used ad hoc or empirical implementations of prior information such as pre-measured absorber or fluorophore spectra, or tissue shapes as estimated by additional imaging tools. A comprehensive analysis would examine what prior information maximizes the accuracy in recovery and value for medical diagnosis, when implemented at separate stages of the NIRS sequence. Individual applications of prior information can show increases in accuracy or improved ability to estimate biochemical features of tissue, while other approaches may not. Most beneficial inclusion of prior information has been in the inversion/reconstruction process, because it solves the mathematical intractability. However, it is not clear that this is always the most beneficial stage.     

结构施工过程中节段参数的连续识别

通过考虑施工因素的相关性,将随机结构分析的概念引入结构施工过程的节段参数识别中。再考虑施工过程中结构体系不断变化的特点,进行系统重构,将节段参数的相关信息引入识别过程。最后根据最大后验概率的参数估计准则,推导得到了对多个节段参数的均值和方差进行连续识别的递进估计算法。数值算例的结果显示,通过考虑实际施工中的相关信息,本文方法对结构施工过程中的节段参数不仅能进行有效的识别,还具有良好的预测功能,可对施工过程控制进行指导。