BUEHLER-MARTIN DISTINGUISHED LECTURER SERIES - March 20, 22, and
23, 2006
University of Minnesota
School of Statistics
College of Liberal Arts
Some
Remarks About Spatial Correlation of Crop Yields
Peter McCullagh
Department of Statistics
University of Chicago
Monday, March 20, 2006
3:30 PM, 131
Physics
Minneapolis, East Bank Campus
Social at 3:00 PM, 300 Ford Hall
Abstract
It
is universally acknowledged that crop yields on nearby plots
are more similar than yields on plots that are far apart.
One consequence of spatial correlation is that the sample variance
of yields for a block of n contiguous plots increases
with n.
In other words, small blocks are more homogeneous than large blocks.
The implications of this fact were apparent to Fisher and Yates
in their development of the theory of efficient statistical design.
Many researchers have speculated about the causes of spatial
correlation, and a few have even gone to the effort of conducting
uniformity trials to study its nature.
The best known empirical study of this sort,
involving 40 trials of various crops in various parts of the world,
was undertaken by Fairfield Smith (1938),
and led to the celebrated power law for variance as a function of
block size. This talk describes a more recent empirical study following
on from
Fairfield Smith, but focusing on geometric properties of agricultural
processes.
These include stationarity, isotropy and an additional geometric
concept called conformal invariance, which implies that spatial
correlations decay at a logarithmic rate.
The aim of the study is to see whether the pattern for some or
any crops follows this rule, and at what scales.