Download lec1 - Department of Statistical Science

STAT 113
Probability and Statistics for
Engineering
Instructor: Sayan Mukherjee
TAs: N. Pillai, H. Wang
Sta 113, fall 2006
Perspectives on stats
There are three kinds of lies: lies, damned lies, and statistics.
B. Disraeli
Sta 113, fall 2006
What is probability ?
Probability is a branch of mathematics that deals with
calculating the likelihood of a given event's occurrence,
which is expressed as a number between 1 and 0.
Sta 113, fall 2006
What is statistics ?
Statistics derives from: Latin -- statisticum collegium ("council of state")
Italian -- statista ("statesman" or "politician").
Statistik: German first introduced by Gottfried Achenwall (1749), originally
designated the analysis of data about the state, or the
"science of state". Acquired the meaning of the collection
and classification of data generally in the early 19th century.
Statistics as inverse probability -- estimating parameters from experimental
data
Sta 113, fall 2006
Well-posed problems
Inverse problems are typically ill-posed
A problem is well-posed if its solution
• exists
• is unique
• is stable, eg depends continuously on the data
Sta 113, fall 2006
Class requirements and rules
Course webpage
Sta 113, fall 2006
First digits
http://en.wikipedia.org/wiki/List_of_world_records
Count entries starting with:
{1,2,3,4,5,6,7,8,9}
Count entries ending with:
{1,2,3,4,5,6,7,8,9}
Accounting fraud
Sta 113, fall 2006
What’s wrong with the heartland ?
Sta 113, fall 2006
It’s the emptiness
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The geometry of randomness
Dido’s problem (Isoperimetry) : Among all closed level curves
of fixed length, find the one that encloses the largest
area.
A
Sta 113, fall 2006
A
The geometry of Gaussian random variables
A Gaussian distribution:
Sta 113, fall 2006
The geometry of Gaussian random variables
A draw of n Gaussian random variables is a point in an ndimensional space. How far from the origin is this point ?
x  x12  x 22  ... x n2
For n large the answer is that with very high probability

Sta 113, fall 2006
x
c
c
1

1
n
n
n
Law of large numbers or central limit theorem
The previous observation is a special case of the following
phenomena:
Given a smooth function of
n variables
x  (x1,..., x n ) the following is true


Pr f x    x f x   h  C1 exp C2 h 2 n .
x1  x 2  ... x n
A classic example : f (x) 
.
n
Sta 113, fall 2006
Regression -- pedestrian detection
Sta 113, fall 2006
Papageorgiou and Poggio, 1998
Daimler Chrysler
Sta 113, fall 2006
Experimental Mercedes
A fast version, integrated
with a real-time obstacle
detection system
MPEG
Sta 113, fall 2006
Constantine Papageorgiou
People classification/detection
Stuttgart
Sta 113, fall 2006
More regression: talking faces
Text-to-visual-speech (TTVS) systems:
Movies in faces directory
STA 293 03, fall 2005
More regression: talking faces
Text-to-visual-speech (TTVS) systems:
Movies in faces directory
STA 293 03, fall 2005
Descriptive statistics and visualization
Click on mandarin in visual
Click on mandarin in visual
STA 293 03, fall 2005
Conclusion
Statistics is about predictive modeling that quantifies
uncertainty
There are known knowns; there are things we know we
know. We also know there are known unknowns; that is
to say we know there are some things we do not know.
---- Donald Rumsfeld
STA 293 03, fall 2005