Identification of stochastic systems with random parameters with particular reference to the recirculating lymphocytes in the immune system Public Deposited

http://ir.library.oregonstate.edu/concern/graduate_thesis_or_dissertations/5q47rs54v

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  • This thesis is composed of four parts: i) system description, ii) model development, iii) parameter estimation, and iv) validation. The natural system used here is an aspect of the immune system, namely, the distribution of recirculating lymphocytes in various organs throughout the body. This distribution gains importance because: i) it is consequential in effective defense of the body, and ii) lymphocyte maldistribution may be a symptom of a disease state. Certain deterministic models of lymphocyte distribution have been published previously. Here, discrete-time and continuous-time stochastic models are developed. The class of models studied here are closed compartmental. The derived structures are a vector bilinear time series with two inputs (or random coefficient autoregression) and a vector stochastic differential equation, respectively, for the discrete and the continuous cases. Various properties of the solutions are studied. Parameter estimation for a 7-compartment system is done using nonlinear optimization with weighted least squares and -2 In likelihood criteria (assuming Gaussianity for convenience, though not completely realistic). The outputs of the models are statistically examined against best available experimental data. The residual errors are analyzed for proximity of fit, validity of the models, Gaussianity, and stationarity. Multiple comparisons are performed to test lack of fit of individual compartments and in so doing major sources of error in estimation are assessed. The particular class of models studied here are structurally unstable. The means are marginally stable and for the estimated values of the parameters the variances diverge.
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  • File scanned at 300 ppi (Monochrome) using Capture Perfect 3.0.82 on a Canon DR-9080C in PDF format. CVista PdfCompressor 4.0 was used for pdf compression and textual OCR.
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