Plenary Talk

Title: On block designs useful in sampling
Presenter: Professor John Stufken, Department of Statistics, University of Georgia, USA
Abstract:

Connections between sampling plans and block designs have been known for a long time. In this presentation we will focus on block designs that have been studied due to their connection to Balanced Sampling Plans for Excluding Contiguous Units, which were introduced in Hedayat, Rao, and Stufken (JSPI, 1988). Such a block design for $v$ varieties, $k$ blocks ($k < v$) and minimum distance $\alpha + 1$ is a binary block design in which varieties $i$ and $j$ appear together in precisely $\almbda$ blocks, say, if $\alpha < | i - j | < v - \alpha$, while they do not appear together in any block otherwise. For $\alpha = 0$, this class of designs consists precisely of the class of balanced incomplete block designs, while the designs are partially balanced incomplete block designs for $\alpha > 0$. The presentation will provide a brief overview of our current knowledge of these designs. The focus will be on the existence and construction of these designs for $\alpha > 0$, on extensions to higher dimensions, and on open problems.