1. Sta 113, fall 2006 Probability and Statistics for Engineering Instructor: Sayan Mukherjee TAs: N. Pillai, H. Wang STAT 113

2. Sta 113, fall 2006 There are three kinds of lies: lies, damned lies, and statistics. B. Disraeli Perspectives on stats

3. 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.

4. 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

5. 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

6. Sta 113, fall 2006 Class requirements and rules Course webpage

7. 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

8. Sta 113, fall 2006 What’s wrong with the heartland ?

9. Sta 113, fall 2006 It’s the emptiness

10. 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.

11. Sta 113, fall 2006 The geometry of Gaussian random variables A Gaussian distribution:

12. 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 ? For n large the answer is that with very high probability

13. Sta 113, fall 2006 Law of large numbers or central limit theorem The previous observation is a special case of the following phenomena:

14. Sta 113, fall 2006 Regression -- pedestrian detection Papageorgiou and Poggio, 1998

15. Sta 113, fall 2006 Daimler Chrysler

16. Sta 113, fall 2006 Experimental Mercedes A fast version, integrated with a real-time obstacle detection system MPEG Constantine Papageorgiou

17. Sta 113, fall 2006 People classification/detection Stuttgart

18. STA 293 03, fall 2005 More regression: talking faces Text-to-visual-speech (TTVS) systems: Movies in faces directory

19. STA 293 03, fall 2005 More regression: talking faces Text-to-visual-speech (TTVS) systems: Movies in faces directory

20. STA 293 03, fall 2005 Descriptive statistics and visualization Click on mandarin in visual

21. 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