Advertisement

A Hidden Markov Random Field with Copula-Based Emission Distributions for the Analysis of Spatial Cylindrical Data

  • Francesco LagonaEmail author
Conference paper

Abstract

A hidden Markov random field is proposed for the analysis of spatial cylindrical series. The model is a mixture of copula-based bivariate densities, whose parameters vary across space according to a latent random field. It is exploited to segment coastal currents data within a finite number of latent classes that represent specific environmental conditions.

Keywords

Cylindrical data Copulas Hidden Markov random fields Marine currents 

Notes

Acknowledgements

F. Lagona was supported by the 2015 PRIN-supported project “Environmental processes and human activities: capturing their interactions via statistical methods,” funded by the Italian Ministry of Education, University and Scientific Research.

References

  1. 1.
    Abe T, Ley C (2017) A tractable, parsimonious and flexible model for cylindrical data, with applications. Econ Stat 4:91–104MathSciNetGoogle Scholar
  2. 2.
    Alfò M, Nieddu L, Vicari D (2008) A finite mixture model for image segmentation. Stat Comput 18:137–150MathSciNetCrossRefGoogle Scholar
  3. 3.
    Besag J (1986) On the statistical analysis of dirty pictures. J R Stat Soc B 48:259–302MathSciNetzbMATHGoogle Scholar
  4. 4.
    Bulla J, Lagona F, Maruotti A, Picone M (2012) A multivariate hidden Markov model for the identification of sea regimes from incomplete skewed and circular time series. J Agric Biol Environ Stat 17:544–567MathSciNetCrossRefGoogle Scholar
  5. 5.
    Celeux G, Forbes F, Peyrard N (2003) EM procedures using mean field-like approximations for Markov model-based image segmentation. Pattern Recogn 6:131–144CrossRefGoogle Scholar
  6. 6.
    Cosoli S, Gacic M, Mazzoldi A (2012) Surface current variability and wind influence in the north-eastern Adriatic Sea as observed from high-frequency (HF) radar measurements. Cont Shelf Res 33:1–13CrossRefGoogle Scholar
  7. 7.
    Guyon X (1995) Random fields on a network. Modeling, statistics, and applications. Springer, New YorkGoogle Scholar
  8. 8.
    Hanks EM, Hooten MB, Alldredge MW (2015) Continuous-time discrete-space models for animal movement. Ann Appl Stat 9:145–165MathSciNetCrossRefGoogle Scholar
  9. 9.
    Holzmann H, Munk A, Suster M, Zucchini W (2006) Hidden Markov models for circular and linear-circular time series. Environ Ecol Stat 13:325–347MathSciNetCrossRefGoogle Scholar
  10. 10.
    Huang G, Wing-Keung Law A, Huang Z (2011) Wave-induced drift of small floating objects in regular waves. Ocean Eng 38:712–718CrossRefGoogle Scholar
  11. 11.
    Jin KR, Ji ZG (2004) Case study: modeling of sediment transport and wind-wave impact in lake Okeechobee. J Hydraul Eng 130:1055–1067CrossRefGoogle Scholar
  12. 12.
    Johnson, RA, Wehrly, TE (1978) Some angular-linear distributions and related regression models. J Am Stat Assoc 73:602–606MathSciNetCrossRefGoogle Scholar
  13. 13.
    Jones MC, Pewsey A, Kato S (2015) On a class of circulas: copulas for circular distributions. Ann Inst Stat Math 67:843–862MathSciNetCrossRefGoogle Scholar
  14. 14.
    Kim G, Silvapulle M, Silvapulle P (2007) Comparison of semiparametric and parametric methods for estimating copulas. Comput Stat Data Anal 51:2836–2850MathSciNetCrossRefGoogle Scholar
  15. 15.
