Local parameter identifiability for one class of hybrid systems

We consider the problem of local parameter identifiability for a hybrid system with components that are continuous and discrete in time. The set of observations is the vector-solution (depending on the parameter that is continuous in time) of the discrete component. Sufficient conditions of local parameter identifiability have been formulated using the earlier introduced notion of normalized separability of the set of parameters from the kernel of a special functional. An example where the condition of normed separability is reduced to some rank criterion is given.     

A Group-Theoretic Approach to Parameter Identifiability of PDE Systems

The contribution is devoted to the parameter identifiability problem of (nonlinear) PDE systems. Especially, we discuss the (local) identifiability of parameters along a trajectory. The analysis relies on a coordinate-free formulation for systems, including boundary conditions, and we motivate an approach by (Lie) transformation groups, whose success for PDE systems depends on a consequent extent to the accompanying boundary conditions. The (non-)identifiability of parameters is related to the (non-)existence of group generators, wherewith (local) conditions can be derived. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Structural identifiability of a model of dialysis

In this paper, structural identifiability from input–output data is considered. A mathematical model to describe a dialysis process based on linear dynamic systems is used and the identifiability of this model is tested. The problem of estimating the parameters and obtaining conditions to assure the uniqueness of the parameters is solved. Some conditions to obtain attractive points for the considered model are given, and finally, the stability problem is analyzed.     

The local parametric identifiability of a linear stationary system from a single observation of its solution

A special case of a system of linear stationary differential equations depending on a parameter is considered. Necessary and sufficient conditions for the local parametric identifiability of such a system from a single observation of its solution are obtained. Relations between the conditions obtained and the behavior of the spectrum of the matrix of the system are analyzed.     

Prevalence of locally parameter identifiable systems

The problem of local parameter identifiability of an input–output system is considered. A set lf of systems is studied for which the property of local parameter identifiability holds for almost all values of input signals and parameters in both topological and metric senses. Sufficient conditions are pointed out under which the set LI contains a prevalent subset. The proof is based on the prevalent transversality theorem proved by Kaloshin. Systems are considered that are characterized by a family of (structural) parameters a and a control block. It is shown that if the dimension of the set of parameters a is large enough (the structure of the system is rich enough), then, generically, a system f _a belongs to the class lf for a set of parameters a having full measure.     

On the identifiability of measurement error in the bifurcating autoregressive model

Huggins and Staudte (1994) considered a mixed linear model for the analysis of cell lineage data and in models for the covariance structure which involved measurement error, it was not immediately clear that the parameters involved were identifiable. Whilst a numerical examination of the Hessian matrix at the estimated parameter values gave some reassurance, this was not theoretically satisfying. Here a matrix formulation of the robust estimating functions of Huggins (1993a, b) as applied in Huggins and Staudte (1994), which include the maximum likelihood estimating functions under the assumption of multivariate normality as a special case, is given along with a direct proof linking identifiability expressed in terms of the estimating functions with the information matrix or its analogue in more general settings. The resulting conditions on the estimating functions may then be checked globally using computer algebra, suggesting a method for establishing identifiability in mixed linear models in general.     

Hankel matrices for system identification

The coefficients of a linear system, even if it is a part of a block-oriented nonlinear system, normally satisfy some linear algebraic equations via Hankel matrices composed of impulse responses or correlation functions. In order to determine or to estimate the coefficients of a linear system it is important to require the associated Hankel matrix be of row-full-rank. The paper first discusses the equivalent conditions for identifiability of the system. Then, it is shown that the row-full-rank of the Hankel matrix composed of impulse responses is equivalent to identifiability of the system. Finally, for the row-full-rank of the Hankel matrix composed of correlation functions, the necessary and sufficient conditions are presented, which appear slightly stronger than the identifiability condition. In comparison with existing results, here the minimum phase condition is no longer required for the case where the dimension of the system input and output is the same, though the paper does not make such a dimensional restriction.     

Identifiability of Dynamic Systems Represented by Bond Graphs

In this paper, the identifiability of dynamical systems is presented from the perspective of the Bond Graph Methodology. Several classical approaches for identifiability are studied and their applicability to bond graphs is discussed. The Markov Parameter method was selected to determine local identifiability of linear systems and a methodical procedure to obtain Markov Parameters directly from the bond graph is presented which is based on its causal paths. This method can easily be implemented in on a computer and works for bond graphs with derivative causality elements and fields.     

Identifiability of intermediate variables on causal paths

We discuss the discovery of causal mechanisms and identifiability of intermediate variables on a causal path. Different from variable selection, we try to distinguish intermediate variables on the causal path from other variables. It is also different from ordinary model selection approaches which do not concern the causal relationships and do not contain unobserved variables. We propose an approach for selecting a causal mechanism depicted by a directed acyclic graph (DAG) with an unobserved variable. We consider several causal networks, and discuss their identifiability by observed data. We show that causal mechanisms of linear structural equation models are not identifiable. Furthermore, we present that causal mechanisms of nonlinear models are identifiable, and we demonstrate the identifiability of causal mechanisms of quadratic equation models. Sensitivity analysis is conducted for the identifiability.     

