Adaptive Bayes sum test for the equality of two nonparametric functions

The statistical difference among massive data sets or signals is of interest to many diverse fields including neurophysiology, imaging, engineering, and other related fields. However, such data often have nonlinear curves, depending on spatial patterns, and have non-white noise that leads to difficulties in testing the significant differences between them. In this paper, we propose an adaptive Bayes sum test that can test the significance between two nonlinear curves by taking into account spatial dependence and by reducing the effect of non-white noise. Our approach is developed by adapting the Bayes sum test statistic by Hart [13 J.D. Hart, Frequentist-Bayes lack-of-fit tests based on Laplace approximations, J. Stat. Theory Practice 3 (2009), pp. 681–704. doi: 10.1080/15598608.2009.10411954[Taylor &; Francis Online] , [Google Scholar]]. The spatial pattern is treated through Fourier transformation. Resampling techniques are employed to construct the empirical distribution of test statistic to reduce the effect of non-white noise. A simulation study suggests that our approach performs better than the alternative method, the adaptive Neyman test by Fan and Lin [9 J. Fan and S. Lin, Test of significance when data are curves, J. Amer. Math. Soc. 93 (1997), pp. 1007–1021.[Web of Science ®] , [Google Scholar]]. The usefulness of our approach is demonstrated with an application in the identification of electronic chips as well as an application to test the change of pattern of precipitations.     

Solving Noisy ICA Using Multivariate Wavelet Denoising with an Application to Noisy Latent Variables Regression

A novel approach to solve the independent component analysis (ICA) model in the presence of noise is proposed. We use wavelets as natural denoising tools to solve the noisy ICA model. To do this, we use a multivariate wavelet denoising algorithm allowing spatial and temporal dependency. We propose also using a statistical approach, named nested design of experiments, to select the parameters such as wavelet family and thresholding type. This technique helps us to select more convenient combination of the parameters. This approach could be extended to many other problems in which one needs to choose parameters between many choices. The performance of the proposed method is illustrated on the simulated data and promising results are obtained. Also, the suggested method applied in latent variables regression in the presence of noise on real data. The good results confirm the ability of multivariate wavelet denoising to solving noisy ICA.     

On the distribution of products of independent beta variates

This paper concerns an inquiry into the problem of generating closed form expressions for the cumulative distribution and probability density functions of products of independent beta variates. Recursive analytical procedures for constructing the equational forms of these functions-from their Mellin inversion integral representations, via the Cauchy residue theorem-are described. A numerical example illustrating details of the construction of a computable form of the distribution function of the product of three independent beta variates is also included.     

Block–Savits Characterization and Star Ordering of Exponential Mixtures

Block and Savits (1980 Block , H. W. , Savits , T. H. ( 1980 ). Laplace transforms for classes of life distributions . Ann. Probab. 8 : 465 – 474 .[Crossref], [Web of Science ®] , [Google Scholar]) established a characterization of life distributions using the Laplace transform. In this article, we remark that one of the necessary conditions to be IFRA distribution is equivalent to the star ordering of exponential mixtures. It leads to the definition of two new classes of life distributions, called LIFR and LIFRA, and their dual classes: LDFR and LDFRA. It occurs that these classes have many useful aging properties and preserve known reliability operations. Properties of the classes are studied and relations with known classes are established.     

国家改革过程中地方政府角色的转型——基于王安石变法时期路级提刑司的研究

北宋熙宁、元丰时期,以王安石为代表的变法派进行了以"富国"、"强兵"为主要目标的著名的改革运动.提点刑狱司这一宋代重要的路级司法、监察机构与此次变法关系密切.在王安石变法时期,改革者对提刑司相关制度进行了一系列改革,如降低提刑官的选任标准、严格考核制度、配备属官、增加武臣提刑等,使之更符合新法的需要.与此同时,改革中最重要的"富国"、"强兵"等职能在提刑司等地方政府身上得到明显增加.从这场著名的变法运动可以看出,提点刑狱司作为宋朝地方统治体系中最重要的"司法、监察官",在北宋中期王安石变法中角色发生明显的转型,司法之外的财政、军事职能得到显著增强.这种"多面手"的角色转型适应了改革的需求,为国家机器的正常运转,改革措施的推行和地方社会的稳定做出了重要贡献.     

中国法律文化如何走向和谐

法律文化作为文化系统中独特而又不可或缺的组成部分,在经历了中国社会的巨大变迁之后．在面临中国法律文化向何处去的困境之时,“和谐”以它深邃的蕴涵再次成为一个备受关注的焦点。笔者在分析中国法律文化现状的基础上,论述了传统法律文化向和谐的法律文化转型的必要性。并努力尝试着对中国法律文化如何走向和谐阐述了自己的看法。     

气体压强对n型a-Si:H薄膜光学性能的影响

用射频等离子增强化学气相沉积(RF-PECVD)制备磷掺杂氢化非晶硅(a-Si:H)薄膜,研究了辉光放电气体压强(20～80Pa)对薄膜折射率、消光系数、光学带隙以及氢含量的影响;用激光拉曼光谱研究了气体压强对a-Si:H薄膜微结构的影响,并与薄膜的光学性能进行了综合讨论。结果表明,随着辉光放电气体压强的增加,a-Si:H薄膜的光学带隙和氢含量都有不同程度的增大,但折射率和消光系数却逐步减小;与此同时,薄膜内非晶网络的短程和中程有序程度逐渐恶化。