1. Sta 114, spring 2008 Probability and statistics Instructor: Sayan Mukherjee TA: Quanlin Li STAT 113

2. Sta 114, spring 2008 There are three kinds of lies: lies, damned lies, and statistics. B. Disraeli Perspectives on stats

3. Sta 114, spring 2008 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 114, spring 2008 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 114, spring 2008 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 114, spring 2008 Class requirements and rules Course webpage

7. Sta 114, spring 2008 First digits 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 114, spring 2008 What’s wrong with the heartland ?

9. Sta 114, spring 2008 It’s the emptiness

10. Sta 114, spring 2008 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 114, spring 2008 The geometry of Gaussian random variables A Gaussian distribution:

12. Sta 114, spring 2008 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 114, spring 2008 Law of large numbers or central limit theorem The previous observation is a special case of the following phenomena:

14. Sta 114, spring 2008 Geometry of real data t Digits in space Digits in space Digits in space t Mandarin tones Mandarin tones Mandarin tones

15. Sta 114, spring 2008 Regression -- pedestrian detection Papageorgiou and Poggio, 1998

16. Sta 114, spring 2008 Daimler Chrysler

17. Sta 114, spring 2008 Experimental Mercedes A fast version, integrated with a real-time obstacle detection system MPEG Constantine Papageorgiou

18. Sta 114, spring 2008 People classification/detection Stuttgart

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

20. STA 293 03, fall 2005 More regression: talking faces Hunter Its automatic Today show

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