基因调控网络的边预测

为构建基因调控网络,提出了一个基于基因表达水平和网络反传递的算法.该算法用网络反传递思想来分析由传统相关性计算方法产生的间接效果,并考虑了调控网络的稀疏性,在模型算法中加入了控制网络稀疏性的l_1范数惩罚项.在大肠杆菌实验数据上测试该算法,这种方法提高了相关性分析对调控网络中边的预测能力,皮尔逊相关系数提高了6.42%,斯皮尔曼相关系数提高了5.92%,互信息提高了9.35%.总的来说,这个模型为修饰大量系统的相关性数据提供一种新思路,可以应用到网络边的预测和推断生物网络的控制动力学中.     

代谢综合征风险、趋势预测和干预模型的构建

结合基因组学数据与生物学背景,利用数学与统计的方法研究代谢综合征的致病机理。首先,利用变异系数筛选出信息含量较高的数据,并且利用变异基因频数统计的方法确定高频变异基因。通过查阅相关文献和数据库可知,大部分高频变异基因都与代谢综合征有关。随后,研究高频变异基因对其他基因的调控情况,并且由此构建出高频变异基因的调控网络以及网络内部的协同和拮抗作用。最后,提出基于调控网络的患病风险预测模型,由此提供预防或治疗方案。     

非概率样本的模型推断

非概率抽样在大数据时代有广阔的应用空间,但其统计推断问题仍有待研究和发展.针对这一问题,提出利用基于模型的推断方法结合配额抽样实现非概率样本的统计推断,其思路是先设定线性回归形式的超总体模型,再利用配额样本观测数据拟合模型估计未知参数,进而利用模型对非观测单元进行预测,案例分析结果显示基于超总体模型的推断方法是解决非概率样本统计推断的有力途径,具有较大的深入研究价值.     

近似Bayes计算前沿研究进展及应用

在大数据和人工智能时代,建立能够有效处理复杂数据的模型和算法,以从数据中获取有用的信息和知识是应用数学、统计学和计算机科学面临的共同难题.为复杂数据建立生成模型并依据这些模型进行分析和推断是解决上述难题的一种有效手段.从一种宏观的视角来看,无论是应用数学中常用的微分方程和动力系统,或是统计学中表现为概率分布的统计模型,还是机器学习领域兴起的生成对抗网络和变分自编码器,都可以看作是一种广义的生成模型.随着所处理的数据规模越来越大,结构越来越复杂,在实际问题中所需要的生成模型也变得也越来越复杂,对这些生成模型的数学结构进行精确地解析刻画变得越来越困难.如何对没有精确解析形式（或其解析形式的精确计算非常困难）的生成模型进行有效的分析和推断,逐渐成为一个十分重要的问题.起源于Bayes统计推断,近似Bayes计算是一种可以免于计算似然函数的统计推断技术,近年来在复杂统计模型和生成模型的分析和推断中发挥了重要作用.该文从经典的近似Bayes计算方法出发,对近似Bayes计算方法的前沿研究进展进行了系统的综述,并对近似Bayes计算方法在复杂数据处理中的应用前景及其和前沿人工智能方法的深刻联系进行了分析和讨论.     

基于高层次结构数据的多水平模型贝叶斯推断及应用

面对具有多层次嵌套结构的数据,构建多水平模型是统计建模的一个重要研究课题。经典的参数估计方法主要采用极大似然估计法(ML),然而当面对高层数量单位小或数据结构不平衡时,极大似然估计在估计精度上存在一定不足;而贝叶斯方法充分应用了有效的先验信息,可以弥补其不足。本文在高层次结构数据多水平模型的研究基础上,探索高层次结构数据的多水平模型贝叶斯推断理论,并以云南省红河州农户收入数据作实证分析,建立了基于县-村-户嵌套结构的农户收入影响因素多水平模型,对比分析模型参数的ML估计、经验贝叶斯(EB-ML)估计和完全贝叶斯估计,从而充分展现了高层次结构数据多水平模型的完全贝叶斯推断方法,在拟合高层数量单位小或数据不平衡时具有的特征和优势。     

多元比例响应数据的贝叶斯推断及其应用

多元比例响应数据具有有界性、归一性以及分量取值稀疏性等特点。本文在多项分布拟似然框架下基于贝叶斯方法研究多元比例数据的估计及其推断问题。通过引入Polya-Gamma分布的潜在变量,得到了易于后验抽样的Gibbs抽样算法。新方法具有估计稳健性、计算量小、推断效率高等特点,且不需要事先对响应数据作近似或变换。大量的数值模拟分析和两个实例分析验证了所提方法的有效性。     

