Research |
Some Statistical Research that Michigan
professors are involved in
 Prof.
Julian Faraway builds statistical models for understanding and predicting
human motion. He is associate director of the
Human Motion Simulation Laboratory known as HuMoSim. “We use
motion capture technology to record the position of markers attached to the
body during motion. Our data consist of the 3D traject ories
of these markers. The challenge is to model such data. We aim to understand
how factors such as height, weight, age and gender affect
motion and to predict new motions. My prediction algorithms are currently
being implemented in Digital Human modeling software such as
Jack and
Safework.
Julian Faraway
faraway@umich.edu
Helping People with Substance Abuse
 Susan
Murphy (Professor and Senior Research Scientist at the Institute for Social
Research ISR) states that you can use statistics to help prevent
substance abuse by high-risk adolescents and to help design
treatments for cocaine abusers. “We use statistics to figure out how to
treat people in a tailored-individualized manner. Different people need
different amounts of treatment and the amount of treatment may vary by other
things going on in their lives (like whether or not they live near drug
dealers and whether or not they a re
getting into big arguments with their parents). How do we do this? We use
statistics to discover what information we should use to decide when and how
to increase our preventive
efforts (like is it really important that you are not getting along with
your parents in
determining whether you will be tempted to overdose on cocaine?). We also
use statistics to
discover the best way to use information (like if you are a high risk kid
and you just got
into a very big row with your parents, is it useful to try to encourage you
to meet with a counselor?).” Statistics is a great way to make
mathematics useful!
Susan Murphy
samurphy@umich.edu
 We
use statistics
in a variety of legal settings. Some examples are the study employment
discrimination, product liability, and in the assessment of damages.
Employment cases can involve gender, race,
and age factors. For
each of these factors, allegations of discrimination
may be found in a
variety of contexts from hiring, to promotion, and to salary increase. At
the heart of each discrimination allegation, we find data describing the
impact of policies and procedures used by individuals within an
organization. The statistician seeks to determine whether the data are
consistent with policies and practices that are neutral to the factors
protected by law. Critical to the analysis is that we attempt to compare
data for comparably situated people but for the factor in question. The
example below shows promotion rates for men appear ---in aggregate ---to be
lower than for women, but higher for every salary grade level.
|
|
Overall % Promoted |
Low Salary Grade
Level |
High Salary Grade
Level |
|
|
% Promoted |
Proportion at low
level |
% Promoted |
Proportion at high
level |
Men
|
10% |
30% |
1/11 |
8% |
10/11 |
|
Women |
20% |
22% |
7/8 |
6% |
1/8 |
Ed
Rothman
erothman@umich.edu
 Suppose
you flip a fair coin 12 times and observe the sequence of Heads and Tails is
HHHHHHTTTTTT. Would that particular sequence surprise you? How about if you
observe the sequence HTHHTHTTTHTH? Does the second sequence look more random
than the first? What if instead of coin flips you observe a basketball
player's sequence of shots (Hit versus Miss)? Would you say there is a
difference between the basketball player who produces the sequence
HHHHHHMMMMMM versus the player who produces the sequence HMHHMHMMMHMH?
Statistics can inform us
of what the actual likelihood of such sequences occurring and we can compare
the "right answer" to people's judgments to see if people have systematic
biases. If
these types of biases exist they may lead to incorrect perceptions about
phenomena. For example, the perception of clusters or patterns that aren't
really there in the sense that they are consistent with what would be
expected by chance. Such "false clusters" have been observed in
people's perceptions of bombing clusters during World War II, the perception
that celebrities "die in threes", and the perception of some disease
outbreaks.
Rich Gonzalez
gonzo@umich.edu
·
Statistical
methods play a major role in industries
– automotive, electronics, textile, chemical, etc.
·
Engineers use
statistical methods to optimize product and process design, to improve
quality and reliability of products, to identify customer needs through
market studies, to estimate warranty costs, determine optimal maintenance
schedules, …
·
Businesses use
statistical techniques to identify good marketing strategies, to profile
customers (separate good customers from high-risk ones), to detect fraud,
etc.
·
Our department
has many faculty members who are working in these areas.
Role of
Statistics in Manufacturing
Vijay Nair
vnn@umich.edu
Statistics in Molecular
Biology
Cells are incredibly complex entities built out of thousands
of different molecular parts. Until recently, statistics played a small
role in studying cells at the molecular level because it was not possible to
experimentally measure the internal state of a cell in a comprehensive way.
In the last 10 years, huge advances in measurement have been made and it is
now possible to obtain a reasonably complete snapshot of the
molecular state of a cell at a given point in time. A single such
experiment may generate hundreds of thousands of data points, which are very
noisy as small quantities of biological material are being measured. One
challenge for statisticians is to screen through such huge volumes of data
to determine which of a cell's parts are altered in diseased cells,
such as cancer cells. Careful statistical analysis is critical to
scientific progress since identifying the wrong candidate may lead
laboratory scientists down the wrong path, costing years of research time
and large amounts of money.
Kerby Shedden kshedden@umich.edu
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