Springer Nature is making Coronavirus research free. View research | View latest news | Sign up for updates

Alarm Systems and Catastrophes from a Diverse Point of View


Using a chain of urns, we build a Bayesian nonparametric alarm system to predict catastrophic events, such as epidemics, black outs, etc. Differently from other alarm systems in the literature, our model is constantly updated on the basis of the available information, according to the Bayesian paradigm. The papers contains both theoretical and empirical results. In particular, we test our alarm system on a well-known time series of sunspots.

This is a preview of subscription content, log in to check access.


  1. Aldous D (1985) Lecture notes in mathematics: exchangeability and related topics. Springer Verlag, New York

  2. Amaral-Turkman MA, Turkman KF (1990) Optimal alarm systems for autoregressive process; a Bayesian approach. Comput Stat Data An 19:307–314

  3. Amerio E, Muliere P, Secchi P (2004) Reinforced urn processes for modeling credit default distributions. Int J Theor Appl Financ 7:407–423

  4. Antunes M, Amaral-Turkman MA, Turkman FK (2003) A Bayesian approach to event prediction. J Time Ser An 24:631–646

  5. Blackwell D, MacQueen JB (1973) Ferguson distributions via Polya-urn schemes. Ann Stat 1:353–355

  6. Brännäs K, Nordström J (2004) An integer-valued time series model for hotels that accounts for constrained capacity. Stud Nonlinear Dyn E 8:97–105

  7. Bulla P (2005) Application of reinforced urn processes to survival analysis. PhD Thesis Bocconi University

  8. Chattopadhyay R (2000) Covariation of critical frequency of F 2-layer and relative sunspot number. Bulletin Astron Soc India

  9. Cifarelli DM, Regazzini E (1978) Problemi statistici non parametrici in condizioni di scambiabilit parziale. Impiego di medie associative. IMF University of Turin scientific report 3, 12. English translation available online:[1].20080528.135739.pdf

  10. Cirillo P (2008) New urn approach to shock and default models. PhD Thesis Bocconi University

  11. Cirillo P, Hüsler J (2009) An urn-based approach to generalized extreme shock models. Stat Probab Lett 79:969–976

  12. Cirillo P, Hüsler J (2011) Extreme shock models: an alternative approach. Stat Probab Lett 81:25–30

  13. Cirillo P, Hüsler J, Muliere P (2010) A nonparametric approach to interacting failing systems with an application to credit risk modeling. Int J Theor Appl Financ 13:1–18

  14. Coppersmith D, Diaconis P (1986) Random walk with reinforcement. Unpublished Manuscript

  15. Cormen TH, Leiserson CE, Rivest RL (1990) Introduction to algorithms. MIT Press and McGraw-Hill

  16. de Finetti B (1975) Theory of probability II. Wiley, New York

  17. de Maré J (1980) Optimal prediction of catastrophes with application to Gaussian process. Ann Probab 8:841–850

  18. Diaconis P, Freedman D (1980) de Finetti’s theorem for Markov chains. Ann Probab 8:115–130

  19. Doksum K (1974) Tailfree and neutral random probabilities and their posterior distributions. Ann Stat 2:183–201

  20. Eggenberger F, Polya G (1923) Über die Statistik verketteter Vorgänge. Zeitschrift für Angewandte Mathematik and Mechanik 1:279–289

  21. Giudici P, Mezzetti M, Muliere P (2003) Mixtures of products of Dirichlet processes for variable selection in survival analysis. J Stat Plan Infer 111:101–115

  22. Grage H, Holst J, Lindgren G, Saklak M (2010) Level crossing prediction with neural networks. Methodol Comput Appl Probab 12:623–645

  23. Grandpierre A (2004) On the origin of solar cycle periodicity. Astrophys Space Sci 243:393–400

  24. Hüsler J (1993) A note on exceedances and rare events of non-stationary sequences. J Appl Probab 30:877–888

  25. Johnson NL, Kotz S (1977). Urn models and their applications. Wiley, New York

  26. Lindgren G (1975a) Prediction for a random time point. Ann Probab 3:412–433

  27. Lindgren G (1975b). Prediction of catastrophes and high level crossings. Bulletin Int Stat Institut 46:225–240

  28. Lindgren G (1980) Model process in non-linear prediction, with application to detection and alarm. Ann Probab 8:775–792

  29. Mahmoud HM (2009) Polya urn models. CRC Press, New York

  30. Marshall AW, Olkin I (1993) Bivariate life distributions from Polya’s urn model for contagion. J Appl Probab 30:497–508

  31. Mclachlan GJ, Krishnan T (1997) The EM algorithm and extensions. Wiley, New York

  32. Mezzetti M, Muliere P, Bulla P (2007) An application of reinforced urn processes to determining maximum tolerated dose. Stat Probab Lett 77:740–747

  33. Monteiro M, Pereira I, Scotto MG (2008) Optimal alarm systems for count process. Commun Stat-Theor M 37:3054–3076

  34. Muliere P, Secchi P, Walker SG (2000) Urn schemes and reinforced random walks. Stoch Proc Appl 88:59–78

  35. Muliere P, Secchi P, Walker SG (2003) Reinforced random processes in continuous time. Stoch Proc Appl 104:117–130

  36. Muliere P, Paganoni AM, Secchi P (2006) A randomly reinforced urn. J Stat Plan Infer 136:1853–1874

  37. Pemantle R (2007) A survey of random processes with reinforcement. Probab Surv 4:1–79

  38. Svensson A, Lindquist R, Lindgren G (1996) Optimal prediction of catastrophes in autoregressive moving average processes. J Time Ser An 17:511–531

  39. Zheng HT, Basawa IV, Datta S (2006) Inference for the p-th order random coefficient integer-valued autoregressive processes. J Time Ser An 27:411–440

Download references

Author information

Correspondence to Pasquale Cirillo.

Additional information

This work has been partially supported by the Swiss National Science Foundation.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Cirillo, P., Hüsler, J. & Muliere, P. Alarm Systems and Catastrophes from a Diverse Point of View. Methodol Comput Appl Probab 15, 821–839 (2013).

Download citation


  • Alarm system
  • Catastrophe
  • Risk analysis
  • Forecasting
  • Exchangeability
  • Urn model

AMS 2010 Subject Classifications

  • 60G20
  • 60G70
  • 60G09
  • 97Kxx