Segmentation of sea current fields by cylindrical hidden Markov models: a composite likelihood approach

Summary   Motivated by segmentation issues in studies of sea current circulation, we describe a hidden Markov random field for the analysis of spatial cylindrical data, i.e. bivariate spatial series of angles and intensities. The model is based on a mixture of cylindrical densities, whose parameters vary across space according to a latent Markov field. It enables segmentation of the data within a finite number of latent classes that represent the conditional distributions of the data under specific environmental conditions, simultaneously accounting for unobserved heterogeneity and spatial auto-correlation. Further, it parsimoniously accommodates specific features of environmental cylindrical data, such as circular–linear correlation, multimodality and skewness. Because of the numerical intractability of the likelihood function, estimation of the parameters is based on composite likelihood methods and essentially reduces to a computationally efficient expectation–maximization algorithm that iteratively alternates the maximization of a weighted composite likelihood function with weights updating. These methods are tested on simulations and exploited to segment the sea surface of the Gulf of Naples by means of meaningful circulation regimes.

[1]  Enrico Zambianchi,et al.  Inshore/offshore water exchange in the Gulf of Naples , 2015 .

[2]  Jo Eidsvik,et al.  Estimation and Prediction in Spatial Models With Block Composite Likelihoods , 2014 .

[3]  Brian J. Reich,et al.  A MULTIVARIATE SEMIPARAMETRIC BAYESIAN SPATIAL MODELING FRAMEWORK FOR HURRICANE SURFACE WIND FIELDS , 2007, 0709.0427.

[4]  Jochen Horstmann,et al.  HF Radar Activity in European Coastal Seas: Next Steps toward a Pan-European HF Radar Network , 2017, Front. Mar. Sci..

[5]  Francesco Lagona,et al.  Model-based segmentation of spatial cylindrical data , 2016 .

[6]  J. Besag.  Statistical Analysis of Non-Lattice Data , 1975 .

[7]  Francesco Lagona,et al.  Hidden Markov random field models for TCA image analysis , 2007, Comput. Stat. Data Anal..

[8]  B. Buonocore,et al.  Dynamics and sea state in the Gulf of Naples: potential use of high-frequency radar data in an operational oceanographic context , 2016 .

[9]  J. Besag.  Efficiency of pseudolikelihood estimation for simple Gaussian fields , 1977 .

[10]  D. Cox,et al.  A note on pseudolikelihood constructed from marginal densities , 2004 .

[11]  Lucio Bellomo,et al.  Toward an integrated HF radar network in the Mediterranean Sea to improve search and rescue and oil spill response: the TOSCA project experience , 2015 .

[12]  K. Mardia,et al.  Maximum likelihood estimation using composite likelihoods for closed exponential families , 2009 .

[13]  Francesco Bartolucci,et al.  A recursive algorithm for Markov random fields , 2002 .

[14]  Gilles Celeux,et al.  EM procedures using mean field-like approximations for Markov model-based image segmentation , 2003, Pattern Recognit..

[15]  Wang,et al.  Nonuniversal critical dynamics in Monte Carlo simulations. , 1987, Physical review letters.

[16]  A. Gelfand,et al.  Modeling Space and Space-Time Directional Data Using Projected Gaussian Processes , 2014 .

[17]  Andrew M. Moore,et al.  Impacts of a 4-dimensional variational data assimilation in a coastal ocean model of southern Tyrrhenian Sea , 2016 .

[18]  Håvard Rue,et al.  Recursive computing and simulation-free inference for general factorizable models , 2007 .

[19]  Rémi Servien,et al.  Unsupervised clustering of multivariate circular data , 2013, Statistics in medicine.

[20]  E. Zambianchi,et al.  Dispersion processes and residence times in a semi‐enclosed basin with recirculating gyres: An application to the Tyrrhenian Sea , 1997 .

[21]  V. P. Godambe.  An Optimum Property of Regular Maximum Likelihood Estimation , 1960 .

[22]  Simone Colella,et al.  Multiplatform observation of the surface circulation in the Gulf of Naples (Southern Tyrrhenian Sea) , 2011 .

[23]  A statistical analysis of Gulf Stream variability from 18+ years of altimetry data , 2013 .

[24]  P. Song,et al.  Composite Likelihood Bayesian Information Criteria for Model Selection in High-Dimensional Data , 2010 .

[25]  Danny Modlin,et al.  Circular conditional autoregressive modeling of vector fields , 2012, Environmetrics.

[26]  A. Maruotti,et al.  A hidden Markov model for the analysis of cylindrical time series , 2015 .

[27]  Mevin B. Hooten,et al.  Continuous-time discrete-space models for animal movement , 2012, 1211.1992.

[28]  Anthony N. Pettitt,et al.  Efficient recursions for general factorisable models , 2004 .

[29]  N. Reid,et al.  On the robustness of maximum composite likelihood estimate , 2011 .