PLACE: 319 Snedecor Hall

SPEAKER:
Grace Chan
Department of Statistics
University of Iowa

TITLE:
A Statistical Application of Fractal Geometry

ABSTRACT:

In two consulting projects, measurement of surface height of some materials were recorded and the investigator wants to find out how "smooth" these materials' surfaces are. These data sets will be introduced at the beginning of this talk. Together with other examples, they demonstrate that considering dimension taking integer values only cannot fully describe their properties. Mandelbrot and others have studies some of these examples for a long time and called them fractals, objects with non-integer dimension.
We will briefly review how they define and calculate these fractal dimensions. And then we will discuss how to estimate fractal dimension from random fractal objects such as sample paths of Gaussian random fields. Properties of these estimators will also be included. Finally the result of the analyses of the data sets, which were introduced at the beginning of this talk, will be presented.
 

COFFEE: 3:45 p.m., 104 Snedecor Hall