Ols parameter estimation for a linear paired confluent model

We investigate OLS parameter estimation for a linear paired model in the case of a passive experiment with errors in both variables. The explicit form of the OLS estimates is obtained, their equivalence to maximum likelihood estimates is demonstrated in the presence of normal errors, and estimate consistency is proved. The OLS estimates are compared analytically and numerically with known parameter estimates of “direct,” “orthogonal,” and “diagonal” regression models.     

Multiple criteria sorting with a set of additive value functions

We present a new multiple criteria sorting method that aims at assigning actions evaluated on multiple criteria to p pre-defined and ordered classes. The preference information supplied by the decision maker (DM) is a set of assignment examples on a subset of actions relatively well known to the DM. These actions are called reference actions. Each assignment example specifies a desired assignment of a corresponding reference action to one or several contiguous classes. The set of assignment examples is used to build a preference model of the DM represented by a set of general additive value functions compatible with the assignment examples. For each action a, the method computes two kinds of assignments to classes, concordant with the DM’s preference model: the necessary assignment and the possible assignment. The necessary assignment specifies the range of classes to which the action can be assigned considering all compatible value functions simultaneously. The possible assignment specifies, in turn, the range of classes to which the action can be assigned considering any compatible value function individually. The compatible value functions and the necessary and possible assignments are computed through the resolution of linear programs.     

Optimal strategies for selecting project portfolios using uncertain value estimates

Practically all organizations seek to create value by selecting and executing portfolios of actions that consume resources. Typically, the resulting value is uncertain, and thus organizations must take decisions based on ex ante estimates about what this future value will be. In this paper, we show that the Bayesian modeling of uncertainties in this selection problem serves to (i) increase the expected future value of the selected portfolio, (ii) raise the expected number of selected actions that belong to the optimal portfolio ex post, and (iii) eliminate the expected gap between the realized ex post portfolio value and the estimated ex ante portfolio value. We also propose a new project performance measure, defined as the probability that a given action belongs to the optimal portfolio. Finally, we provide analytic results to determine which actions should be re-evaluated to obtain more accurate value estimates before portfolio selection. In particular, we show that the optimal targeting of such re-evaluations can yield a much higher portfolio value in return for the total resources that are spent on the execution of actions and the acquisition of value estimates.     

Lie series method for vector fields and Hamiltonian perturbation theory

We consider a rigorous Hamiltonian perturbation theory based on the transformation of the vector field of the system, realized by the Lie method. Such a perturbative technique presents some advantages over the standard one, which uses the transformation of the Hamilton functions. Indeed, the present method is simple, and furnishes quite detailed informations on the normal form. Moreover, it leads to estimates which are better and/or simpler than those of the scalar Lie methods. The perturbation method is presented with reference to two model problems, both pertaining to the realm of the well known Nekhoroshev theorem: the confining of actions for exponentially long times in a system of coupled harmonic oscillators, and an application to the so called problem of the realization of a holonomic constraint in classical mechanics.     

Credit scoring for profitability objectives

In consumer credit markets lending decisions are usually represented as a set of classification problems. The objective is to predict the likelihood of customers ending up in one of a finite number of states, such as good/bad payer, responder/non-responder and transactor/non-transactor. Decision rules are then applied on the basis of the resulting model estimates. However, this represents a misspecification of the true objectives of commercial lenders, which are better described in terms of continuous financial measures such as bad debt, revenue and profit contribution. In this paper, an empirical study is undertaken to compare predictive models of continuous financial behaviour with binary models of customer default. The results show models of continuous financial behaviour to outperform classification approaches. They also demonstrate that scoring functions developed to specifically optimize profit contribution, using genetic algorithms, outperform scoring functions derived from optimizing more general functions such as sum of squared error.     

Accelerating autonomous learning by using heuristic selection of actions

This paper investigates how to make improved action selection for online policy learning in robotic scenarios using reinforcement learning (RL) algorithms. Since finding control policies using any RL algorithm can be very time consuming, we propose to combine RL algorithms with heuristic functions for selecting promising actions during the learning process. With this aim, we investigate the use of heuristics for increasing the rate of convergence of RL algorithms and contribute with a new learning algorithm, Heuristically Accelerated Q-learning (HAQL), which incorporates heuristics for action selection to the Q-Learning algorithm. Experimental results on robot navigation show that the use of even very simple heuristic functions results in significant performance enhancement of the learning rate.     

Active controlled structural systems under delta-correlated random excitation: Linear and nonlinear case

Reduction of structural vibration in active controlled dynamical system is usually performed by means of convenient control forces dependent of the dynamic response. In this paper the existent studies will be extended to dynamical systems subjected to non-Gaussian random process accounting for the time delay involved in the application of active control actions. Control forces acting with time-delay effects will be expanded in Taylor series evaluating response statistics by means of the extended Itô differential rule to consider the effects of the non-normality of the input processes. Numerical application provided shows the feasibility of the proposed method to analyze stochastic dynamic systems with delayed actions under delta-correlated process contrasting statistics of response with estimates from Monte Carlo simulation.     

