Heavy tails

Weird things about rare massive events

January 13, 2020 β€” September 18, 2021

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. πŸ—

Figure 1

1 Incoming

2 References

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