OpenLB
Open Library of Bioscience
Advanced Search
Scientific reports
09 28, 2020;10 (1): 15889.

On modifications to the Poisson-triggered hidden Markov paradigm through partitioned empirical recurrence rates ratios and its applications to natural hazards monitoring.

Moinak Bhaduri
Author Information
  1. Moinak Bhaduri: Department of Mathematical Sciences, Bentley University, Waltham, MA, 02452, United States. mbhaduri@bentley.edu.
PMID: 32985544 DOI: 10.1038/s41598-020-72803-z

Abstract

Hidden Markov models (HMMs), especially those with a Poisson density governing the latent state-dependent emission probabilities, have enjoyed substantial and undeniable success in modeling natural hazards. Classifications among these hazards, induced through quantifiable properties such as varying intensities or geographic proximities, often exist, enabling the creation of an empirical recurrence rates ratio (ERRR), a smoothing statistic that is gradually gaining currency in modeling literature due to its demonstrated ability in unearthing interactions. Embracing these tools, this study puts forth a refreshing monitoring alternative where the unobserved state transition probability matrix in the likelihood of the Poisson based HMM is replaced by the observed transition probabilities of a discretized ERRR. Analyzing examples from Hawaiian volcanic and West Atlantic hurricane interactions, this work illustrates how the discretized ERRR may be interpreted as an observed version of the unobserved hidden Markov chain that generates one of the two interacting processes. Surveying different facets of traditional inference such as global state decoding, hidden state predictions, one-out conditional distributions, and implementing related computational algorithms, we find that the latest proposal estimates the chances of observing a high-risk period, one threatening several hazards, more accurately than its established counterpart. Strongly intuitive and devoid of forbidding technicalities, the new prescription launches a vision of surer forecasts and stands versatile enough to be applicable to other types of hazard monitoring (such as landslides, earthquakes, floods), especially those with meager occurrence probabilities.

