Sylvia Frühwirth-Schnatter, Vienna University of Economics and Business
Factor analysis is a popular method to obtain a sparse representation of the covariance matrix of multivariate observations. The present talk reviews some recent research in the area of sparse Bayesian factor analysis that tries to estimate the number of factors and to achieve additional sparsity in a factor model through the use of point mass mixture priors. As a first contribution, identifiability issues that arise from introducing zeros in the factor loading matrix are discussed in detail. We introduce the class of generalized lower triangular (GLT) factor models that generalizes common way of solving rotational invariance. We discuss the mathematical properties of this class and show that every covariance matrix has a unique GLT representation. As a second contribution, we discuss practical Bayesian inference for this class. We introduce a RJMCMC sampler that operates in an overfitting exploratory GLT factor model and estimate the number of factors, based on a sparsity prior that is related to the two-parameter Indian Buffet prior. Several applications serve as an illustration.
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Meeting ID: 962 1923 4870
in presence: room 3-E4-SR03