基于灰色理论的线性模型参数理论及应用

线性模型是经典统计学的基本内容,主要应用于随机数据的建模分析。如何对非随机的模糊或灰色等不分明性数据进行模型构建和统计分析。基于灰色系统理论,在一系列关于灰色统计推断理论的研究基础上,将灰色估计和灰色假设检验等方法拓展到线性模型的参数估计和假设检验中。与经典统计分析方法进行对比,为不分明数据的建模分析提供新的方法。     

关于推断分布理论

本文研究Fisher信仰推断理论的推广——推断分布理论,进一步阐述推断分布的含义及公理化条件,介绍寻求优良推断分布的方法,探讨推断分布理论的用途,提出优良推断分布应满足的条件。     

纵向数据下变系数测量误差模型的渐近估计

本文主要研究纵向数据下变系数测量误差模型的估计问题.利用B样条方法逼近模型中未知的变系数,构造关于B样条系数的二次推断函数来处理未知的个体内相关和测量误差,得到变系数的二次推断函数估计,建立估计方法和结果的渐近性质.数值模拟结果显示本文提出的估计方法具有一定的实用价值.     

纵向数据下半参数工具变量模型的经验似然推断

本文研究纵向数据下半参数工具变量模型中回归系数的区间估计问题.首先利用B-样条方法逼近半参数模型中的非参数函数.为了处理内生变量和纵向数据的组内相关性,对模型中回归系数提出了基于工具变量和二次推断函数的有效经验对数似然比统计量,并证明所提出统计量渐近服从标准卡方分布,由此构造回归系数的置信域.     

Modelling non-stationary dynamic gene regulatory processes with the BGM model

Recently, a Bayesian network model for inferring non-stationary regulatory processes from gene expression time series has been proposed. The Bayesian Gaussian Mixture (BGM) Bayesian network model divides the data into disjunct compartments (data subsets) by a free allocation model, and infers network structures, which are kept fixed for all compartments. Fixing the network structure allows for some information sharing among compartments, and each compartment is modelled separately and independently with the Gaussian BGe scoring metric for Bayesian networks. The BGM model can equally be applied to both static (steady-state) and dynamic (time series) gene expression data. However, it is this flexibility that renders its application to time series data suboptimal. To improve the performance of the BGM model on time series data we propose a revised approach in which the free allocation of data points is replaced by a changepoint process so as to take the temporal structure into account. The practical inference follows the Bayesian paradigm and approximately samples the network, the number of compartments and the changepoint locations from the posterior distribution with Markov chain Monte Carlo (MCMC). Our empirical results show that the proposed modification leads to a more efficient inference tool for analysing gene expression time series.     

An improved method for inference of piecewise linear systems by detecting jumps using derivative estimation

Inference of dynamical systems using piecewise linear models is a promising active research area. Most of the investigations in this field have been stimulated by the research in functional genomics. In this article we study the inference problem in piecewise linear systems. We propose first identifying the state transitions by detecting the jumps of the derivative estimates, then finding the guard conditions of the state transitions (thresholds) from the values of the state variables at the state transition time and finally using the conventional gene regulatory network inference methods to infer the regulatory relations. This approach does not require a priori information or assumption on the guard conditions and provides robustness to environmental or measurement noise underlined by the used jump detection filter. We discuss the particular problems where the suggested method can improve the efficiency and demonstrate the results on a comparative basis.     

The numerical implementation of risk

If one is to estimate environmemtal risk based on data or predict risk based on expert opinion, the parameter environmental risk must be defined precisely so that when data becomes available the numerical values of the estimates and/or prediction can be evaluated. Also, the definition must be precise so that it may be successfully used in regulatory and litigation activities. The presentation is a development of a definition which lends to statistical analysis and the inference in addition lends to ease of engineering interpretation. Various implications and useful extensions in measuring numerically for two or more dimensional mixed effects of several toxicants could be developed in further research.     

