Heavy tails

Weird things about rare massive events



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 .illustration} :::

References

Asmussen, Søren, Klemens Binswanger, and Bjarne Højgaard. 2000. “Rare Events Simulation for Heavy-Tailed Distributions.” Bernoulli 6 (2): 303–22. https://doi.org/10.2307/3318578.
Asmussen, Søren, and Dirk P. Kroese. 2006. “Improved Algorithms for Rare Event Simulation with Heavy Tails.” Advances in Applied Probability 38 (2): 545–58. http://www.jstor.org/stable/20443455.
Chatfield, Ken, Victor Lempitsky, Andrea Vedaldi, and Andrew Zisserman. 2011. “The Devil Is in the Details: An Evaluation of Recent Feature Encoding Methods,” November. http://eprints.pascal-network.org/archive/00008315/.
Cirillo, Pasquale, and Nassim Nicholas Taleb. 2020. “Tail Risk of Contagious Diseases.” Nature Physics 16 (6): 606–13. https://doi.org/10.1038/s41567-020-0921-x.
Crane, Riley, Frank Schweitzer, and Didier Sornette. 2010. “Power Law Signature of Media Exposure in Human Response Waiting Time Distributions.” Physical Review E 81 (5): 056101. https://doi.org/10.1103/PhysRevE.81.056101.
Dinh, Vu, Lam Si Tung Ho, Duy Nguyen, and Binh T. Nguyen. 2016. “Fast Learning Rates with Heavy-Tailed Losses.” In NIPS. http://arxiv.org/abs/1609.09481.
Embrechts, Paul, Filip Lindskog, and Alexander J McNeil. 2003. “Modelling Dependence with Copulas and Applications to Risk Management.” Handbook of Heavy Tailed Distributions in Finance 8 (329-384): 1. https://people.math.ethz.ch/~embrecht/ftp/copchapter.pdf.
Gnecco, Nicola, Nicolai Meinshausen, Jonas Peters, and Sebastian Engelke. 2021. “Causal Discovery in Heavy-Tailed Models.” The Annals of Statistics 49 (3): 1755–78. https://doi.org/10.1214/20-AOS2021.
Grinstein, G., and R. Linsker. 2008. “Power-Law and Exponential Tails in a Stochastic Priority-Based Model Queue.” Physical Review E 77 (1): 012101. https://doi.org/10.1103/PhysRevE.77.012101.
Gudmundsson, Thorbjörn, and Henrik Hult. 2014. “Markov Chain Monte Carlo for Computing Rare-Event Probabilities for a Heavy-Tailed Random Walk.” Journal of Applied Probability 51 (2): 359–76. https://doi.org/10.1239/jap/1402578630.
Harvey, Andrew, and Alessandra Luati. 2014. “Filtering With Heavy Tails.” Journal of the American Statistical Association 109 (507): 1112–22. https://doi.org/10.1080/01621459.2014.887011.
Lux, Thomas, and Didier Sornette. 2002. “On Rational Bubbles and Fat Tails.” Journal of Money, Credit and Banking 34: 589–610. https://doi.org/10.2307/3270733.
Markovitch, Natalia M, and Udo R Krieger. 2002. “The Estimation of Heavy-Tailed Probability Density Functions, Their Mixtures and Quantiles.” Computer Networks 40 (3): 459–74. https://doi.org/10.1016/S1389-1286(02)00306-7.
McNeil, Alexander J. 1997. “Estimating the Tails of Loss Severity Distributions Using Extreme Value Theory.” ASTIN Bulletin: The Journal of the IAA 27 (1): 117–37. https://doi.org/10.2143/AST.27.1.563210.
S. Cavalcante, Hugo L. D. de, Marcos Oriá, Didier Sornette, Edward Ott, and Daniel J. Gauthier. 2013. “Predictability and Suppression of Extreme Events in a Chaotic System.” Physical Review Letters 111 (19): 198701. https://doi.org/10.1103/PhysRevLett.111.198701.
Sodin, S. 2007. “Tail-Sensitive Gaussian Asymptotics for Marginals of Concentrated Measures in High Dimension.” In Geometric Aspects of Functional Analysis, edited by Vitali D. Milman and Gideon Schechtman, 1910:271–95. Berlin, Heidelberg: Springer Berlin Heidelberg. https://doi.org/10.1007/978-3-540-72053-9_16.
Sornette, Didier. 2003. “Critical Market Crashes.” Physics Reports 378 (1): 1–98. https://doi.org/10.1016/S0370-1573(02)00634-8.
———. 2009. “Dragon-Kings, Black Swans and the Prediction of Crises.” arXiv:0907.4290 [physics] 2 (1). http://arxiv.org/abs/0907.4290.
Sornette, Didier, and Peter Cauwels. 2015. “Managing Risk in a Creepy World.” Journal of Risk Management in Financial Institutions 8 (1): 83–108. http://arxiv.org/abs/1401.3281.
Stowell, Dan, Lisa Gill, and David Clayton. 2016. “Detailed Temporal Structure of Communication Networks in Groups of Songbirds.” Journal of The Royal Society Interface 13 (119): 20160296. https://doi.org/10.1098/rsif.2016.0296.
Taleb, Nassim Nicholas. 2013. “Where Do Thin Tails Come From?” arXiv:1307.6695 [physics, q-Fin, Stat], July. http://arxiv.org/abs/1307.6695.
———. 2020. “On the Statistical Differences Between Binary Forecasts and Real-World Payoffs.” International Journal of Forecasting, April. https://doi.org/10.1016/j.ijforecast.2019.12.004.
Vázquez, Alexei, João Gama Oliveira, Zoltán Dezsö, Kwang-Il Goh, Imre Kondor, and Albert-László Barabási. 2006. “Modeling Bursts and Heavy Tails in Human Dynamics.” Physical Review E 73 (3): 036127. https://doi.org/10.1103/PhysRevE.73.036127.
Weitzman, Martin L. 2011. “Fat-Tailed Uncertainty in the Economics of Catastrophic Climate Change.” Review of Environmental Economics and Policy 5 (2): 275–92. https://doi.org/10.1093/reep/rer006.
Wheatley, Spencer, Benjamin Sovacool, and Didier Sornette. 2017. “Of Disasters and Dragon Kings: A Statistical Analysis of Nuclear Power Incidents and Accidents.” Risk Analysis 37 (1): 99–115. https://doi.org/10.1111/risa.12587.
Zhou, Wei-Xing, and Didier Sornette. 2002. “Statistical Significance of Periodicity and Log-Periodicity with Heavy-Tailed Correlated Noise.” International Journal of Modern Physics C 13 (02): 137–69. https://doi.org/10.1142/S0129183102003024.

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