Statistics for Spatial Data.

Differential-Difference Equations. By Richard Bellman and Kenneth L. Cooke. Pp. xvi, 465. 1963. (Academic Press)

動注化学療法における pharmacokinetics と臨床

Diffusion and ecological problems : mathematical models

Summary We propose a new method for estimating parameters in models that are defined by a system of non-linear differential equations Such equations represent changes in system outputs by linking the behaviour of derivatives of a process to the behaviour of the process itself Current methods for estimating parameters in differential equations from noisy data are computationally intensive and often poorly suited to the realization of statistical objectives such as inference and interval estimation The paper describes a new method that uses noisy measurements on a subset of variables to estimate the parameters defining a system of non-linear differential equations The approach is based on a modification of data smoothing methods along with a generalization of profiled estimation We derive estimates and confidence intervals, and show that these have low bias and good coverage properties respectively for data that are simulated from models in chemical engineering and neurobiology The performance of the method is demonstrated by using real world data from chemistry and from the progress of the autoimmune disease lupus

/pdf/parameter-estimation-for-differential-equations-a-1tk31cgdqs.pdf

Parameter estimation for differential equations: a generalized smoothing approach

Some effective approaches to check the identifiability of uncontrolled nonlinear systems

In this paper we give a necessary condition for structural identifiability of uncontrolled autonomous systems. This condition only turns on the identifiability of the right-hand side of the nonlinear differential system. We prove that this necessary condition becomes sufficient when the state is one-dimensional. To the best of our knowledge, the theoretical results obtained in this paper are new although the proofs are trivial. But they give an easy to check condition as it is shown by the study of some typical examples, in which we do much less computation than the involved literature to prove identifiability properties.

An easy to check criterion for (un)indentifiability of uncontrolled systems and its applications

NATHALIE VERDIERE∗, LILIANNE DENIS-VIDAL∗∗ GHISLAINE JOLY-BLANCHARD∗, DOMINIQUE DOMURADO∗∗∗ ∗ Department Genie Informatique, University of Technology of Compiegne BP 20 529, 60 205 Compiegne Cedex, France e-mail: nathalie.verdiere@dma.utc.fr, ghislaine.joly-blanchard@utc.fr ∗∗ University of Sciences and Tech. Lille, France e-mail: denvid@attglobal.net ∗∗∗ CRBA — Faculty of Pharmacy BP 14 491, 34093 Montpellier Cedex 5, France e-mail: domurado@univ-montp1.fr

/pdf/identifiability-and-estimation-of-pharmacokinetic-parameters-53avhyzl7c.pdf

Lilianne Denis-Vidal

Papers

Some effective approaches to check the identifiability of uncontrolled nonlinear systems

An easy to check criterion for (un)indentifiability of uncontrolled systems and its applications

Identifiability and estimation of pharmacokinetic parameters for the ligands of the macrophage mannose receptor

Equivalence and identifiability analysis of uncontrolled nonlinear dynamical systems

An Algorithm to Test Identifiability of Non-Linear Systems