We review the discrete latent variable approach, which is very popular in statistics and related fields. It allows us to formulate interpretable and flexible models that can be used to analyze complex datasets in the presence of articulated dependence structures among variables. Specific models including discrete latent variables are illustrated, such as finite mixture, latent class, hidden Markov, and stochastic block models. Algorithms for maximum likelihood and Bayesian estimation of these models are reviewed, focusing, in particular, on the expectation-maximization algorithm and the Markov chain Monte Carlo method with data augmentation. Model selection, particularly concerning the number of support points of the latent distribution, is discussed. The approach is illustrated by summarizing applications available in the literature; a brief review of the main software packages to handle discrete latent variable models is also provided. Finally, some possible developments in this literature are suggested.

Bartolucci, F., Pandolfi, S., Pennoni, F. (2022). Discrete Latent Variable Models. ANNUAL REVIEW OF STATISTICS AND ITS APPLICATION, 9(1), 425-452 [10.1146/annurev-statistics-040220-091910].

Discrete Latent Variable Models

Pennoni, Fulvia
2022

Abstract

We review the discrete latent variable approach, which is very popular in statistics and related fields. It allows us to formulate interpretable and flexible models that can be used to analyze complex datasets in the presence of articulated dependence structures among variables. Specific models including discrete latent variables are illustrated, such as finite mixture, latent class, hidden Markov, and stochastic block models. Algorithms for maximum likelihood and Bayesian estimation of these models are reviewed, focusing, in particular, on the expectation-maximization algorithm and the Markov chain Monte Carlo method with data augmentation. Model selection, particularly concerning the number of support points of the latent distribution, is discussed. The approach is illustrated by summarizing applications available in the literature; a brief review of the main software packages to handle discrete latent variable models is also provided. Finally, some possible developments in this literature are suggested.
Articolo in rivista - Review Essay
data augmentation, expectation-maximization algorithm, finite mixture model, hidden Markov model, latent class model, model selection, stochastic block model
English
nov-2021
2022
9
1
425
452
none
Bartolucci, F., Pandolfi, S., Pennoni, F. (2022). Discrete Latent Variable Models. ANNUAL REVIEW OF STATISTICS AND ITS APPLICATION, 9(1), 425-452 [10.1146/annurev-statistics-040220-091910].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/337128
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