Bayesian hidden Markov modelling using circular‐linear general projected normal distribution

@article{Mastrantonio2014BayesianHM,
  title={Bayesian hidden Markov modelling using circular‐linear general projected normal distribution},
  author={Gianluca Mastrantonio and Antonello Maruotti and Giovanna Jona-Lasinio},
  journal={Environmetrics},
  year={2014},
  volume={26},
  pages={145 - 158}
}
We introduce a multivariate hidden Markov model to jointly cluster time‐series observations with different support, that is, circular and linear. Relying on the general projected normal distribution, our approach allows for bimodal and/or skewed cluster‐specific distributions for the circular variable. Furthermore, we relax the independence assumption between the circular and linear components observed at the same time. Such an assumption is generally used to alleviate the computational burden… 
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References

SHOWING 1-10 OF 76 REFERENCES
Directional data analysis under the general projected normal distribution.
Semiparametric Hidden Markov Models
Hidden Markov models (HMMs) are widely used for dependent data modeling. Classically, the state-dependent distributions, that is, the distribution of the observation given the hidden state, belong to
Bayesian analysis of multivariate Gaussian hidden Markov models with an unknown number of regimes
Multivariate Gaussian hidden Markov models with an unknown number of regimes are introduced here in the Bayesian setting and new efficient reversible jump Markov chain Monte Carlo algorithms for
A note on the mixture transition distribution and hidden Markov models
We discuss an interpretation of the mixture transition distribution (MTD) for discrete‐valued time series which is based on a sequence of independent latent variables which are occasion‐specific. We
A hidden Markov approach to the analysis of space–time environmental data with linear and circular components
TLDR
A multivariate hidden Markov model that includes features of the data within a single framework, associated with easily interpretable components of large-scale and small-scale spatial variation, and provides a parsimonious representation of the sea surface in terms of alternating environmental states.
Model-based clustering of multivariate skew data with circular components and missing values
Motivated by classification issues that arise in marine studies, we propose a latent-class mixture model for the unsupervised classification of incomplete quadrivariate data with two linear and two
Finite Mixture and Markov Switching Models
TLDR
This book should help newcomers to the field to understand how finite mixture and Markov switching models are formulated, what structures they imply on the data, what they could be used for, and how they are estimated.
A Bayesian regression model for circular data based on the projected normal distribution
TLDR
This paper presents a Bayesian analysis of a regression model for circular data using the projected normal distribution using samples from the posterior densities obtained using the Gibbs sampler after the introduction of suitable latent variables.
A Multivariate Hidden Markov Model for the Identification of Sea Regimes from Incomplete Skewed and Circular Time Series
The identification of sea regimes from environmental multivariate times series is complicated by the mixed linear–circular support of the data, by the occurrence of missing values, by the skewness of
...
...