Nonparametric inference in multiplicative intensity model by discrete time observation

This paper deals with nonparametric inference problems in the multiplicative intensity model for counting processes. We propose a Nelson–Aalen type estimator based on discrete observation. The functional asymptotic normality of the estimator is proved. The limit process is the same as that in the continuous observation case, thus the proposed estimator based on discrete observation has the same properties as the Nelson–Aalen estimator based on continuous observation. For example, the asymptotic efficiency of proposed estimator is valid based on less information than the continuous observation case. A Kaplan–Meier type estimator is also discussed. Nonparametric goodness of fit test is considered, and an asymptotically distribution free test is proposed.     

The conditioning of least‐squares problems in variational data assimilation

In variational data assimilation a least‐squares objective function is minimised to obtain the most likely state of a dynamical system. This objective function combines observation and prior (or background) data weighted by their respective error statistics. In numerical weather prediction, data assimilation is used to estimate the current atmospheric state, which then serves as an initial condition for a forecast. New developments in the treatment of observation uncertainties have recently been shown to cause convergence problems for this least‐squares minimisation. This is important for operational numerical weather prediction centres due to the time constraints of producing regular forecasts. The condition number of the Hessian of the objective function can be used as a proxy to investigate the speed of convergence of the least‐squares minimisation. In this paper we develop novel theoretical bounds on the condition number of the Hessian. These new bounds depend on the minimum eigenvalue of the observation error covariance matrix and the ratio of background error variance to observation error variance. Numerical tests in a linear setting show that the location of observation measurements has an important effect on the condition number of the Hessian. We identify that the conditioning of the problem is related to the complex interactions between observation error covariance and background error covariance matrices. Increased understanding of the role of each constituent matrix in the conditioning of the Hessian will prove useful for informing the choice of correlated observation error covariance matrix and observation location, particularly for practical applications.     

Anthropology and O.R.: The Place of Observation in Management Science Process

This paper is an argument to combine the methods of observation with O.R. techniques to form the basis of a management science process. The paper begins by defining a typology showing where observation methods seem to be most appropriate in O.R. interventions. This is followed by a section outlining some of the techniques and problems of observation as seen from the field of anthropology. Using this theory, combined with personal experience, an observation process is developed. An example of using the process is then given.     

Separation principle for impulse control with partial information

This article is concerned with the impulse control of stochastic systems, the internal state of which is only known by a noisy observation with both continuous and discontinuous components. It is shown that among the controls depending on the observation there exists an optimal one, that can be recursively constructed as a function of the filter associated with the system.     

基于相对误差意义下的最小二乘法

最小二乘法一直广泛应用于科学技术各领域 ,但仅适用于等精度数据———因其评价依据是大致相同的绝对误差。而大多数科研及观测数据往往按被观测量的相对误差进行评价 ,即被观测量愈大 ,允许及实际测量误差也愈大。从这个意义上讲 ,若以相对拟合误差的平方和最小为条件 ,建立一套新的最小二乘法 ,那么当然可以期望新方法将具更广泛的用途和实际的意义。本文给出了新最小二乘法的实用结果     

Dynamical reconstruction of unknown inputs in nonlinear differential equations

We present an algorithm for the identification of an unknown but bounded input to a nonlinear finite-dimensional system, based on observations taken at discrete time instants and corrupted by observation errors. This algorithm is stable with respect to observation and computational errors.If we have the further information that the unknown input is a signal of bounded variation, then we can give explicit convergence estimates of the algorithm.     

Approximate solutions to Dirichlet control problems for the wave equation in Sobolev classes and dual observation problems

Dual control and observation problems for the wave equation with variable coefficients subject to Dirichlet boundary conditions are solved by a variational method. This method was earlier proposed by the author for an approximate analysis of linear equations with nonuniform perturbations of the operator. Explicit bounds on the constant that are required to implement the method are obtained using the correct solvability property of the dual observation problem. Finite-dimensional approximations of the control and observation problems are obtained by the difference method preserving the duality relation. The convergence of approximate solutions is established in the norms of the corresponding dual spaces.     

