A unified approach to variability in compartmental models

SUMMARY Variability in compartmental models is shown to be related to interparticle correlations. This permits a unified study of a wide variety of models. In the single-compartment case explicit expressions are given for this interparticle correlation, and hence for the variability of the model, while in the multicompartment setting increased variability of many models is shown to be a consequence of exchangeability and de Finetti's theorem.

[1]  L. Shenton,et al.  Study of age dependent half-life of iodine in man: A reinforcement-depletion urn model , 1985 .

[2]  P. Purdue,et al.  Non-linear compartmental systems: Extensions of S.R. Bernard's urn model , 1985 .

[3]  M. Faddy Nonlinear stochastic compartmental models. , 1985, IMA journal of mathematics applied in medicine and biology.

[4]  Keith Godfrey,et al.  Compartmental Models and Their Application , 1983 .

[5]  L. Shenton A reinforcement depletion urn problem—II. Application and generalization , 1983 .

[6]  M. Faddy,et al.  Ovarian follicle dynamics in mice: a comparative study of three inbred strains and an F1 hybrid. , 1983, The Journal of endocrinology.

[7]  Sheldon M. Ross,et al.  Stochastic Processes , 2018, Gauge Integral Structures for Stochastic Calculus and Quantum Electrodynamics.

[8]  P. Purdue Variability in a single compartment system: A note on S. R. Bernard's model , 1981 .

[9]  James H. Matis,et al.  Compartmental models with multiple sources of stochastic variability: The one-compartment models with clustering , 1981 .

[10]  On stochastic compartmental modeling , 1979 .

[11]  James H. Matis,et al.  Stochastic Models of Compartmental Systems , 1979 .

[12]  J. Kingman Random partitions in population genetics , 1978, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[13]  S. R. Bernard An urn model study of variability within a compartment , 1977 .

[14]  Peter Purdue,et al.  A semi-markov approach to stochastic compartmental models , 1977 .

[15]  M. J. Faddy,et al.  A Note on the General Time-Dependent Stochastic Compartmental Model , 1976 .

[16]  B. E. Rodda,et al.  The One-compartment Open Model: Some Statistical Aspects of Parameter Estimation , 1975 .