References

  1. Ho, C.-H., Zhong, G., Cui, F. & Bhaduri, M. Modeling interaction between bank failure and size. J. Financ. Bank Manag. 4, 15–33 (2016).
  2. Ho, C.-H. & Bhaduri, M. A quantitative insight into the dependence dynamics of the Kilauea and Mauna Loa Volcanoes Hawaii. Math. Geosci. 49, 893–911 (2017).
  3. Bhaduri, M. & Ho, C.-H. On a temporal investigation of hurricane strength and frequency. Environ. Model. Assess. 24, 495–507 (2018).
  4. Daley, D. J. Stochastically monotone Markov Chains. Z. Wahrsch. Verwandte Gebiete 10, 305–317 (1968).
  5. Zhan, F. et al. Beyond cumulative sum charting in non-stationarity detection and estimation. IEEE Access 7, 140860–140874 (2019).
  6. Koutras, M. V. On a Markov chain approach for the study of reliability structures. J. Appl. Probab. 33, 357–367 (1996).
  7. Brown, L. A. On the use of Markov chains in movement research. Econ. Geogr. 46, 393 (1970).
  8. Baum, L. E. & Petrie, T. Statistical inference for probabilistic functions of finite state Markov Chains. Ann. Math. Stat. 37, 1554–1563 (1966).
  9. Baum, L. E. & Eagon, J. A. An inequality with applications to statistical estimation for probabilistic functions of Markov processes and to a model for ecology. Bull. Am. Math. Soc. 73, 360–364 (1967).
  10. Leonard E Baum, G. S., Petrie, Ted & Weiss, N. A maximization technique occurring in the statistical analysis of probabilistic functions of Markov Chains. Ann. Math. Stat. 41, 164–171 (1970).
  11. Ghahramani, Z. An introduction to hidden Markov models and Bayesian networks. Int. J. Pattern Recognit. Artif. Intell. 15, 9–42 (2001).
  12. Marti, U.-V. & Bunke, H. Using a statistical language model to improve the performance of an HMM-based cursive handwriting recognition system. Int. J. Pattern Recognit. Artif. Intell. 15, 65–90 (2001).
  13. Wilson, A. & Bobick, A. Hiden Markov models for modeling and recognizing gesture under variation. Int. J. Pattern Recognit. Artif. Intell. 15, 123–160 (2001).
  14. Yu, K., Jiang, X. & Bunke, H. Sentence lipreading using hidden Markov model with integrated grammar. Int. J. Pattern Recognit. Artif. Intell. 15, 161–176 (2001).
  15. Bui, H., Venkatesh, S. & West, G. Tracking and surveillance in wide-area spatial environments using the abstract hidden Markov model. Int. J. Pattern Recognit. Artif. Intell. 15, 177–196 (2001).
  16. Caelli, T., Mccabe, A. & Briscoe, G. Shape tracking and production using hidden Markov models. Int. J. Pattern Recognit. Artif. Intell. 15, 197–221 (2001).
  17. Muller, S., Eickeler, S. & Rigoll, G. An integrated approach to shape and color-based image retrieval of rotated objects using hidden Markov models. Int. J. Pattern Recognit. Artif. Intell. 15, 223–237 (2001).
  18. Li, N. & Stephens, M. Modeling linkage disequilibrium and identifying recombination hotspots using single-nucleotide polymorphism data. Genetics 165, 2213–2233 (2003). [PMID: 14704198]
  19. Atwi, A. A Case Study in Robust Quickest Detection for Hidden Markov Models (Massachusetts Institute of Technology, Massachusetts, 2010).
  20. Yin, J. & Meng, Y. Abnormal behavior recognition using self-adaptive hidden Markov models. In Lecture Notes in Computer Science 337–346 (Springer, Berlin, 2009).
  21. Bhaduri, M., Zhan, J. & Chiu, C. A novel weak estimator for dynamic systems. IEEE Access 5, 27354–27365 (2017).
  22. Bhaduri, M., Zhan, J., Chiu, C. & Zhan, F. A novel online and non-parametric approach for drift detection in big data. IEEE Access 5, 15883–15892 (2017).
  23. Macdonald, I. L. & Raubenheimer, D. Hidden Markov models and animal behaviour. Biometr. J. 37, 701–712 (1995).
  24. Mutschler, C. & Philippsen, M. Learning event detection rules with noise hidden Markov models. In 2012 NASA/ESA Conference on Adaptive Hardware and Systems (AHS) (IEEE, 2012). https://doi.org/10.1109/ahs.2012.6268645 .
  25. Lanchantin, P. & Pieczynski, W. Unsupervised restoration of hidden nonstationary Markov chains using evidential priors. IEEE Trans. Signal Process. 53, 3091–3098 (2005).
  26. Boudaren, M. E. Y., Monfrini, E. & Pieczynski, W. Unsupervised segmentation of random discrete data hidden with switching noise distributions. IEEE Signal Process. Lett. 19, 619–622 (2012).
  27. Tan, S., Bhaduri, M. & Ho, C.-H. A statistical model for long-term forecasts of strong sand dust storms. J. Geosci. Environ. Protect. 02, 16–26 (2014).
  28. Ho, C.-H. & Bhaduri, M. On a novel approach to forecast sparse rare events: Applications to Parkfield earthquake prediction. Nat. Hazards 78, 669–679 (2015).
  29. Lipman, P. W. The southeast rift zone of Mauna Loa: Implications for structural evolution of Hawaiian volcanoes. Am. J. Sci. 280, 20 (1980).
  30. Klein, F. W. Patterns of historical eruptions at Hawaiian volcanoes. J. Volcanol. Geoth. Res. 12, 1–35 (1982).
  31. Miklius, A. & Cervelli, P. Interaction between Kilauea and Mauna Loa. Nature 421, 229–229 (2003). [PMID: 12529631]
  32. Walter, T. R. & Amelung, F. Volcano-earthquake interaction at Mauna Loa volcano Hawaii. J. Geophys. Res. Solid Earth 111, 20 (2006).
  33. Emanuel, K. Tropical cyclones. Annu. Rev. Earth Planet. Sci. 31, 75–104 (2003).
  34. Emanuel, K. Hurricanes: Tempests in a greenhouse. Phys. Today 59, 74–75 (2006).
  35. Emanuel, K. Environmental Factors Affecting Tropical Cyclone Power Dissipation. J. Clim. 20, 5497–5509 (2007).
  36. Bhaduri, M. & Zhan, J. Using empirical recurrence rates ratio for time series data similarity. IEEE Access 6, 30855–30864 (2018).
  37. Anderson, W. J. Continuous-Time Markov Chains (Springer, New York, 1991). https://doi.org/10.1007/978-1-4612-3038-0 . [DOI: 10.1007/978-1-4612-3038-0]
  38. Wang, C., Wu, J., Wang, X. & He, X. Application of the hidden Markov model in a dynamic risk assessment of rainstorms in Dalian China. Stoch. Environ. Res. Risk Assess. 32, 2045–2056 (2018).
  39. Khadr, M. Forecasting of meteorological drought using Hidden Markov Model (case study: The upper Blue Nile river basin Ethiopia). Ain Shams Eng. J. 7, 47–56 (2016).
  40. Wu, Z. A hidden Markov model for earthquake declustering. J. Geophys. Res. 115, 20 (2010).
  41. Wu, Z. Quasi-hidden Markov model and its applications in cluster analysis of earthquake catalogs. Journal of Geophysical Research 116, 20 (2011).
  42. Joshi, J. C., Kumar, T., Srivastava, S., Sachdeva, D. & Ganju, A. Application of Hidden Markov Model for avalanche danger simulations for road sectors in North-West Himalaya. Nat. Hazards 93, 1127–1143 (2018).
  43. Zhu, Y., Zhong, Z., Zheng, W. & Zhou, D. HMM-based [Formula: see text] filtering for discrete-time Markov jump LPV systems over unreliable communication channels. IEEE Trans. Syst. Man Cybern. Syst. 48, 2035–2046 (2018).
  44. Zucchini, W. & MacDonald, I. L. Hidden Markov Models for Time Series (Chapman and Hall, New York, 2009). https://doi.org/10.1201/9781420010893 . [DOI: 10.1201/9781420010893]
  45. Albert, P. S. A two-state Markov mixture model for a time series of epileptic seizure counts. Biometrics 47, 1371 (1991). [PMID: 1786324]
  46. Leroux, B. G. Maximum-likelihood estimation for hidden Markov models. Stoch. Processes Appl. 40, 127–143 (1992).
  47. Le, N. D., Leroux, B. G., Puterman, M. L. & Albert, P. S. Exact likelihood evaluation in a Markov mixture model for time series of seizure counts. Biometrics 48, 317 (1992). [PMID: 1581489]
  48. Leroux, B. G. & Puterman, M. L. Maximum-penalized-likelihood estimation for independent and Markov-dependent mixture models. Biometrics 48, 545 (1992). [PMID: 1637977]
  49. Can, C., Ergun, G. & Gokceoglu, C. Prediction of earthquake hazard by hidden Markov model (around Bilecik NW Turkey). Open Geosci. 6, 20 (2014).
  50. Orfanogiannaki, K., Karlis, D. & Papadopoulos, G. A. Identifying seismicity levels via Poisson hidden Markov models. Pure Appl. Geophys. 167, 919–931 (2010).
  51. Mendoza-Rosas, A. T. & Cruz-Reyna, SDla. A mixture of exponentials distribution for a simple and precise assessment of the volcanic hazard. Nat. Hazards Earth Syst. Sci. 9, 425–431 (2009).
  52. Bebbington, M. S. Identifying volcanic regimes using Hidden Markov Models. Geophys. J. Int. 171, 921–942 (2007).
  53. Akaike, H. A new look at the statistical model identification. IEEE Trans. Autom. Control 19, 716–723 (1974).
  54. Witx, E., van den Heuvel, E. & Romeijn, J.-W. All models are wrong...’: An introduction to model uncertainty. Stat. Neerland. 66, 217–236 (2012).
  55. Forney, G. D. The viterbi algorithm. Proc. IEEE 61, 268–278 (1973).
  56. Montgomery, D. C., Vining, G. G. & Peck, E. A. Introduction to Linear Regression Analysis 5th edn. (Wiley, Oxford, 2012).
  57. McPhillips, L. E. et al. Defining extreme events: A cross-disciplinary review. Earth’s Future 6, 441–455 (2018).
  58. Ross, S. Simulation 5th edn. (Academic Press, London, 2014).
  59. Guo, H. Understanding global natural disasters and the role of earth observation. Int. J. Digit. Earth 3, 221–230 (2010).
Journal Article