复杂疾病的分子网络模型研究

复杂疾病是危害人类健康的主要杀手.不同于单基因缺陷性遗传病,复杂疾病的发生发展与多个基因之间、基因与环境之间的相互作用有关,致病机理复杂,其早期诊断及治疗困难是21世纪生物医学研究的重大挑战之一.随着生物知识的不断积累和多层次"组学"数据的井喷式涌现,复杂疾病研究迎来了新的"组学革命",研究模式从以往的只关注某个分子扩展到对分子之间相互形成的生物分子网络的系统分析.作为系统生物学核心概念,生物分子网络系统整合大量生物知识和高通量生物数据,是研究复杂疾病的强有力工具.本文以分子网络为主线,以数学建模为工具来研究复杂疾病,针对复杂疾病关系和复杂疾病的发生发展机制等复杂疾病研究的关键热点问题,分析和集成高通量多层次组学数据,构建并求解生物分子网络的数学模型,在若干复杂疾病相关系统生物学问题中取得有生物学意义的结果.本文提出若干生物网络建模、分析及应用的方法并提供若干应用软件,为从系统层面理解复杂疾病提供重要参考;同时,网络模型在若干实例中的应用得到若干有生物学意义的结论,为揭示复杂疾病机理、推动疾病治疗与预防起到了一定的作用.     

An algebraic theory for statistical information based on the theory of hints

Statistical problems were at the origin of the mathematical theory of evidence, or Dempster–Shafer theory. It was also one of the major concerns of Philippe Smets, starting with his PhD dissertation. This subject is reconsidered here, starting with functional models, describing how data is generated in statistical experiments. Inference is based on these models, using probabilistic assumption-based reasoning. It results in posterior belief functions on the unknown parameters. Formally, the information used in the process of inference can be represented by hints. Basic operations on hints are combination, corresponding to Dempster’s rule, and focussing. This leads to an algebra of hints. Applied to functional models, this introduces an algebraic flavor into statistical inference. It emphasizes the view that in statistical inference different pieces of information have to be combined and then focussed onto the question of interest. This theory covers Bayesian and Fisher type inference as two extreme cases of a more general theory of inference.     

基于MASIM的社会推理与计算系统

随着计算机和信息技术的发展,信息科学技术的研究越来越重视与社会科学的交叉,社会计算已成为国内外计算机及相关领域的最新研究热点.社会计算与社会智能研究的核心之一是社会因果关系推理和行为评判问题.基于认知和心理学理论,介绍一个社会推理计算模型MASIM以及基于MASIM的社会计算系统实例,并以此阐述建立社会推理机制和社会计算系统的若干技术方面.     

Bayesian selection of graphical regulatory models

We define a new class of coloured graphical models, called regulatory graphs. These graphs have their own distinctive formal semantics and can directly represent typical qualitative hypotheses about regulatory processes like those described by various biological mechanisms. They admit an embellishment into classes of probabilistic statistical models and so standard Bayesian methods of model selection can be used to choose promising candidate explanations of regulation. Regulation is modelled by the existence of a deterministic relationship between the longitudinal series of observations labelled by the receiving vertex and the donating one. This class contains longitudinal cluster models as a degenerate graph. Edge colours directly distinguish important features of the mechanism like inhibition and excitation and graphs are often cyclic. With appropriate distributional assumptions, because the regulatory relationships map onto each other through a group structure, it is possible to define a conditional conjugate analysis. This means that even when the model space is huge it is nevertheless feasible, using a Bayesian MAP search, to a discover regulatory network with a high Bayes Factor score. We also show that, like the class of Bayesian Networks, regulatory graphs also admit a formal but distinctive causal algebra. The topology of the graph then represents collections of hypotheses about the predicted effect of controlling the process by tearing out message passers or forcing them to transmit certain signals. We illustrate our methods on a microarray experiment measuring the expression of thousands of genes as a longitudinal series where the scientific interest lies in the circadian regulation of these plants.     

对含未知基因型个体的家系进行单倍型推断的EM方法

单倍型推断在现代连锁分析和关联分析中起着非常关键的作用.目前的单倍型推断方法基本上是根据基因型去推断个体的单倍型,而实际家系中某些个体的基因型经常是有部分缺失或者是完全未知的.本文给出了当家系中含有部分缺失或者完全缺失基因型个体时的单倍型推断的EM方法,并且给出了参数估计的标准差,最后通过模拟研究证实了我们的方法的可行性.     

Bayesian inference for clustered extremes

We consider Bayesian inference for the extremes of dependent stationary series. We discuss the virtues of the Bayesian approach to inference for the extremal index, and for related characteristics of clustering behaviour. We develop an inference procedure based on an automatic declustering scheme, and using simulated data we implement and assess this procedure, making inferences for the extremal index, and for two cluster functionals. We then apply our procedure to a set of real data, specifically a time series of wind-speed measurements, where the clusters correspond to storms. Here the two cluster functionals selected previously correspond to the mean storm length and the mean inter-storm interval. We also consider inference for long-period return levels, advocating the posterior predictive distribution as being most representative of the information required by engineers interested in design level specifications.