Date of Award
Doctor of Philosophy
The growth patterns of cell tumors may be modelled stochastically by a multi-type lattice interacting particle system. The process is Markovian in time with spatial nearest-neighbor interactions. The cell population growth depends on several numerical parameters. These parameters specify the fission rates for individual cells and the types of resulting offspring cells.;Experimental methodology allows such a process to be observed at a specific time. It is assumed that the data obtained at this time is in the form of counts of cells of different types and locations. Based on such data, it is shown that certain statistics such as cell counts, counts of "boundary" cells and various neighborhood statistics are useful in identifying and estimating the parameters of the simplest systems. These results are obtained through a combination of analytical and numerical techniques.;A local inverse regression procedure is described for obtaining approximate moment estimators. It is demonstrated that the moments of the process are continuous in the parameters using a coupling argument. Coupling results are used to investigate other properties in the one type case.;Differential equations are derived for the moments of counts for the one and two type systems. These are integrated numerically and are used to obtain estimators for the parameters when observations are available from independent processes at different times. Consistency of these estimators is demonstrated in some cases.;Some in vivo data from the biological literature which is in the form of tumor volumes only is used to demonstrate the adequacy of the interacting particle model.
Braun, Willard J., "Statistical Inference For An Interacting Particle System" (1991). Digitized Theses. 2087.