Sparse Bayesian Factor Analysis When the Number of Factors Is Unknown

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Resumo

There has been increased research interest in the subfield of sparse Bayesian factor analysis with shrinkage priors, which achieve additional sparsity beyond the natural parsimonity of factor models. In this spirit, we estimate the number of common factors in the widely applied sparse latent factor model with spike-and-slab priors on the factor loadings matrix. Our framework leads to a natural, efficient and simultaneous coupling of model estimation and selection on one hand and model identification and rank estimation (number of factors) on the other hand. More precisely, by embedding the unordered generalised lower trian gular loadings representation into overfitting sparse factor modelling, we obtain posterior summaries regarding factor loadings, common factors as well as the factor dimension via postprocessing draws from our efficient and customized Markov chain Monte Carlo scheme.

Palavras-chave

Hierarchical model; Identifiability; Point-mass mixture priors; Marginal data augmentation; Reversible jump MCMC; Prior distribution; Sparsity; Heywood problem; Rotational invariance; Ancillarity-sufficiency interweaving strategy; Fractional priors
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Bayesian Anal. Advance Publication
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Inglês

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Área do Conhecimento CNPQ

CIENCIAS EXATAS E DA TERRA::MATEMATICA

CIENCIAS EXATAS E DA TERRA::PROBABILIDADE E ESTATISTICA

ENGENHARIAS::ENGENHARIA ELETRICA

CIENCIAS EXATAS E DA TERRA::CIENCIA DA COMPUTACAO

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