Heavy tails

Weird things about rare massive events

January 13, 2020 — September 18, 2021

point processes

Heavy tailed RVs do some weird things that make them unintuitive. I should collect a list of what. See also densities and intensities, survival analysis, extreme value theory, risk management

Also, should list the many diverse phenomena that are associated, e.g. fractals etc. 🏗

Figure 1

1 Incoming

2 References

Asmussen, Binswanger, and Højgaard. 2000. Rare Events Simulation for Heavy-Tailed Distributions.” Bernoulli.
Asmussen, and Kroese. 2006. Improved Algorithms for Rare Event Simulation with Heavy Tails.” Advances in Applied Probability.
Chatfield, Lempitsky, Vedaldi, et al. 2011. The Devil Is in the Details: An Evaluation of Recent Feature Encoding Methods.”
Cirillo, and Taleb. 2020. Tail Risk of Contagious Diseases.” Nature Physics.
Crane, Schweitzer, and Sornette. 2010. Power Law Signature of Media Exposure in Human Response Waiting Time Distributions.” Physical Review E.
de S. Cavalcante, Oriá, Sornette, et al. 2013. Predictability and Suppression of Extreme Events in a Chaotic System.” Physical Review Letters.
Dinh, Ho, Nguyen, et al. 2016. Fast Learning Rates with Heavy-Tailed Losses.” In NIPS.
Embrechts, Lindskog, and McNeil. 2003. Modelling Dependence with Copulas and Applications to Risk Management.” Handbook of Heavy Tailed Distributions in Finance.
Gnecco, Meinshausen, Peters, et al. 2021. Causal Discovery in Heavy-Tailed Models.” The Annals of Statistics.
Grinstein, and Linsker. 2008. Power-Law and Exponential Tails in a Stochastic Priority-Based Model Queue.” Physical Review E.
Gudmundsson, and Hult. 2014. Markov Chain Monte Carlo for Computing Rare-Event Probabilities for a Heavy-Tailed Random Walk.” Journal of Applied Probability.
Harvey, and Luati. 2014. Filtering With Heavy Tails.” Journal of the American Statistical Association.
Lux, and Sornette. 2002. On Rational Bubbles and Fat Tails.” Journal of Money, Credit and Banking.
Markovitch, and Krieger. 2002. The Estimation of Heavy-Tailed Probability Density Functions, Their Mixtures and Quantiles.” Computer Networks.
McNeil. 1997. Estimating the Tails of Loss Severity Distributions Using Extreme Value Theory.” ASTIN Bulletin: The Journal of the IAA.
Sodin. 2007. Tail-Sensitive Gaussian Asymptotics for Marginals of Concentrated Measures in High Dimension.” In Geometric Aspects of Functional Analysis.
Sornette. 2003. Critical Market Crashes.” Physics Reports.
———. 2009. Dragon-Kings, Black Swans and the Prediction of Crises.” arXiv:0907.4290 [Physics].
Sornette, and Cauwels. 2015. Managing Risk in a Creepy World.” Journal of Risk Management in Financial Institutions.
Stowell, Gill, and Clayton. 2016. Detailed Temporal Structure of Communication Networks in Groups of Songbirds.” Journal of The Royal Society Interface.
Taleb. 2013. Where Do Thin Tails Come From? arXiv:1307.6695 [Physics, q-Fin, Stat].
———. 2020. On the Statistical Differences Between Binary Forecasts and Real-World Payoffs.” International Journal of Forecasting.
Vázquez, Oliveira, Dezsö, et al. 2006. Modeling Bursts and Heavy Tails in Human Dynamics.” Physical Review E.
Weitzman. 2011. Fat-Tailed Uncertainty in the Economics of Catastrophic Climate Change.” Review of Environmental Economics and Policy.
Wheatley, Sovacool, and Sornette. 2017. Of Disasters and Dragon Kings: A Statistical Analysis of Nuclear Power Incidents and Accidents.” Risk Analysis.
Zhou, and Sornette. 2002. Statistical Significance of Periodicity and Log-Periodicity with Heavy-Tailed Correlated Noise.” International Journal of Modern Physics C.