    Klauenberg K, Lagona F (2007) Hidden Markov random field models for TCA image analysis. Comput Stat Data Anal 52:855–868MathSciNetCrossRefGoogle Scholar
  16. 16.
    Lagona F (2002) Adjacency selection in Markov random fields for high spatial resolution hyper-spectral data. J Geogr Syst 4:53–68CrossRefGoogle Scholar
  17. 17.
    Lagona F, Picone M (2011) A latent-class model for clustering incomplete linear and circular data in marine studies. J Data Sci 9:585–605MathSciNetGoogle Scholar
  18. 18.
    Lagona F, Picone M (2012) Model-based clustering of multivariate skew data with circular components and missing values. J Appl Stat 39:927–945MathSciNetCrossRefGoogle Scholar
  19. 19.
    Lagona F, Picone M (2016) Model-based segmentation of spatial cylindrical data. J Stat Comput Simul 86:2598–2610MathSciNetCrossRefGoogle Scholar
  20. 20.
    Lagona F, Picone M, Maruotti A, Cosoli S (2015) A hidden Markov approach to the analysis of space-time environmental data with linear and circular components. Stoch Environ Res Risk Assess 29:397–409CrossRefGoogle Scholar
  21. 21.
    Lagona F, Picone M, Maruotti A (2015) A hidden Markov model for the analysis of cylindrical time series. Environmetrics 26:534–544MathSciNetCrossRefGoogle Scholar
  22. 22.
    Mastrantonio G, Maruotti A, Jona-Lasinio G. (2015) Bayesian hidden Markov modelling using circular-linear general projected normal distribution. Environmetrics 26:145–158MathSciNetCrossRefGoogle Scholar
  23. 23.
    McLachlan G, Peel D (2000) Finite mixture models. Wiley, New YorkCrossRefGoogle Scholar
  24. 24.
    Mihanovic H, Cosoli S, Vilibic I, Ivankovic D, Dadic V, Gacic M (2011) Surface current patterns in the northern Adriatic extracted from high frequency radar data using self organizing map analysis. J Geophys Res 116:C08033CrossRefGoogle Scholar
  25. 25.
    Modlin D, Fuentes M, Reich B (2012) Circular conditional autoregressive modeling of vector fields. Environmetrics 23:46–53MathSciNetCrossRefGoogle Scholar
  26. 26.
    Pleskachevsky A, Eppel D, Kapitza H (2009) Interaction of waves, currents and tides, and wave-energy impact on the beach area of Sylt island. Ocean Dyn 59:451–461CrossRefGoogle Scholar
  27. 27.
    Plötz T, Fink GA (2009) Markov models for offline handwriting recognition: a survey. Int J Doc Anal Recogn 12:269–298CrossRefGoogle Scholar
  28. 28.
    Ranalli M, Lagona F, Picone M, Zambianchi E (2018) Segmentation of sea current fields by cylindrical hidden Markov models: a composite likelihood approach. J R Stat Soc C 67:575–598MathSciNetCrossRefGoogle Scholar
  29. 29.
    Strauss DJ (1977) Clustering on coloured lattices. J Appl Probab 14:135–143MathSciNetCrossRefGoogle Scholar
  30. 30.
    Swendsen RH, Wang JS (1987) Nonuniversal critical dynamics in Monte Carlo simulations. Phys Rev Lett 58:86–88CrossRefGoogle Scholar
  31. 31.
    Wang F, Gelfand AE (2014) Modeling space and space-time directional data using projected Gaussian processes. J Am Stat Assoc 109:1565–1580MathSciNetCrossRefGoogle Scholar
  32. 32.
    Wang F, Gelfand A, Jona-Lasinio G (2015) Joint spatio-temporal analysis of a linear and a directional variable: space-time modeling of wave heights and wave directions in the Adriatic sea. Stat Sin 25:25–39MathSciNetzbMATHGoogle Scholar
  33. 33.
    Wu C (1983) On the convergence properties of the EM algorithm. Ann Stat 11:95–103MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.University of Roma TreRomeItaly

Personalised recommendations