Discrete–time nonlinear filtering with marked point process observations: ii. risk–sensitive filters

We discuss in this article the risk–sensitive filtering problem of estimating a nonlinear signal process, with nonadditive non–Gaussian noise, via a marked point process observation. This extends to the risk sensitive case all the risk–neutral results studied in Dufour and Kannan [2].By going into a change of measure, we derive the unnormalized conditional density of the signal conditioned on the observation history. We also derive the unnormalized prediction density. Using these, we present two separate expressions for the optimal estimate of the signal. A similar analysis of the smoothing density of the signal is also studied under both the risk–sensitive and risk–neutral cases. We specialize the above optimal estimation to the linear signal dynamics and marked point process observation under some Gaussian assumptions. We obtain a Kalman type risk-sensitive filter. Due to the special nature of the observation process, the conditional mean and covariance estimates directly depend now on the point process     

一类半线性双曲系统的状态观测问题

本文考虑一类半线性双曲系统的状态观测问题,给出了一个(求解)算法并证明了其在某种相当强的意义上的有效性.     

On-line state estimation for nonlinear dynamical systems

A problem of estimation of states of a dynamical object on the base of incomplete and inexact measurements is studied. The focus is on a set-based estimation of states required for construction of optimal guaranteeing feedbacks. In particular, the aim is to construct at every current time instant polyhedral approximations of sets of all states consistent with the obtained measurements. A problem of constructing estimates, associated with these approximations, is called an optimal observation problem. This note presents a numerical method for solving optimal observation problems for nonlinear dynamical systems. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

基于径向基的自适应惩罚样条回归模型

传统惩罚样条回归模型中惩罚项的设置未考虑数据的空间异质性,因而对复杂数据的拟合缺乏自适应性.文章通过对径向基函数的几何意义分析,以节点两侧相邻区域内数据点的纵向极差为基础,构造局部惩罚权重向量并加入到约束回归模型的惩罚项中,构造了基于径向基的自适应惩罚样条回归模型.新模型在观测数据波动较大的区域,给予拟合曲线较小的惩罚,而在观测数据波动较小的区域,给予拟合曲线较大的惩罚,从而使拟合曲线能自适应地反映观测数据的局部变化特征.模拟和应用结果显示新模型的拟合效果显著优于传统的惩罚样条回归模型.     

Real-time calculation of the current state estimates for a class of delay systems

The linear optimal observation problem is examined for one type of nonstationary delay system with an uncertainty in the initial state. A fast implementation of the dual method is proposed for calculating estimates of the initial state. This implementation is based on the quasi-reduction of the fundamental matrix of solutions to the mathematical model of delay systems. It is shown that an iteration step of the dual method only requires that auxiliary systems of ordinary differential equations be integrated on small time intervals. An algorithm is described for the real-time calculation of current state estimates. The results are illustrated by the optimal observation problem for a third-order stationary delay system.     

基于不确定性回报的行为控制博弈分析

不确定型的行为控制较之确定型的行为控制更为复杂,但在现实中又有一定的广泛性,且目前的研究基础比较薄弱.把研究的视角放在不确定性回报下行为控制的博弈机理上,考察了博弈双方的行为观测偏差,定义了在信息不对称条件下管理者对被管理者的行为的观测矩阵、管理者的博弈策略矩阵、被管理者对管理者观测能力的估计矩阵及对管理者博弈策略的估计矩阵等,分析了管理者与被管理者之间的动态博弈过程和行为策略选择,给出了满足博弈均衡的不确定性回报的设计要求.这些都可以推广应用于各种具体管理制度的设计和改进当中,为行为控制研究提供了定量分析的新方法.在此基础上,选择房地产投资开发行为控制机制的实例进行了诊断研究.     

