广义变系数模型的Bayesian B样条估计

提出了广义变系数模型函数系数的一种新的估计方法．我们用B样条函数逼近函数系数,不具体选择节点的个数,而是节点个数取均匀的无信息先验,样条函数系数取正态先验,用Bayesian模型平均的方法估计各个函数系数．这种估计方法一个主要特点是允许各个函数系数所需节点个数的后验分布不同,因此允许不同函数系数使用不同的光滑参数．另外,本文还给出了Bayesian B样条估计的计算方法,并通过模拟例子,说明广义变系数模型的函数系数可以由Bayesian B样条估计方法得到很好的估计．     

基于支持向量回归机的水文混沌时间序列预测

支持向量机在系统辨识和分类研究方面比较成熟,目前尚没有提出有效的支持向量回归理论来解决非线性、时变、干扰的复杂问题.支持向量回归机主要用于因果关系点对的回归预测,把支持向量回归机应用于水文混沌时间序列的预测研究是一个有意义的工作.在支持向量机一般理论基础上,提出了水文混沌时间序列支持向量回归机模型,并就模型进行仿真计算,讨论了模型参数对支持向量回归机预测精度的影响,为模型参数寻优提供一般指导原则.直门达水文站径流量混沌时间序列支持向量回归机预测实验表明,水文混沌时间序列支持向量回归机模型是有效的.     

A latent variables approach for clustering mixed binary and continuous variables within a Gaussian mixture model

For clustering objects, we often collect not only continuous variables, but binary attributes as well. This paper proposes a model-based clustering approach with mixed binary and continuous variables where each binary attribute is generated by a latent continuous variable that is dichotomized with a suitable threshold value, and where the scores of the latent variables are estimated from the binary data. In economics, such variables are called utility functions and the assumption is that the binary attributes (the presence or the absence of a public service or utility) are determined by low and high values of these functions. In genetics, the latent response is interpreted as the ??liability?? to develop a qualitative trait or phenotype. The estimated scores of the latent variables, together with the observed continuous ones, allow to use a multivariate Gaussian mixture model for clustering, instead of using a mixture of discrete and continuous distributions. After describing the method, this paper presents the results of both simulated and real-case data and compares the performances of the multivariate Gaussian mixture model and of a mixture of joint multivariate and multinomial distributions. Results show that the former model outperforms the mixture model for variables with different scales, both in terms of classification error rate and reproduction of the clusters means.     

Bayesian nonparametric modeling for functional analysis of variance

Analysis of variance is a standard statistical modeling approach for comparing populations. The functional analysis setting envisions that mean functions are associated with the populations, customarily modeled using basis representations, and seeks to compare them. Here, we adopt the modeling approach of functions as realizations of stochastic processes. We extend the Gaussian process version to allow nonparametric specifications using Dirichlet process mixing. Several metrics are introduced for comparison of populations. Then we introduce a hierarchical Dirichlet process model which enables comparison of the population distributions, either directly or through functionals of interest using the foregoing metrics. The modeling is extended to allow us to switch the sampling scheme. There are still population level distributions but now we sample at levels of the functions, obtaining observations from potentially different individuals at different levels. We illustrate with both simulated data and a dataset of temperature versus depth measurements at different locations in the Atlantic Ocean.     

Recursive state and parameter estimation with applications in water resources

Hydrologic models, as well as measurements of hydrologic processes, are corrupted by noise. The Kalman filter is a convenient tool to estimate the true but unknown state of a hydrologic system. It is, however, difficult to specify the necessary error covariances. A procedure is proposed to estimate the error covariances recursively in a combined state and parameter filter. Applications of the procedure yield meaningful results for two hydrologic data series of very different character. A major benefit of the proposed algorithm seems to be its robustness against instability.     

The maximum earthquake in future T years: Checking by a real catalog

The studies of disaster statistics are being largely carried out in recent decades. Some recent achievements in the field can be found in Pisarenko and Rodkin (2010). An important aspect in the seismic risk assessment is the using historical earthquake catalogs and the combining historical data with instrumental ones since historical catalogs cover very long time periods and can improve seismic statistics in the higher magnitude domain considerably. We suggest the new statistical technique for this purpose and apply it to two historical Japan catalogs and the instrumental JMA catalog. The main focus of these approaches is on the occurrence of disasters of extreme sizes as the most important ones from practical point of view. Our method of statistical analysis of the size distribution in the uppermost range of extremely rare events was suggested, based on maximum size M_max(τ) (e.g. earthquake energy, ground acceleration caused by earthquake, victims and economic losses from natural catastrophes, etc.) that will occur in a prescribed time interval τ. A new approach to the problem discrete data that we called “the magnitude spreading” is suggested. This method reduces discrete random value to continuous ones by addition a small uniformly distributed random components. We analyze this method in details and apply it to verification of parameters derived from two historical catalogs: the Usami earthquake catalog (599–1884) and the Utsu catalog (1885–1925). We compare their parameters with ones derived from the instrumental JMA catalog (1926–2014). The results of this verification are following: The Usami catalog is incompatible with the instrumental one, whereas parameters estimated from the Utsu catalog are statistically compatible in the higher magnitude domain with sample of M_max(τ) derived from the JMA catalog.     

