Sta 113, fall 2006
Probability and Statistics for Probability and Statistics for Engineering Engineering
Instructor: Sayan MukherjeeTAs: N. Pillai, H. Wang
STAT 113
Sta 113, fall 2006
There are three kinds of lies: lies, damned lies, and statistics.
B. Disraeli
Perspectives on stats
Sta 113, fall 2006
What is probability ?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 ?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
A problem is well-posed if its solution
• exists
• is unique
• is stable, eg depends continuously on the data
Inverse problems are typically ill-posed
Sta 113, fall 2006
Class requirements and rulesClass requirements and rules
Course webpage
Sta 113, fall 2006
First digitsFirst 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 ?What’s wrong with the heartland ?
Sta 113, fall 2006
It’s the emptinessIt’s the emptiness
Sta 113, fall 2006
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
A
Sta 113, fall 2006
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 n-dimensional space. How far from the origin is this point ?
x x12 x2
2 ... xn2
For n large the answer is that with very high probability
1c
nx
n1
c
n
Sta 113, fall 2006
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,...,xn ) the following is true
Pr f x x f x h C1 exp C2h2n .
A classic example : f (x) x1 x2 ... xnn
.
Sta 113, fall 2006
Regression -- pedestrian detection
Papageorgiou and Poggio, 1998
Sta 113, fall 2006
Daimler ChryslerDaimler Chrysler
Sta 113, fall 2006
Experimental MercedesExperimental Mercedes
A fast version, integrated with a real-time obstacle
detection system
MPEG
Constantine Papageorgiou
Sta 113, fall 2006
People classification/detectionPeople classification/detection
Stuttgart
STA 293 03, fall 2005
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
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