On convex modified output least-squares for elliptic inverse problems: stability,regularization, applications,and numerics

Abstract

Inverse problems of identifying parameters in partial differential equations constitute an important class of problems with diverse real-world applications. These identification problems are commonly explored in an optimization framework and there are many optimization formulations having their own advantages and disadvantages. Although a non-convex output least-squares (OLS) objective is commonly used, a convex-modified output least-squares (MOLS) has shown encouraging results in recent years. In this work, we focus on various aspects of the MOLS approach. We devise a rigorous (quadratic and non-quadratic) regularization framework for the identification of smooth as well as discontinuous coefficients. This framework subsumes the total variation regularization that has attracted a great deal of attention in identifying sharply varying coefficients and also in image processing. We give new existence results for the regularized optimization problems for OLS and MOLS. Restricting to the Tikhonov (quadratic) regularization, we carry out a detailed study of various stability aspects of the inverse problem under data perturbation and give new stability estimates for general inverse problems using OLS and MOLS formulations. We give a discretization scheme for the continuous inverse problem and prove the convergence of the discrete inverse problem to the continuous one. We collect discrete formulas for OLS and MOLS and compute their gradients and Hessians. We present applications of our theoretical results. To show the feasibility of the MOLS framework, we also provide computational results for the inverse problem of identifying parameters in three different classes of partial differential equations .     

An integral model structure and truncation theory for coherent group actions

In this work we study the homotopy theory of coherent group actions from a global point of view, where we allow both the group and the space acted upon to vary. Using the model of Segal group actions and the model categorical Grothendieck construction we construct a model category encompassing all Segal group actions simultaneously. We then prove a global rectification result in this setting. We proceed to develop a general truncation theory for the model-categorical Grothendieck construction and apply it to the case of Segal group actions. We give a simple characterization of n-truncated Segal group actions and show that every Segal group action admits a convergent Postnikov tower built out of its n-truncations.     

Problems with the estimation of stochastic differential equations using structural equations models

The present paper deals with the identification and maximum likelihood estimation of systems of linear stochastic differential equations using panel data. So we only have a sample of discrete observations over time of the relevant variables for each individual. A popular approach in the social sciences advocates the estimation of the “exact discrete model” after a reparameterization with LISREL or similar programs for structural equations models. The “exact discrete model” corresponds to the continuous time model in the sense that observations at equidistant points in time that are generated by the latter system also satisfy the former. In the LISREL approach the reparameterized discrete time model is estimated first without taking into account the nonlinear mapping from the continuous to the discrete time parameters. In a second step, using the inverse mapping, the fundamental system parameters of the continuous time system in which we are interested, are inferred. However, some severe problems arise with this “indirect approach”. First, an identification problem may arise in multiple equation systems, since the matrix exponential function denning some of the new parameters is in general not one‐to‐one, and hence the inverse mapping mentioned above does not exist. Second, usually some sort of approximation of the time paths of the exogenous variables is necessary before the structural parameters of the system can be estimated with discrete data. Two simple approximation methods are discussed. In both approximation methods the resulting new discrete time parameters are connected in a complicated way. So estimating the reparameterized discrete model by OLS without restrictions does not yield maximum likelihood estimates of the desired continuous time parameters as claimed by some authors. Third, a further limitation of estimating the reparameterized model with programs for structural equations models is that even simple restrictions on the original fundamental parameters of the continuous time system cannot be dealt with. This issue is also discussed in some detail. For these reasons the “indirect method” cannot be recommended. In many cases the approach leads to misleading inferences. We strongly advocate the direct estimation of the continuous time parameters. This approach is more involved, because the exact discrete model is nonlinear in the original parameters. A computer program by Hermann Singer that provides appropriate maximum likelihood estimates is described.     

On Planar Sampling with Gaussian Kernel in Spaces of Bandlimited Functions

We show some non-standard Poincaré type estimates in the biparametric setting with appropriate weights. We will derive these results using variants from classical estimates exploiting the interplay between maximal functions and fractional integrals. We also provide a sharper result by using extrapolation techniques.

     

Divisible and exponent actions of semigroups

In this paper we consider divisible actions of semigroups which have a completely simple minimal ideal and establish that these actions are determined by the divisible actions of the Schützenberger group of the minimal ideal. In the third section, we discuss the concept of an exponent action and present a result which relates the notion of divisible action to the notion of exponent action. The fourth section of this paper exhibits a characterization of exponent functions. To find such a characterization was the original objective of this project.     