An additive utility mixed integer programming model for nonlinear discriminant analysis

Mathematical programming (MP) discriminant analysis models can be used to develop classification models for assigning observations of unknown class membership to one of a number of specified classes using values of a set of features associated with each observation. Since most MP discriminant analysis models generate linear discriminant functions, these MP models are generally used to develop linear classification models. Nonlinear classifiers may, however, have better classification performance than linear classifiers. In this paper, a mixed integer programming model is developed to generate nonlinear discriminant functions composed of monotone piecewise-linear marginal utility functions for each feature and the cut-off value for class membership. It is also shown that this model can be extended for feature selection. The performance of this new MP model for two-group discriminant analysis is compared with statistical discriminant analysis and other MP discriminant analysis models using a real problem and a number of simulated problem sets.     

AN AUTOMATED METHOD FOR EXTENDING SENSITIVITY ANALYSIS TO MODEL FUNCTIONS

Abstract Parameter sensitivity analysis is a relatively well‐developed field compared with function sensitivity analysis. How sensitive are model conclusions to the choice of functions used in the right‐hand side of difference or differential equation models? Most work in this area has been scenario based where alternative functions are tested. This requires knowledge of plausible alternatives and is usually restricted to well‐known functions. In this work, a method is proposed for function sensitivity analysis, which it is hoped will provide a starting point for discussion and stimulating further research on this important but neglected topic. The method provides information on the sensitivity of a model's results to changes in the shape of the functions. This is done in an automated way without the need to specify alternative functional forms. The proposed method is illustrated on a small ecosystem model.     

Efficient Quantile Estimation for Functional-Coefficient Partially Linear Regression Models

The quantile estimation methods are proposed for functional-coefficient partially linear regression (FCPLR) model by combining nonparametric and functional-coefficient regression (FCR) model. The local linear scheme and the integrated method are used to obtain local quantile estimators of all unknown functions in the FCPLR model. These resulting estimators are asymptotically normal, but each of them has big variance. To reduce variances of these quantile estimators, the one-step backfitting technique is used to obtain the efficient quantile estimators of all unknown functions, and their asymptotic normalities are derived. Two simulated examples are carried out to illustrate the proposed estimation methodology.     

Heteroscedastic mixture transition distribution (HMTD) model

The paper further studies the heteroscedastic mixture transition distribution (HMTD) model introduced by Berchtold. Both the expectation and the standard deviation of each component are written as functions of the past of the process. The stationarity conditions are derived. An expectation conditional maximization (ECM) algorithm is used and shown to work well for estimation, the model selection problem is addressed, and the formulaes for computing the observed information matrix are derived. The shape changing feature of conditional distributions makes the model capable of modelling time series with asymmetric or multimodal distribution. The model is applied to several simulated and real datasets with satisfactory results.     

Polar sets for anisotropic Gaussian random fields

This paper studies polar sets for anisotropic Gaussian random fields, i.e. sets which a Gaussian random field does not hit almost surely. The main assumptions are that the eigenvalues of the covariance matrix are bounded from below and that the canonical metric associated with the Gaussian random field is dominated by an anisotropic metric. We deduce an upper bound for the hitting probabilities and conclude that sets with small Hausdorff dimension are polar. Moreover, the results allow for a translation of the Gaussian random field by a random field, that is independent of the Gaussian random field and whose sample functions are of bounded Hölder norm.     

The Zhukovskii problem of the flow around a sheet pile

The solution of the Zhukovskii problem of the flow around a sheet pile is given using the principles of two-dimensional steady-state seepage in the case when, accompanying the motion of the seeping water, there is a layer of saline ground waters at a certain depth under the sheet pile and this layer is located above an impermeable thickness of rock salt. The mixed boundary-value problem of the theory of analytic functions which arises is solved using Polubarinova-Kochina's method, which is based on the application of the analytical theory of linear differential equations and, also, the method, developed by us, of the conformal mappings of circular polygons in polar meshes, which are extremely typical for the velocity hodograph domains of such flows. While reflecting the specific details and individual properties of such flows, the solution constructed below turns out to be expressed in closed form in terms of elementary functions and, consequently, it is the simplest and most convenient solution. In addition, it is the most general solution for the class of problems being considered. The well known results Zhukovskii, Vedernikov and others are obtained from it as special and limiting çases A detailed hydrodynamic analysis and the specific features of the seepage process being considered, as well as the effects of all the physical parameters of the model on the pattern of the phenomenon, are presented using this solution and by numerical calculations.     

