This thesis investigates Bayesian optimal design for change-point problems. While there is a large optimal design literature for linear and some non-linear problems, this is the first time optimality has been addressed for change-point problems. / In designing a longitudinal study, the decision as to when to collect data can have a large impact on the quality of the final inferences. If a change may occur in the distribution of one or more variables under study, the timing of observations can greatly influence the chances of detecting any effects. / Two classes of problems are considered. First, optimal design for the mixture of densities is investigated. Here, a finite sequence of random variables is available for observation. Each observation may come from one of two distributions with a given probability, which may differ from observation to observation. Such a problem may also be regarded as an application of the multi-path change point problem. Assume subjects may each undergo a single change at random change points with common before and after change point distributions, and at any instant a known proportion of the ensemble of paths will have changed. In either case, the goal is to select which data points to observe, in order to provide the most accurate estimates of the means of both distributions. / Second, we study optimal designs for more classical change point problems. We consider three cases: (i) when only the means of the before and after change point distributions are of interest, (ii) when only the location of the change point is of interest, and (iii) when both the change point and the means of the before and after change point distribution are of interest. / In addressing these problems, both analytic closed form solutions and modern statistical computing algorithms such as Monte Carlo integration and simulated an nealing are used to find the optimal designs. Examples that concern human growth patterns and changes in CFC-12 concentrations in the atmosphere are used to illustrate the methods.
| Identifer | oai:union.ndltd.org:LACETR/oai:collectionscanada.gc.ca:QMM.35667 |
| Date | January 1997 |
| Creators | Zhou, Xiaojie. |
| Contributors | Wolfson, D. (advisor), Joseph, L. (advisor) |
| Publisher | McGill University |
| Source Sets | Library and Archives Canada ETDs Repository / Centre d'archives des thèses électroniques de Bibliothèque et Archives Canada |
| Language | English |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
| Format | application/pdf |
| Coverage | Doctor of Philosophy (Department of Mathematics and Statistics.) |
| Rights | All items in eScholarship@McGill are protected by copyright with all rights reserved unless otherwise indicated. |
| Relation | alephsysno: 001658016, proquestno: NQ44662, Theses scanned by UMI/ProQuest. |
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