应急预案响应程序模块化研究

应急响应程序是应急预案的重要组成部分,通过按照一定逻辑关系构成的行动网络图对响应过程进行可视化与数字化,应急响应程序模块化就是试图将行动间逻辑关系稳定且在多个程序中多次出现的“子网络”提取出来,作为响应程序模块,在以后的应用中,根据实际需要直接调用模块,通过模块之间的重新组合,增加制定新应急响应程序的效率。为此,文章在定义了行动间紧密度和模块代表性的基础上,以模块内行动间紧密度之和与模块代表性之和最大化为目标,满足一个行动仅能存在与一个模块的约束下,建立数学规划模型,以蚁群算法为基础设计启发式算法,最后对航空公司多个应急响应程序进行模块化,说明该方法的有效性。     

A STATE SPACE BIOECONOMIC MODEL OF PACIFIC HALIBUT

Abstract Evaluation of potential economic consequences of alternative management actions requires an understanding of how the biological stock will be affected by the management action and an understanding of the response of economic systems to changes in the timing, magnitude, and size distribution of harvests and changes in the location and catchability of the biological stock. We use a hybrid structural time series model to represent Pacific halibut (Hippoglossus stenolepis) stock and recruitment dynamics and a system of structural equations to represent supply and demand relationships for Pacific halibut from Alaska and British Columbia. Model simulations explore the economic effects of changes in recruitment success, growth rate, and carrying capacity, and changes in international supplies of halibut.     

A new approach for parameter estimation of finite Weibull mixture distributions for reliability modeling

The aim of this paper is to model lifetime data for systems that have failure modes by using the finite mixture of Weibull distributions. It involves estimating of the unknown parameters which is an important task in statistics, especially in life testing and reliability analysis. The proposed approach depends on different methods that will be used to develop the estimates such as MLE through the EM algorithm. In addition, Bayesian estimations will be investigated and some other extensions such as Graphic, Non-Linear Median Rank Regression and Monte Carlo simulation methods can be used to model the system under consideration. A numerical application will be used through the proposed approach. This paper also presents a comparison of the fitted probability density functions, reliability functions and hazard functions of the 3-parameter Weibull and Weibull mixture distributions using the proposed approach and other conventional methods which characterize the distribution of failure times for the system components. GOF is used to determine the best distribution for modeling lifetime data, the priority will be for the proposed approach which has more accurate parameter estimates.     

切Poisson作用及约化

本文证明了单连通Poisson紧李群切作用及约化Poisson作用于Poisson流形，若带有等动量映射，则可通过调整Poisson流形的Poisson结构，变成保Poisson结构的Poisson作用，并且该作用限制到Poisson流形的辛叶片上，相对于新Poisson结构是Hamiltion作用。我们把Meyer-Marsden-Weinstein约化从Hamiltion作用推广到切Poisson作用，包括正则值和非正则值两种形式。     

Uniform estimates for spherical functions on complex semisimple Lie groups

We prove new estimates for spherical functions and their derivatives on complex semisimple Lie groups, establishing uniform polynomial decay in the spectral parameter. This improves the customary estimate arising from Harish-Chandra's series expansion, which gives only a polynomial growth estimate in the spectral parameter. In particular, for arbitrary positive-definite spherical functions on higher rank complex simple groups, we establish estimates for which are of the form in the spectral parameter and have uniform exponential decay in regular directions in the group variable a _t . Here is an explicit constant depending on G, and may be singular, for instance.?The uniformity of the estimates is the crucial ingredient needed in order to apply classical spectral methods and Littlewood—Paley—Stein square functions to the analysis of singular integrals in this context. To illustrate their utility, we prove maximal inequalities in L ^p for singular sphere averages on complex semisimple Lie groups for all p in . We use these to establish singular differentiation theorems and pointwise ergodic theorems in L ^p for the corresponding singular spherical averages on locally symmetric spaces, as well as for more general measure preserving actions. Submitted: May 2000, Revised version: October 2000.     

Parameter estimation in moving boundary problems

We describe an approximation scheme which can be used to estimate unknown parameters in moving boundary problems. The model equations we consider are fairly general nonlinear diffusion/reaction equations of one spatial variable. Here we give conditions on the parameter sets and model equations under which we can prove that the estimates obtained using the approximations will converge to best-fit parameters for the original model equations. We conclude with a numerical example.     

Constrained Global Optimization of Expensive Black Box Functions Using Radial Basis Functions

We present a new strategy for the constrained global optimization of expensive black box functions using response surface models. A response surface model is simply a multivariate approximation of a continuous black box function which is used as a surrogate model for optimization in situations where function evaluations are computationally expensive. Prior global optimization methods that utilize response surface models were limited to box-constrained problems, but the new method can easily incorporate general nonlinear constraints. In the proposed method, which we refer to as the Constrained Optimization using Response Surfaces (CORS) Method, the next point for costly function evaluation is chosen to be the one that minimizes the current response surface model subject to the given constraints and to additional constraints that the point be of some distance from previously evaluated points. The distance requirement is allowed to cycle, starting from a high value (global search) and ending with a low value (local search). The purpose of the constraint is to drive the method towards unexplored regions of the domain and to prevent the premature convergence of the method to some point which may not even be a local minimizer of the black box function. The new method can be shown to converge to the global minimizer of any continuous function on a compact set regardless of the response surface model that is used. Finally, we considered two particular implementations of the CORS method which utilize a radial basis function model (CORS-RBF) and applied it on the box-constrained Dixon–Szegö test functions and on a simple nonlinearly constrained test function. The results indicate that the CORS-RBF algorithms are competitive with existing global optimization algorithms for costly functions on the box-constrained test problems. The results also show that the CORS-RBF algorithms are better than other algorithms for constrained global optimization on the nonlinearly constrained test problem.