输电系统的部分可观Petri网故障诊断器设计

采用部分可观Petri网的故障诊断方法来解决变电站输电系统中不可观事件和不可观运行状态的故障诊断问题.首先,将系统可观测序列分解为长度为1的基础观测序列,应用线性不等式矩阵计算与基础观测序列相符的点火序列集;然后,基于整数线性规划问题,利用向前向后函数拓宽诊断区间,同时应用参数K限定故障诊断序列长度,通过分析系统可观事件和系统部分可观状态,给出故障诊断结果.最后,构造变电站输电系统的部分可观Petri网模型,应用提出的故障诊断算法对输电系统进行诊断,诊断结果准确给出了故障发生与否及故障发生位置.算法适用于在线故障诊断,计算复杂性线性相关于观序列长度.     

静园草坪灌溉系统的改进

在本文中 ,我将讨论一个从自己的实际观察中总结出来的数学模型——静园草坪的灌溉系统问题 .文中证明了灌溉系统的最大效率是 3 32π .这个结论还可以应用于其他的一些领域 .这实际上是一个决策问题 ,它归结为用小块的图形去覆盖平面区域 .我们需要找到一种最佳的覆盖方法 ,使得重叠的部分最少 .这样 ,我们就有两个问题要解决 ,首先是如何评价覆盖方法的优劣 ,其次是如何找到最佳的覆盖方法 .文中给出了合理的评价准则 ,并且提出了一些深入研究的方向和建议 .     

基于有限区域量化的系统稳定性分析与设计

针对基于输出反馈和具有有限区域信号量化的离散时间系统,进行了系统稳定性分析与量化参数设计的研究.首先,分别对状态观测误差系统和对象系统在有限区域对数量化作用下的系统渐近稳定性进行了分析,得到了相应的稳定性条件,接着针对对数型量化器,给出了两个系统稳定性之间的内在关联,同时得到了各有限区域量化器的量化区间上界值.在此基础上,得到了保证各子系统稳定的系统通信速率比值.最后,给出了在时变量化作用下基于状态观测的控制策略和仿真例子.     

Existence of infinite Viterbi path for pairwise Markov models

For hidden Markov models one of the most popular estimates of the hidden chain is the Viterbi path — the path maximizing the posterior probability. We consider a more general setting, called the pairwise Markov model, where the joint process consisting of finite-state hidden regime and observation process is assumed to be a Markov chain. We prove that under some conditions it is possible to extend the Viterbi path to infinity for almost every observation sequence which in turn enables to define an infinite Viterbi decoding of the observation process, called the Viterbi process. This is done by constructing a block of observations, called a barrier, which ensures that the Viterbi path goes through a given state whenever this block occurs in the observation sequence.     

State observation problem for general time reversible system and applications

This paper is concerned with a state observation problem for the general time reversible system, i.e., to recover the initial state of the given system from suitable observation data. An abstract unified framework is presented. By means of an iterative time reversal technique, we derive two asymptotic formulae of reconstructing the initial state approximately with explicit convergence rates. General results are then applied to the state observation problems for the Schrödinger equation and the wave equation.     

Identification of two independent coefficients with one observation for the Schrödinger operator in an unbounded strip

This article is devoted to prove a stability result for two independent coefficients (each one depending on only one variable) for a Schrödinger operator in an unbounded strip with only one observation on an unbounded subset of the boundary. For that, we first use the global Carleman estimate proved in Cardoulis et al. (2008) [3]. Then, with a Carleman-type estimate for a first order differential operator (cf. Immanuvilov and Yamamoto (2005) [4]) and an energy estimate, we prove the simultaneous identification of the diffusion coefficient and the potential with only one observation.     

Measurement and the verificationist theory/observation distinction

In the following article, we propose to show that following the general verificationist epistemic programme (its demand that the truth of our judgments be verifiable), the analysis of measurement on the one hand, and the classical positivist analysis of common-sense observation on the other, do not lead to same conclusions. This is especially important, because the differences in conclusions concern the positivist theory/observation distinction. In particular, the analysis of measurement does not fully support this distinction. This fact might have important consequences for the problem of scientific realism and related ontological and epistemological problems in the philosophy of science.