W 9/3 and F 9/5: Topics from this write-up. Thumbtacks, coin-tossing, Persi's conjecture, fine-grain principle, local uniformity principle; predictions from local uniformity principle, asteroid near-misses.
M 9/8: Benford's law. Mixing physical objects. Experiment 1.
W 9/10: Mathematics of card shuffling (write-up is sketchy).
F 9/12: Endowment effect, risk aversion in games of chance,
failure of invariance. Experiment 2.
M 9/15: Anchoring, Probability matching,
conservatism and base rate discounting, conjunction fallacy (write-up is very sketchy).
W 9/17 and F 9/19: The long term and the Kelly criterion;
one safe and one risky asset..
M 9/22: mean-variance analysis.
W 9/24: Coincidences in Wikipedia.
F 9/26 Lester Mackey
will talk about his work on the Netflix Prize project.
M 9/29: Student talks
W 10/1: Student talks
F 10/3: Student talks
M 10/6: Student talks
W 10/8 : Normal approximation for data - is it realistic?
F 10/10 : Categorical data with many categories. And just for fun,
Washington Scandals and Baby Names
M 10/13 and W 10/15: Genetics: not paint mixing, advantageous mutations,
just-supercritical Galton-Watson process, phase transitions and scaling laws.
F 10/17 : Neutral theory, Wright-Fisher model,
diversity formula, time to MRCA.
M 10/20 : Coding as compression or encryption;
asymptotic equipartition property.
W 10/22 : Entropy as optimal coding rate.
Lempel-Ziv algorithms.
F 10/24 : Language trees and zipping
with critique and rejoinder.
And Coincidences and near-misses.
M 10/27 : Size-biasing and
Social Networks and the Diffusion of Economic Behavior.
W 10/29 : Network models;
overview and specified degree distribution.
F 10/31 : Epidemic and product adoption models over
social networks..
M 11/3 : A comparative analysis of influenza vaccination programs.
W 11/5 : Topics from Global Catastrophic Risks; supervolcanos and
Evidence for cometary bombardment episodes.
F 11/7 : [no class]
M 11/10 : Can you visualize a 1 in a million chance?
W 11/12 : Game theory and evolutionary dynamics. Prisoners dilemma,
Hawk-Dove, battle of the sexes [from Haigh].
F 11/14 :
Streaky hitting in baseball.
M 11/17 :
A Brownian Motion Model for the Progress of Sports Scores and
On Probabilistic Excitement of Sports Games.
W 11/19 : Spatial random networks.
F 11/21 [no class]
M 11/24 Student talks
W 11/26 Student talks
M 12/1 Student talks
W 12/3 Student talks
F 12/5 Student talks
M 12/8 Student talks
[extra class] Tuesday 12/9, 4.00pm - 5.10pm. Student talks.
W 12/10 Student talks
1. Style of course. Risks: in everyday life [Ropeik-Gray] and specific to UCB. Psychology of risks [Nickerson] - are people rational or irrational?
2. Mixing and sorting: physical objects and computer algorithms. Card shuffling; riffle shuffle as inverse of a sorting algorithm. 1970 draft lottery; mixing business cards.
3. Sports (focused on later analogy with stock market). Two approaches to prediction: use previous match results or use individual player stats (fantasy leagues). (analogous to technical/fundamental analysis of stocks). Randomness within-game and randomness over a season. Regression analysis of latter.
4. Physical randomness and the fine-grain principle [my Chap 1 handout]. Cards, coin-tossing, Benford's law. Informationless priors and estimation of future durations . Griffiths-Tenenbaum paper; lifetime of Berlin Wall, Microsoft, Homo Sapiens.
5. Game theory. Rock-paper-scissors, GOPS, Swedish lottery. Hawk-Dove, battle of the sexes [from Haigh].
6. Psychology of probability. [Nickerson]. Examples of: anchoring; conservatism vs base rate discounting; invariance, domination, framing; probability-matching; endowment; conjunction fallacy.
7-8. Stock market. What is "market", "stock". Data on monthly returns. Competing explanations of why/how prices fluctuate. IID model and Kelly criterion. Rough examples in optimal stock-bond allocation. How small a day-day serial correlation could be exploited? Different forms of efficient market hypothesis.
9-11. Critial points and scaling laws. Physics analogy of freezing + boiling. Queueing and Galton-Watson branching processes as basic examples; calculation of their scaling exponents. Contact process. Use of Erdos-Renyi random graph as epidemic model. Self-organized criticality in epidemic/forest fire model.
12. Complex networks and random graphs. My MSRI slides plus chalk-talk on 3 basic properties and examples.
13. Transportation networks.
14. Algorithms: counting and sampling. Elementary examples, working up to Markov Chain Monte Carlo for number of c-colorings of a graph G.
15. Coding, randomness and entropy. Basic math theory, emphasising Asymptotic Equipartition Property. Shannon codes. Lempel-Ziv and language-tree paper.
16. Genetics. Illustrate by calculation of chance you're genetically related to a particular 10th generation ancestor.
17. What maintains genetic diversity?. Selective sweeps, neutral theory, Wright-Fisher; 1+ 4 theta formula.
18. Time since most recent common ancestor in constant-size or in growing populations. Significance of 150K years since mitichondrial Eve; and of 500K years since split with Neanderthal.
19. Phylogenetic trees. My talk on overhead slides.
20. Food webs. Predator-prey graph; connection with body size.
21. Probability and the law. SIDS case in U.K. Island problem [from Senn]. Aligning lawyer and client interest [Polinsky-Rubinfeld paper].