Robustness and convergence in the Lee–Carter model with cohort effects

Interest in cohort effects in mortality data has increased dramatically in recent years, with much of the research focused on extensions of the Lee–Carter model incorporating cohort parameters. However, some studies find that these models are not robust to changes in the data or fitting algorithm, which limits their suitability for many purposes. It has been suggested that these robustness problems may be the result of an unresolved identifiability issue. In this paper, after investigating systemically the robustness of cohort extensions of the Lee–Carter model and the convergence of the algorithms used to fit it to data, we demonstrate the existence of such an identifiability issue and propose an additional approximate identifiability constraint which solves many of the problems found.     

动力学方程组中参数识别模型及其优化性质

本文建立了动力学方程组中参数优化识别的数学模型.这是个含有动态约束的泛函极小化问题.应用线性算子的连续性,证明了该问题最优解的存在性,即参数的可识别性.最后依据弱Gateaux微分,给出并证明达到最优解的一个必要条件.     

AN OPTIMAL MODEL AND ITS IDENTIFICATION FOR THE THERMODYNAMICS OF KEROGEN EV

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Identifiability analysis of an epidemiological model in a structured population

We investigate the parameter identifiability problem for a system of nonlinear integro-partial differential equations of transport type, representing the spread of a disease with a long infectious but undetectable period in an individual population. After obtaining the expression of the model input-output relationships, we give sufficient conditions on the initial and boundary conditions of the system that guarantee the parameter identifiability on a finite time horizon. We finally illustrate our findings with numerical simulations.     

Gauss因果模型中因果效应识别方法的比较

一个Gauss因果模型中常常存在不只一种识别因果效应的方法, 不同的方法对应的估计可能不同. 该文对Pearl等人提出的前门准则, 后门准则,工具变量准则等识别方法的估计精度进行了分析比较, 并给出了相应的模拟结果, 为实践中选择更优的识别准则提供了依据.     

Identifiability conditions for covariate effects model on survival times under informative censoring

We provide the identifiability conditions for the covariate effects modeling of bivariate survival data when one survival time is dependently censored by the other survival time. The covariate effects are specified through three components of the copula decomposition. Many commonly used copula families are shown to satisfy the identifiable condition. A condition for causal interpretation is also provided.     

LINEAR CONTROL SYSTEMS WITH TIME-LAG:CONTROLLABILITY AND LOCAL PARAMETRICAL IDENTIFIABILITY WITH EXTENSIONS IN PRE-HILBERT SPACES

Conditions are given for controllability, output controllability and local identifiabitity of a parametrization in a subset of of linear differential systems with time-lags.     

Identifiability issues in dynamic stress–strength modeling

In many real-life scenarios, system reliability depends on dynamic stress–strength interference, where strength degrades and stress accumulates concurrently over time. In some other cases, shocks appear at random time points, causing damage which is only effective at the instant of shock arrival. In this paper, we consider the identifiability problem of a system under deterministic strength degradation and stochastic damage due to shocks arriving according to a homogeneous Poisson process. We provide conditions under which the models are identifiable with respect to lifetime data only. We also consider current status data and suggest to collect additional information and discuss the issues of model identifiability under different data configurations.     

Persistence and stability for a two-species ratio-dependent predator-prey system with distributed time delay

A two-species ratio-dependent predator-prey model with distributed time delay is investigated. It is shown that the system is persistent under some appropriate conditions, and sufficient conditions are obtained for both the local and global stability of the positive equilibrium of the system.     

带时滞的比率型的食物链系统的持久性和稳定性

A delayed three-species ratio-dependent predator-prey food-chain model without dominating instantaneous negative feedback is investigated. It is shown that the system is permanent under some appropriate conditions, and sufficient conditions are obtained for the local asymptotic stability of a positive equilibrium of the system.     

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??In survival analysis, most existing approaches for analysing right-censored failure time data assume that the censoring time is independent of the failure time. However, investigators often face problems involving dependent censoring, i.e., failure time and censoring time are possibly dependent and they may be censored one another, especially in clinical trials. Without accounting for such dependence, survival distributions cannot be estimated consistently. Numerous attempts to model this dependence have been made. Among them, copula models are of particular interest because of their simple structure. Proportional hazard model analysis for informative right-censored data has been discussed in this paper. An Archimedean copula is assumed for the joint distribution function of failure time and censoring time variables. Under the conditions of identifiability of the parameter of the Archimedean copula, the maximum likelihood estimators of the parameter of Archimedean copula, the parameters and the cumulative hazard function of PH model are worked out. Extensive simulation studies show that the feasibility of the proposed method and the consistency of the estimators.