Word Cloud

Created with Highcharts 10.0.0hazardsMarkovprobabilitiesERRRmonitoringstatehiddenespeciallyPoissonmodelingnaturalempiricalrecurrenceratesinteractionsunobservedtransitionobserveddiscretizedoneHiddenmodelsHMMsdensitygoverninglatentstate-dependentemissionenjoyedsubstantialundeniablesuccessClassificationsamonginducedquantifiablepropertiesvaryingintensitiesgeographicproximitiesoftenexistenablingcreationratiosmoothingstatisticgraduallygainingcurrencyliteratureduedemonstratedabilityunearthingEmbracingtoolsstudyputsforthrefreshingalternativeprobabilitymatrixlikelihoodbasedHMMreplacedAnalyzingexamplesHawaiianvolcanicWestAtlantichurricaneworkillustratesmayinterpretedversionchaingeneratestwointeractingprocessesSurveyingdifferentfacetstraditionalinferenceglobaldecodingpredictionsone-outconditionaldistributionsimplementingrelatedcomputationalalgorithmsfindlatestproposalestimateschancesobservinghigh-riskperiodthreateningseveralaccuratelyestablishedcounterpartStronglyintuitivedevoidforbiddingtechnicalitiesnewprescriptionlaunchesvisionsurerforecastsstandsversatileenoughapplicabletypeshazardlandslidesearthquakesfloodsmeageroccurrencemodificationsPoisson-triggeredparadigmpartitionedratiosapplications

Similar Articles

Cited By

No available data.