Factor Analysis is a popular method for modeling dependence in multivariate data. However, determining the number of factors and obtaining a sparse orientation of the loadings are still major challenges. In this paper, we propose a decision-theoretic approach that brings to light the relation between a sparse representation of the loadings and factor dimension. This relation is done through a summary from information contained in the multivariate posterior. To construct such summary, we introduce a threestep approach. In the first step, the model is fitted with a conservative factor dimension. In the second step, a series of sparse point-estimates, with a decreasing number of factors, is obtained by minimizing an expected predictive loss function. In step three, the degradation in utility in relation to the sparse loadings and factor dimensions is displayed in the posterior summary. The findings are illustrated with applications in classical data from the Factor Analysis literature. We used different prior choices and factor dimensions to demonstrate the flexibility of the proposed method.
Over the past decade, various methods have been proposed for the reconstruction of networks modeled as Gaussian Graphical Models. In this work, we analyzed three different approaches: the Graphical Lasso (GLasso), the Graphical Ridge (GGMridge), and the Local Partial Correlation (LPC). For the evaluation of the methods, we used high dimensional data generated from simulated random graphs (Erdös-Rényi, Barabási-Albert, Watts-Strogatz). The performance was assessed through the Receiver Operating Characteristic (ROC) curve. In addition, the methods were used to reconstruct the co-expression network for differentially expressed genes in human cervical cancer data. The LPC method outperformed the GLasso in most simulated cases. The GGMridge produced better ROC curves then both the other methods. Finally, LPC and GGMridge obtained similar outcomes in real data studies.
The Government of India sponsors the Mahalanobis International Award, which, managed by the International Statistical Institute, is presented every other year at the International Statistical Institute World Statistics Congress. The Mahalanobis Award recognises an individual for lifetime achievements in statistics in a developing country or region. This article celebrates the 2021 winner, Prof. Heleno Bolfarine, who, unfortunately, passed away a few days before the award ceremony.
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