基于Mamdani型模糊推理的震中烈度预测模型

对应用模糊推理进行系统预测进行了深入的研究,建立了以震级和震源深度为输入的基于Mamdani型模糊推理的震中烈度预测模型.并以四川地区震例数据为例,对数据信息提取,模糊规则建立等关键环节进行了详细的介绍,预测结果分析表明推理模型是可行和有效的.     

固定效应部分线性可加面板数据模型的惩罚二次推断估计

具有较强解释力和灵活性的部分线性可加面板数据模型在各学科领域应用广泛.针对个体内存在相关结构的固定效应部分线性可加面板数据模型,本文在结合幂样条函数和最小二乘虚拟变量(LSDV)法的基础上,利用惩罚二次推断函数(PQIF)法对模型进行估计,在一定的正则条件下,证明了参数估计的渐近正态性和非参数估计的收敛性,Monte Carlo数值模拟显示所述估计方法具有良好的有限样本表现,同时,我们还将估计技术应用于实际数据分析中.     

Bayesian statistical process control for Phase I count type data

Count data, most often modeled by a Poisson distribution, are common in statistical process control. They are traditionally monitored by frequentist c or u charts, by cumulative sum and by exponentially weighted moving average charts. These charts all assume that the in‐control true mean is known, a common fiction that is addressed by gathering a large Phase I sample and using it to estimate the mean. “Self‐starting” proposals that ameliorate the need for a large Phase I sample have also appeared. All these methods are frequentist, ie, they allow only retrospective inference during Phase I, and they have no coherent way to incorporate less‐than‐perfect prior information about the in‐control mean. In this paper, we introduce a Bayesian procedure that can incorporate prior information, allow online inference, and should be particularly attractive for short‐run settings where large Phase I calibration exercises are impossible or unreasonable.     

Bayesian planning of step‐stress accelerated degradation tests under various optimality criteria

Step‐stress accelerated degradation testing (SSADT) has become a common approach to predicting lifetime for highly reliable products that are unlikely to fail in a reasonable time under use conditions or even elevated stress conditions. In literature, the planning of SSADT has been widely investigated for stochastic degradation processes, such as Wiener processes and gamma processes. In this paper, we model the optimal SSADT planning problem from a Bayesian perspective and optimize test plans by determining both stress levels and the allocation of inspections. Large‐sample approximation is used to derive the asymptotic Bayesian utility functions under 3 planning criteria. A revisited LED lamp example is presented to illustrate our method. The comparison with optimal plans from previous studies demonstrates the necessity of considering the stress levels and inspection allocations simultaneously.     

Statistical inference for coherent systems with Weibull distributed component lifetimes under complete and incomplete information

Point estimators for the parameters of the component lifetime distribution in coherent systems are evolved assuming to be independently and identically Weibull distributed component lifetimes. We study both complete and incomplete information under continuous monitoring of the essential component lifetimes. First, we prove that the maximum likelihood estimator (MLE) under complete information based on progressively Type‐II censored system lifetimes uniquely exists and we present two approaches to compute the estimates. Furthermore, we consider an ad hoc estimator, a max‐probability plan estimator and the MLE for the parameters under incomplete information. In order to compute the MLEs, we consider a direct maximization of the likelihood and an EM‐algorithm–type approach, respectively. In all cases, we illustrate the results by simulations of the five‐component bridge system and the 10‐component parallel system, respectively.     

Degradation modeling of 2 fatigue‐crack growth characteristics based on inverse Gaussian processes: A case study

Most modern products that are highly reliable are complex in their inner and outer structures. This situation indicates quality characterization by the interaction of multiple performance characteristics, which motivates the utilization of robust reliability models to obtain robust estimates. It is paramount to obtaining substantial information about a product's life cycle; therefore, when multiple performance characteristics are dependent, it is important to find models that address the joint distribution of performance degradation of such. In this paper, a reliability model for products with 2 fatigue‐crack growth characteristics related to 2 degradation processes is developed. The proposed model considers the dependence among degradation processes by using copula functions considering the marginal degradation processes as inverse Gaussian processes. The statistical inference is performed by using a Bayesian approach to estimate the parameters of the joint bivariate model. A time‐scale transformation is considered to assure monotone paths of the degradation trajectories. The comparison results of the reliability analysis, under both dependent and independent assumptions, are reported with the implementation of the proposed modeling in a case study, which consists of the crack propagation data of 2 terminals of an electronic device.     

