Spring Seminar Series - April 3, 2003
University of
Minnesota
School of Statistics
College of Liberal
Arts
Filtering for Point Processes and Its Applications
Zhiyi Chi
Department of Statistics
The University of Chicago
Thursday, April 3, 2003
4:00 PM, 115
Ford Hall
Minneapolis, East Bank Campus
Social at 3:30 PM, 300
Ford Hall
Abstract
In many applications, pattern detection can be formulated as searching for
clusters of points (``targets'') that exhibit a certain temporal and/or spatial
pattern from data, I will describe a solution to the detection problem
using linear filtering. The data is regarded as a series of delta functions
and convolved with various filters. Targets are located by peaks in the
filter responses. Under a mixture Poisson model for the temporal and/or
spatial distribution of the points, each convolution is equivalent to a likelihood-ratio-based
test. I will show applications of the filtering approach in acoustic detection
and neuroscience, especially in detection of replayed pattern in spontaneous
sleep neuronal activity.