Ph.d Research Proposal Data Models and Estimation Accuracy in Stereology

1 Proposed Study Stereology, a form of sampling theory, is a group of statistical methods used for estimating properties such as volume and surface area of a three-dimensional object using information only available on a two-dimensional plane section through the object 2, 9]. It has applications in many areas of science, in particular anatomy, geology and materials science 2]. Conceptually, stereological methods are analogous to a survey sampling problem where the three-dimensional object is considered as the \popula-tion" and the two-dimensional plane sections taken from it are \samples" from which we obtain information for estimating certain population parameters of interest 2]. Many stereological estimators have been developed for the quantities of interest for example, the volume fraction, V V and the surface area fraction, S V. However, the existing sampling theory does not provide information about the accuracy of these estimators. Further, little is known about the statistical modelling and analysis of stereological data. Hence, this project aims to develop new theories for the precision of estimators and the statistical modelling of stereological data. The main aims of the project are To develop a statistical modelling approach to the analysis of stereological data, particularly discrete count data obtained from diierent kinds of sampling designs.