Statistics Colloquium

Speaker:
Dr. Tatiyana V. Apanasovich
Associate Professor
Department of Statistics

Data indexed by spatial coordinates have become ubiquitous in a large number of applications, for instance in environmental, climate and social sciences, hydrology and ecology. Recently, the availability of high resolution microscopy together with advances in imaging technology has increased the importance of spatial data to detect meaningful patterns as well as to make predictions in medical applications (brain imaging) and systems biology (images of fluorescently labeled proteins, lipids, DNA). The defining feature of multivariate spatial data is the availability of several measurements at each spatial location. Such data may exhibit not only correlation between variables at each site, but also spatial correlation within each variable and spatial cross-correlation between variables at neighboring sites.  Any analysis or modeling must therefore allow for flexible, but computationally tractable specifications for the multivariate spatial effects processes. In practice we assume that such processes, probably after some transformation, are not too far from Gaussian and characterized well by the first two moments. The model for the mean follows from the context. However, the challenge is to find a valid specification for cross-covariance matrices which is estimable, and yet flexible enough to incorporate a wide range of correlation structures.