| Consider observations y1, ..., yn associated with locations 1, 2, ..., n, respectively, where yi is assumed to come from a N(thetai, sigma 2) distribution. We assume that an unknown partition divides the n observations into contiguous components or blocks. For all locations i within a block S, the means theta i are assumed to be equal. The change point problem involves estimating the means i and the underlying partition. Other distributions have been studied from both frequentist and Bayesian points of view. This thesis studies change point problems in which data are available at each node of a graph. A regression model is assumed to apply within each block of a partition of the graph. We use Bayesian methods to estimate the partition and the regression coefficients in each block. We consider particular examples including partitions of a line, partitions of a two-dimensional grid, and partitions of a minimum spanning tree. |
