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We propose a variable selection method for multivariate hidden Markov models with continuous responses that are partially or completely missing at a given time occasion. Through this procedure, we achieve a dimensionality reduction by selecting the subset of the most informative responses for clustering individuals and simultaneously choosing the optimal number of these clusters corresponding to latent states. The approach is based on comparing different model specifications in terms of the subset of responses assumed to be dependent on the latent states, and it relies on a greedy search algorithm based on the Bayesian information criterion seen as an approximation of the Bayes factor. A suitable expectation-maximization algorithm is employed to obtain maximum likelihood estimates of the model parameters under the missing-at-random assumption. The proposal is illustrated via Monte Carlo simulation and an application where development indicators collected over eighteen years are selected, and countries are clustered into groups to evaluate their growth over time. [ABSTRACT FROM AUTHOR]

We provide a comparison between marginal likelihood and data augmented Markov chain Monte Carlo (MCMC) algorithms for Bayesian estimation of hidden Markov models. In particular, we focus on a specification of these models based on a multivariate Gaussian distribution for the response variables. We evaluate the performance of both methods on the basis of simulated samples and an empirical application, where we compare these approaches in terms of standard measures of estimation and time efficiency. The results show that the augmented algorithm is preferable, obtaining optimal convergence properties and producing larger values of the effective sample size. Instead of using variable dimensional techniques for model selection, we suggest a method based on the so-called parallel sampling for this aim. [ABSTRACT FROM AUTHOR]

The original article can be found online at https://doi.org/10.1007/s00357-023-09457-9.Erratum to: Journal of Classificationhttps://doi.org/10.1007/s00357-023-09457-9The new version corrects a missing "l" in the surname of one author, now corrected as "Pandolfi".The original article has been corrected.Publisher's NoteSpringer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.By Fulvia Pennoni; Francesco Bartolucci and Silvia PandolfiReported by Author; Author; Author [Extracted from the article]

• We propose an exact algorithm for the variational version of the log-likelihood of dynamic SBM. • The algorithm is compared with that of Matias and Miele (2017) based on approximate steps. • The improvement of the exact algorithm is assessed in terms of adjusted Rand index. An exact algorithm for estimating the dynamic stochastic block model is proposed. This model assumes a hidden Markov chain for the evolution of the social behavior of a group of individuals at repeated time occasions and may be used to assign these individuals to the latent blocks in a dynamic fashion. For the estimation of this model, the proposed exact algorithm maximizes the target function introduced by Matias and Miele [7]. This function is derived from a variational approximation of the model log-likelihood, based on the assumption that the latent variables identifying the blocks are a posteriori independent across individuals, but not across time occasions. A simulation study is performed to compare the exact algorithm with the approximate maximization algorithm proposed by Matias and Miele [7]. Results show that there is a certain advantage of the first in terms of dynamic assignment of individuals to the latent blocks in comparison to the true blocking structure, as measured by the adjusted Rand index. [ABSTRACT FROM AUTHOR]

We develop the recursion for hidden Markov (HM) models proposed by Bartolucci and Besag (), and we show how it may be used to implement an estimation algorithm for these models that requires an amount of memory not depending on the length of the observed series of data. This recursion allows us to obtain the conditional distribution of the latent state at every occasion, given the previous state and the observed data. With respect to the estimation algorithm based on the well-known Baum-Welch recursions, which requires an amount of memory that increases with the sample size, the proposed algorithm also has the advantage of not requiring dummy renormalizations to avoid numerical problems. Moreover, it directly allows us to perform global decoding of the latent sequence of states, without the need of a Viterbi method and with a consistent reduction of the memory requirement with respect to the latter. The proposed approach is compared, in terms of computing time and memory requirement, with the algorithm based on the Baum-Welch recursions and with the so-called linear memory algorithm of Churbanov and Winters-Hilt. The comparison is also based on a series of simulations involving an HM model for continuous time-series data. [ABSTRACT FROM AUTHOR]