Differential analysis of polarity: Polar Hamilton-Jacobi,conservation laws,and Monge Ampère equations

We develop a differential theory for the polarity transform parallel to that of the Legendre transform, which is applicable when the functions studied are “geometric convex”, namely, convex, non-negative, and vanish at the origin. This analysis establishes basic tools for dealing with this duality transform, such as the polar subdifferential map, and variational formulas. Another crucial step is identifying a new, non-trivial, sub-class of C ² functions preserved under this transform. This analysis leads to a new method for solving many new first order equations reminiscent of Hamilton–Jacobi and conservation law equations, as well as some second order equations of Monge–Ampère type. This article develops the theory of strong solutions for these equations which, due to the nonlinear nature of the polarity transform, is considerably more delicate than its counterparts involving the Legendre transform. As one application, we introduce a polar form of the homogeneous Monge–Ampère equation that gives a dynamical meaning to a new method of interpolating between convex functions and bodies. A number of other applications, e.g., to optimal transport and affine differential geometry are considered in sequels.     

具有高斯过程误差的函数型线性模型的统计诊断

提出了具有高斯过程误差的函数型回归模型的几种诊断方法.在此模型中,首先,在样条基的基础上,推导了回归系数函数的估计.随后,证明了数据删失模型和均值漂移模型的等价性.然后,研究了三种诊断方法,即残差分析、Cook距离和似然距离来诊断异常和强影响数据.最后,通过一个模拟例子和一个实例来阐述方法的有效性.     

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One key difference of analyzing functional data from multidimensional data is that one needs to take phase variation (described by warping functions) into consideration as well as amplitude variation. Nonparametric estimation of warping functions may not generate summary measures that are easily interpreted or compared. We propose a local nonlinear parametric model to capture major local variation including both phase variation and amplitude variation. The parameters are interpretable, and can be easily compared among different curves. Simulation and real data analysis are performed to illustrate the powerfulness of the method.     

Using principal components in a proportional hazards model with applications in condition-based maintenance

This paper proposes the application of a principal components proportional hazards regression model in condition-based maintenance (CBM) optimization. The Cox proportional hazards model with time-dependent covariates is considered. Principal component analysis (PCA) can be applied to covariates (measurements) to reduce the number of variables included in the model, as well as to eliminate possible collinearity between the covariates. The main issues and problems in using the proposed methodology are discussed. PCA is applied to a simulated CBM data set and two real data sets obtained from industry: oil analysis data and vibration data. Reasonable results are obtained.     

Scalar characterizations of weakly cone-convex and weakly cone-quasiconvex functions

The principal aim of this paper is to show that weakly cone-convex vector-valued functions, as well as weakly cone-quasiconvex vector-valued functions, can be characterized in terms of usual weakly convexity and weakly quasiconvexity of certain real-valued functions, defined by means of the extreme directions of the polar cone or by Gerstewitz’s scalarization functions.     

Simulated annealing and object point processes: Tools for analysis of spatial patterns

This paper introduces a three-dimensional object point process—the Bisous model—that can be used as a prior for three-dimensional spatial pattern analysis. Maximization of likelihood or penalized-likelihood functions based on this model requires global optimization techniques, such as the simulated annealing algorithm. Theoretical properties of the model are discussed and the convergence of the proposed optimization method is proved. Finally, a simulation study is presented.     

180°弯曲方管牛顿流体及一种非牛顿流体湍性流动的数值模拟

运用湍流k-ε模式及实测壁面函数分别模拟牛顿流体(清水)及一种非牛顿流体(聚合物稀薄减阻溶液)流经180°弯曲方管的湍性流动,取得与实测速度分布吻合较好的结果.对于湍流模式对存在大涡的复杂流动的适应性,根据计算和试验结果进行了分析和讨论.     

Convergence of the Simulated Annealing Algorithm for Continuous Global Optimization

A class of simulated annealing algorithms for continuous global optimization is considered in this paper. The global convergence property is analyzed with respect to the objective value sequence and the minimum objective value sequence induced by simulated annealing algorithms. The convergence analysis provides the appropriate conditions on both the generation probability density function and the temperature updating function. Different forms of temperature updating functions are obtained with respect to different kinds of generation probability density functions, leading to different types of simulated annealing algorithms which all guarantee the convergence to the global optimum.