
Article: Bayesian Hidden Markov Modelling Using CircularLinear General Projected Normal Distribution
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ABSTRACT: We introduce a multivariate hidden Markov model to jointly cluster observations with different support, i.e. circular and linear. Relying on the general projected normal distribution, our approach allows us to have clusters with bimodal marginal 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 involved in the parameter estimation step, but it is hard to justify in empirical applications. We carry out a simulation study using different simulation schemes to investigate model behavior, focusing on how well the hidden structure is recovered. Finally, the model is used to fit a real data example on a bivariate time series of wind velocity and direction.08/2014; 
Article: Bayesian inference for the multivariate skewnormal model: a Population Monte Carlo approach
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ABSTRACT: Frequentist and likelihood methods of inference based on the multivariate skewnormal model encounter several technical difficulties with this model. In spite of the popularity of this class of densities, there are no broadly satisfactory solutions for estimation and testing problems. A general population Monte Carlo algorithm is proposed which: 1) exploits the latent structure stochastic representation of skewnormal random variables to provide a full Bayesian analysis of the model and 2) accounts for the presence of constraints in the parameter space. The proposed approach can be defined as weakly informative, since the prior distribution approximates the actual reference prior for the shape parameter vector. Results are compared with the existing classical solutions and the practical implementation of the algorithm is illustrated via a simulation study and a real data example. A generalization to the matrix variate regression model with skewnormal error is also presented.Computational Statistics & Data Analysis. 02/2013; 63.  [Show abstract] [Hide abstract]
ABSTRACT: In this paper we consider Markov chains associated with the MetropolisHastings algorithm. We propose conditions under which the sequence of the successive densities of such a chain converges to the target density according to the total variation distance for any choice of the initial density. In particular we prove that the positiveness of the target and the proposal densities is enough for the chain to converge.02/2013;
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Christian P. Robert 