PREDICTABILITY. THEORY and APPLICATIONS

PREDICTABILITY. THEORY and APPLICATIONS PHYS 480

2013 Winter

Instructor: Péter Érdi, Henry R. Luce Professor Office: OU 208/B. Email: [email protected] TA: Judit Szente, Email: [email protected] Class time: MW 2.40-3.55pm Classroom: Dow 108 Goal: We will learn the scope and limits of scientific methods to make statements about future events. Concepts and techniques of three disciplines, namely of nonlinear dynamics, of statistics of random processes and of machine learning will be discussed. Applications for natural and social phenomena will be presented. Extreme events both in nature and society, such as earthquakes, landslides, wildfires, solar flares, stock market crashes, the destruction of very tall tower buildings, engineering failures, outbreaks of epidemics etc. may appear to be surprising phenomena whose occurrence does not follow any rules. Of course, such kinds of extreme events are rare, but they influence our everyday lives dramatically. Can we understand, assess, predict and maybe control these events? Prerequisite: The class is for advanced seniors. Sophomores and juniors with strong science background can take it with permission. Course structure: The class is mostly lecture-based. There will be weekly quiz questions. Weekly Student reports – discussion forums (week 2-9). 1. Introduction: looking into the past predicting the future 2. Dynamic Models Basic Dynamic Phenomena. From linear to nonlinear world view. Predicting periodicity. Positive and negative feedback. Self-organized criticality: concepts, phenomena and numerical simulations.

3. Statistics of random processes Binomial, Gaussian, distributions.

Poisson,

exponential,

log-normal

and

power

law

Random walk. The Efficient Market Hypothesis. Black Swans, Dragon Kings, and Prediction of Crises. Power law distributions in natural and social systems. Stock market crashes: large deviation from the Gaussian distribution. Wealth and income distributions: the Pareto distribution. Extreme events: widening the limits of predictability. Dragon King outliers: Bose-Einstein condensates. Paris and the distribution of the French city sizes. Avalanche Models for Solar Flares. Intermittent criticality: simulation and statistical evaluation. 4. Bayesian approach: between statistics and machine learning Reasoning under uncertainty. Bayes theorem. Bayesian decision theory. How to be a good Bayesian 5. Machine learning One view of machine learning is that it is about how to program computers to predict well. Machine learning algorithms: an overview Predicting dynamics: Kalman filter

Student reports - discussion forum: selected chapters of the Silver book. (financial crisis: Ch1; weather forecasts: Ch4; earthquakes: Ch5; Epidemics: Ch7, Bayesian analysis: Ch8; market: Ch11, Climate: Ch12; Terrorism: Ch13. Readings: Didier Sornette: Dragon-Kings, Black Swans and the Prediction of Crises http://arxiv.org/pdf/0907.4290v1 Markus Aschwanden: Self-Organized Criticality in Astrophysics. http://geza.kzoo.edu/~erdi/SOC-astr/ Nate Silver: The Signal and the Noise: Why So Many Predictions Fail — but Some Don't Penguin Press HC, 2012 Charbonneau, P., McIntosh, S.W., Liu, H.-L., & Bogdan, T.J. 2001, Avalanche Models for Solar Flares. Solar Physics, 203, 321

http://geza.kzoo.edu/~erdi/solar/charbonneau01.pdf C Chen, YT Lee, LY Chiao. Intermittent criticality in the long-range connective sandpile (LRCS) model. Physics Letters A, 2008 372(4340-4343) YT Lee, C Chen, T Hasumi, HL Hsu: Precursory phenomena associated with large avalanches in the long-range connective sandpile model II: An implication to the relation between the b-value and the Hurst exponent in seismicity. Geophysical Research Letters, 2009 http://www.csse.monash.edu.au/bai/tutorial/BOMJuly06.pdf Kalman filter: http://www.stanford.edu/class/ee363/lectures/kf.pdf Exam, grading: There will be a sixty minutes long written midterm and an oral exam. Grades are calculated based on quizes (25%), midterm exam (25%) and final (50%),