Research on Flood Loss Distribution and Catastrophe Bond Pricing Based on Bayesian Inference

Taking flood catastrophe risk in China as the research background, aiming at the characteristics of flood loss ``low frequency and high loss', Bayesian inference method is used to fit the loss distribution, and Bayesian inference is used to obtain the loss frequency distribution and loss quota distribution of flood in China. On this basis, Monte Carlo simulation method is used to calculate the probability distribution of annual flood loss in China under different trigger conditions, and then CAPM is used to study the pricing of flood catastrophe bonds in China. It is concluded that under different trigger conditions, as the trigger value increases gradually, the corresponding trigger is triggered. Comparing the three types of bonds, it can be found that the price of bonds decreases with the decrease of principal guarantee ratio and the increase of principal loss ratio, that is, the investment risk is directly proportional to the return, which provides reference for issuing flood catastrophe bonds in China.     

基因调控网络推断研究进展

随着高通量技术的发展,越来越多的生物医学组学数据亟需处理与分析,基于运筹优化的生物信息学方法是有效解析高维生物医学数据的重要途径之一。综述了近年来在基因调控网络推断方面的研究进展。针对不同类型的转录组学数据和研究目的,分别建立了相应的基因调控网络推断方法,主要包括先验基因调控网络数据库的建立、基于条件互信息的因果网络推断、基于微分方程的动态基因调控网络推断、转录调控和转录后调控协同作用的网络推断以及基因调控网络活性评价等,并展望了基因调控网络推断的重要研究方向。     

玉米叶片重金属铅含量的SVD-ANFIS高光谱预测模型

重金属污染农作物后可通过食物链进入人体从而严重危害身体健康。如何快速准确地监测农作物中重金属含量已成为当今生态与粮食安全等领域的重要研究内容。常规的生化监测方法存在操作繁琐、过程长、具有破坏性等缺点,而高光谱遥感具有光谱分辨率高、信息量大、生化反演能力强、方便快捷、对监测对象无损伤等优势,因此利用高光谱遥感技术监测农作物中重金属含量已成为遥感领域的热点研究之一。以不同浓度Pb(NO₃)₂溶液胁迫下盆栽玉米植株为研究对象,基于不同铅离子(Pb2+)胁迫梯度下玉米叶片的反射光谱及其中Pb2+含量的测定数据,结合奇异值分解(SVD)理论和自适应模糊神经网络推理系统(ANFIS)结构,建立了一种Pb2+含量预测的SVD-ANFIS模型。首先对各胁迫梯度下玉米的老叶(O)、中叶(M)、新叶(N)三种叶片的反射光谱数据进行SVD处理,获取原始光谱信息的奇异值;然后选择O,M和N叶片对应的奇异值来寻求ANFIS结构的最佳输入组合,最终选定O-M（双输入）组合作为ANFIS结构的输入量,通过训练和学习获得最优模糊规则库后,ANFIS结构的输出量即为叶片中Pb2+含量,从而实现了SVD-ANFIS模型的预测性能。研究结果表明,该模型的输出误差值较小,精度较高,在模糊训练过程中隶属函数选为钟型函数时预测效果最佳。利用多参数的反向传播(BP)神经网络预测模型对SVD-ANFIS模型的预测优越性进行验证时,得到BP模型和SVD-ANFIS模型的决定系数(R2)分别为0.977 6和0.988 7,均方根误差(RMSE)分别为2.455 9和0.601 3,可见SVD-ANFIS模型的拟合度更高,预测效果更好。同时选取不同年份的Pb污染玉米叶片等光谱数据对SVD-ANFIS模型进行可行性检验,其R2和RMSE分别为0.986 4和0.887 4,说明SVD-ANFIS模型能较好的用于玉米叶片中Pb2+含量预测且具有较高的鲁棒性,可作为预测玉米叶片中重金属含量的一种方法。     

Bayes in the sky: Bayesian inference and model selection in cosmology

The application of Bayesian methods in cosmology and astrophysics has flourished over the past decade, spurred by data sets of increasing size and complexity. In many respects, Bayesian methods have proven to be vastly superior to more traditional statistical tools, offering the advantage of higher efficiency and of a consistent conceptual basis for dealing with the problem of induction in the presence of uncertainty. This trend is likely to continue in the future, when the way we collect, manipulate and analyse observations and compare them with theoretical models will assume an even more central role in cosmology.

This review is an introduction to Bayesian methods in cosmology and astrophysics and recent results in the field. I first present Bayesian probability theory and its conceptual underpinnings, Bayes' Theorem and the role of priors. I discuss the problem of parameter inference and its general solution, along with numerical techniques such as Monte Carlo Markov Chain methods. I then review the theory and application of Bayesian model comparison, discussing the notions of Bayesian evidence and effective model complexity, and how to compute and interpret those quantities. Recent developments in cosmological parameter extraction and Bayesian cosmological model building are summarised, highlighting the challenges that lie ahead.